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## Über dieses Buch

This book presents selected papers from the 7th International Congress on Computational Mechanics and Simulation, held at IIT Mandi, India. The papers discuss the development of mathematical models representing physical phenomena and apply modern computing methods to analyze a broad range of applications including civil, offshore, aerospace, automotive, naval and nuclear structures. Special emphasis is given on simulation of structural response under extreme loading such as earthquake, blast etc. The book is of interest to researchers and academics from civil engineering, mechanical engineering, aerospace engineering, materials engineering/science, physics, mathematics and other disciplines.

## Inhaltsverzeichnis

### Propagation of Elastic Waves in Nonlocal Bars and Beams

In this paper, wave dispersion properties in nonlocal theories of elasticity models are critically examined. Both gradient type as well as integral-type non-locality within a setting of the rod and beam are considered. The mathematical framework here involves the Fourier frequency analysis that leads to the frequency spectrum relation (FSR) and system transfer function. Utilizing the FSR, wave modes and group speeds are examined. One main difference that arises between the two nonlocal model types is in the number of wave modes that are possible from the FSR. In gradient-type non-locality, the number of modes is finite and equal to the order of the displacement gradient in the governing equation of motion. However, in an integral-type non-locality, wave modes are infinite in number. Further, in contrast to classical theories there exist nonclassical wave modes showing the existence of nonphysical features, such as either exponential instabilities or undefined wavenumbers, negative group speeds, infinitesimally small, and infinite group speed values. Existence of such features, then, naturally raises the aspect of physically realizable wave motion and causality in these models. In literature, there exist dispersion relations or Kramers–Kronig (K-K) relations as an aid to examine wave motion in a linear, passive, and causal system. In this paper, K-K relations are utilized in order to further examine the wave dispersion properties. Discrepancies are seen between FSR predictions and K-K predictions, especially at frequencies with nonphysical features. An example is also presented that contradicts the general concept that all time-domain formulations agree well with the K-K relations.

V. S. Mutnuri, S. Gopalakrishnan

### Mechanics of Damage at Steel-Concrete Interface in RC Structures

One of the major problems affecting present infrastructure is shortening of service life due to durability issues. A large number of steel-concrete composite structures fail not from overloading but because of durability issues. One of the main causes of short service life is corrosion of steel in steel-concrete composite structures. The current state of practice in design codes deals with this issue by assuming a perfect bond between steel and concrete for design considerations and provision of minimum cover depth for prevention against corrosion. The degradation at the interface that can have long-term deteriorative effects on strength and durability cannot be addressed with the present framework. Thus a need for more exact design and analysis recommendations is needed to address and deal with the issue of durability caused by corrosion. The objective of this study is to investigate the effect of corrosion at the steel-concrete interface on the structural behaviour of steel-concrete composite structures through numerical methods. The mechanics of degradation of the interface have been studied using finite element method. Effects of corrosion at the steel-concrete interface such as weakening of the interface, reduction of structural steel area and de-lamination at the interface have been studied. These phenomenon can be modelled using finite element approaches. Modelling of corrosion using solid elements presented with problems of mesh refinement, coupling damage with a constitutive response. To address the above, a UEL has been implemented in ABAQUS using a traction separation law based on the Mohr-Coulomb failure criteria, which will be used to model corrosion at the interface. Experimental data on corrosion samples were used to obtain the material properties. The developed model shall provide a way to study the effect of the presence of varying amounts of corrosion on the performance of a structure. The present study aims to provide a robust numerical scheme to analyse composite structures with varying degrees of corrosion. On the basis of obtained results, recommendations for addressing deterioration due to corrosion would be recommended.

Saiwal Krishna, Pritam Chakraborty, S. K. Chakrabarti

### A Discussion on Locking and Nonlocking Gradient-Enhancement Formulations for Concrete Behavior

Modeling of strain-softening behavior exhibited by quasi-brittle materials such as concrete and rocks leads to mesh-sensitive and physically objectionable solutions upon mesh refinement and thereby causing ill-posedness of the boundary value problem. These numerical difficulties can be avoided by employing regularization methods that include an internal length scale. Although integral-type nonlocal regularization and gradient-type methods among those are widely accepted in the scientific community, gradient methods remain as a convenient approach due to its straightforwardness in linearization. The present paper provides a comparison of two different types of implicit-gradient formulations that consider an equivalent strain measure and the damage variable for gradient-enhancement. It discusses the locking and nonlocking effects on softening behavior. An elasticity-based isotropic damage model is adopted for the comparison in gradient-enhanced modeling.

Ajmal Hasan Monnamitheen Abdul Gafoor, Dieter Dinkler

### On Flexure of Shear Deformable Isotropic Rectangular Propped Cantilever Beams

This paper presents a comparison study on the flexure of shear deformable isotropic rectangular propped cantilever beams by utilizing newly developed variationally consistent two-variable-refined beam theory, variationally inconsistent single-variable refined beam theory, and variationally inconsistent Levinson beam theory. The beam is assumed to be under the action of uniformly distributed transverse load. It should be noted that governing differential equations of two-variable-refined beam theory are derived by utilizing Hamilton’s principle. Whereas, beam gross equilibrium equations are utilized in the case of single-variable-refined beam theory as well as Levinson beam theory to derive their respective governing differential equations. All three beam theories take into account a parabolic variation of the beam transverse shear strain and hence the beam transverse shear stress through the beam thickness. These theories satisfy transverse shear stress-free beam surface conditions. Hence, these theories do not require a shear correction factor. Effects of the beam thickness-to-length ratio on the location of maximum beam transverse displacement and values of maximum non-dimensional beam transverse displacement, non-dimensional beam axial stress, and non-dimensional beam transverse shear stress are presented. Profiles of the non-dimensional beam transverse displacement, non-dimensional beam axial stress, and non-dimensional beam transverse shear stress for various values of the beam thickness-to-length ratio are also presented.

Kedar S. Pakhare, P. J. Guruprasad, Rameshchandra P. Shimpi

### Progressive Collapse Potential of Steel Frames Sustaining Post-Hazard Support-Yielding

Hazards such as fire, blast or severe seismic event may cause a local failure of columns leading to disproportionate or progressive collapse of a structure. Progressive collapse is a complex dynamic process greatly influenced by several factors including the integrity and tie-strength of beam-and-slab system over the damaged column, load-redistribution mechanism and post-hazard-exposure condition of the columns’ bases. In the present study, simple steel space frames designed conventionally as per Indian standard codes of practice are considered for numerical parametric study. Column removal locations as recommended by Unified Facilities Criteria (UFC 4-023-03) are considered. Progressive collapse potential is assessed for different column sections subjected to loss of major load-bearing element while adjoining columns have partially lost their fixity with the base. This is modelled by varying support conditions as fixed, hinged or roller; whilst joints adjacent to the lost column are changed to pinned connections. The effect of material properties degradation is also evaluated considering variation in steel grade. The progressive collapse potential is seen to be higher for frames with yielded supports emphasizing that the static indeterminacy plays an important role in progressive collapse potential of frames. Amongst the steel sections considered herein, square-section columns are found to be the most effective against progressive collapse.

Anil Kumar, Niranjan Muley, Pranesh Murnal, Vasant A. Matsagar

### Influence of Concrete Fill on the Buckling Characteristics of Slender Circular Steel Tubes

The strength, stiffness and buckling characteristics of hollow structural steel tubes can be significantly enhanced by filling it with concrete. AISC 360-16 classifies circular concrete-filled steel tubes (CFSTs) as compact, non-compact and slender based on the section slenderness ratio λ = D/t (outer diameter/thickness of the steel tube). The steel in compact and non-compact sections yield before buckling, and slender sections are assumed to buckle elastically. However, a comparison of the design provisions suggested by AISC 360-16 with the existing experimental results shows that the predicted strength is highly conservative for slender sections. To investigate the influence of concrete core on the buckling characteristics of slender circular CFSTs, a finite element (FE) analysis is performed using ABAQUS. A parametric study is conducted to study the influence of the input parameters of the concrete damage plasticity model. The post-peak branch of the stress-strain relation of unconfined concrete is also modified to account for the increase in the peak-axial strain of confined concrete. The results from the FE analysis of a slender CFST short column is in good agreement with the experimental observations. The analysis shows that the steel tube did not elastically buckle, and crushing of concrete led to the failure of the specimen. This is contrary to AISC 360-16 provisions, which assumes that slender CFSTs fail by elastic local buckling. This could probably be the reason for the overly conservative prediction of the ultimate load capacity of slender CFSTs by AISC 360-16, and needs further investigation.

Rebecca Mary Paul, M. Madhu Karthik, M. V. Anil Kumar

### Vibration of Flexible Member in Offshore Structures

There are many flexible vertical members in offshore platforms like mooring lines and risers. These are exposed to wave, vessel motion and drilling loads during operation. For the smooth operation of these structures, the lateral excursion of these members should be minimal. This paper explains about the vibration analysis of a flexible vertical member subjected to base excitation. Initially, the flexible member was analysed as a SDOF non-linear spring-mass system. A qualitative understanding of the system was determined by solving the system using continuation method. Further, a numerical and experimental analysis was carried out on this member. Numerically, the member was analysed as an Euler–Bernoulli beam in MATLAB using the finite element method with three degrees of freedom at each node. The buckling load was determined using the Eigen value analysis. The minimum length required for buckling under gravity load was determined. The system was subjected to base excitation and the variation in the maximum response with respect to base excitation frequency was noted in the axial and lateral direction. The maximum response was obtained near the resonant frequency. Experimentally, the flexible member with a force transducer at its base was connected to the modal exciter through a stinger. The material of the member chosen was acrylic polymer as it buckles easily and can be used for testing. Forced excitation was provided using the modal exciter. On varying the frequency, the response of the member was observed. The length of the member was also a parameter that was varied such that the excursion was within controllable limits. Also, the area of the cross section in the upper half of the section was increased as an additional parameter for controlling the excursion. It was observed that the excursion was reduced as obtained from the theoretical analysis.

### Nonlinear Analysis of Mooring System for an Offshore Desalination Platform

The article describes the analysis and design of an optimum mooring system for the given spar configuration. National Institute of Ocean Technology (NIOT), Chennai has studied various configurations of floating platform and has designed and tested scaled down models of Semi-submersible and Spar based floating platform for accommodating Low Temperature Thermal Desalination (LTTD) plant. The Spar platform is to be permanently moored at 1000 m of water depth. The mooring configuration is very critical in the overall operation of the system. Hence a detailed study on this was carried out taking care of the nonlinearities of external forces induced in the system. Low frequency motions in surge, sway and yaw are excited by second order, nonlinear coupled effects between the wave and the Spar. The forces induced in the moorings are as well nonlinear due to nonlinear characteristics of the mooring material. The nonlinear mooring behavior characteristics and its effect on the platform motion discussed in the article, were carried out in potential/diffraction commercial simulation tool MOSES. The crucial parameters for the design including length, material, and mooring pretension were arrived from the simulation.

Ashwani Vishwanath, Purnima Jalihal

### Finite Element Studies and Dynamic Analysis of Initially Stressed Functionally Graded Plates Using a Refined Higher Order Shear Deformation Theory

A C0isoparametric finite element formulation is presented to calculate the required number of lowest natural frequencies of functionally graded plates (FGPs)subjected to in-plane prestress. The material properties of the FGPs are assumed to vary continuously from one surface to another, according to a simple power law distribution in terms of the constituent volume fractions. The present theory is based on a higher-order displacement model and the three-dimensional Hooke’s laws for plate material. The theory represents a more realistic quadratic variation of the transverse shearing and normal strains through the thickness of the plate. Nine-noded Lagrangian elements have been used for the purpose of discretization using a refined Higher Order Shear deformation Theory (HOST12) that includes the effects of transverse shear deformations, transverse normal deformation and rotary inertia. The plate structure is idealized into an assemblage of nine-noded isoparametric quadrilateral elements with twelve degrees of freedom per node. Hamilton’s principle is used for the formulation. The effect of in-plane pre-stress is taken care by calculating the geometric stiffness matrix. The same shape functions are used to calculate the elastic stiffness matrix, geometric stiffness matrix and the element mass matrix. Subspace Iteration technique is applied to extract the natural frequencies. Numerical results for first seven natural frequencies are presented for rectangular plates under various boundary conditions. The results show good agreement with three-dimensional analytical formulation.

S. Jayaraman, Tarun Kant, N. Shanmuga Sundaram

### Vibration Analysis of Functionally Graded Material Plate

Functionally graded materials (FGMs) are the advanced materials in the family of engineering composites made of two or more constituent phases with continuous and smoothly varying composition. Nine noded heterosis plate element is used to formulate the elastic stiffness matrix and mass matrix. The results are also extracted from Abaqus CAE by using S8R5 shell elements. Free vibration analysis is done to obtain the different modes as well as the frequencies. Harmonic sine load is applied at the centre of the FGM plate to obtain a forced vibration response. Impulse forces of rectangular, half-cycle sine, triangular shapes are applied on the top of the plate at the centre and the shock spectra of C-Si C FGM plate is plotted.

N. I. Narayanan, Sauvik Banerjee, Akshay Prakash Kalgutkar, T. Rajanna

### ANN-Based Random First-Ply Failure Analyses of Laminated Composite Plates

This paper presents the random first-ply failure analyses of laminated composite plates by using an artificial neural network (ANN)-based surrogate model. In general, materials and geometric uncertainties are unavoidable in such structures due to their inherent anisotropy and randomness in system configuration. To map such variabilities, stochastic analysis corroborates the fact of inevitable edge towards the quantification of uncertainties. In the present study, the finite element formulation is derived based on the consideration of eight-noded elements wherein each node consists of five degrees of freedom (DOF). The five failure criteria namely, maximum stress theory, maximum strain theory, Tsai-Hill (energy-based criterion) theory, Tsai-Wu (interaction tensor polynomial) theory and Tsai-Hill’s Hoffman failure criteria are considered in the present study. The input parameters include the ply orientation angle, assembly of ply, number of layers, ply thickness and degree of orthotropy, while the first-ply failure loads for five criteria representing output quantity of interest. The deterministic results are validated with past experimental results. The results obtained from the ANN-based surrogate model are observed to attain fitment with the results obtained by Monte Carlo Simulation (MCS). The statistical results are presented for both deterministic, as well as stochastic domain.

Subrata Kushari, A. Chakraborty, T. Mukhopadhyay, S. R. Maity, S. Dey

### Interaction of Higher Buckling Modes in Uniformly Compressed Simply Supported Unstiffened Plates

The effective width method (EWM) for calculating the ultimate strength of cold-formed steel (CFS) members assumes simply supported boundary conditions along the plate edges. Unstiffened plates, simply supported along three edges and unsupported along one longitudinal edge buckle in a single half-wave equal to plate length when subjected to uniform compression. It has been observed from the finite element analysis results that the simply supported unstiffened plates with large length to width ratios ( $$L/b \ge$$ L / b ≥ 10) the deformation pattern changes from a single half-wave to a combination of three half-waves corresponding to the ultimate load. One of the possible reasons for this is the nearly same elastic buckling stresses in the first few modes leading to the interaction of higher buckling modes. At larger L/b ratios the interaction of the third buckling mode with fundamental mode was observed causing the reduction in the ultimate strength. A similar reduction in the ultimate strength due to buckling mode interactions are also found in CFS plain equal angle sections, as such sections composed of only unstiffened plates which buckle simultaneously. In sections like plain channels, where additional rotational restraint along the supported longitudinal edge is present, such mode interactions are found to not influence the strength of unstiffened elements in sections.

K. C. Kalam Aswathy, M. V. Anil Kumar

### Natural Frequency of Higher-Order Shear Deformable FGM Plates with Initial Geometric Imperfection Resting on Elastic Foundation

In this paper, the natural frequency of higher order shear deformable FGM plates with initial geometric imperfections is investigated. The plates are resting on a Winkler–Pasternak elastic foundation. The effective material properties of the FGM plates are varied along the thickness direction using a simple power-law distribution. The formulations are based on Reddy’s higher order shear deformation theory. A special function (i.e. the product of trigonometric and hyperbolic functions) is added to the transverse displacement to incorporate the initial geometrical imperfection. The fundamental equations are derived using a variational approach by adopting traction-free boundary conditions on the top and bottom faces of the plates. The results are obtained using the finite element method associated with C0 continuous Lagrange’s isoparametric elements. Comparison and convergence studies have been performed to confirm the efficacy of the present model. Numerical results cover the effects of different parameters like power-law index, plate aspect ratio, side-to-thickness ratio, imperfection size, and foundation parameters on the natural frequency of FGM plates.

### A Geometrically Inspired Model for Kirchhoff Shells with Cartan’s Moving Frames

This work attempts at an entirely novel reformulation of Kirchhoff shells using the theory of moving frames which is a powerful alternative method to describe the geometry of smooth manifolds. In this setup, the defining geometrical features of the non-Euclidean manifold co-evolve with deformation, which means that the model is inherently equipped to accurately describe (possibly irreversible) changes in the referential geometry. Insights from the geometrically transparent kinematics as well as an analytical solution reported for thin strips undergoing very large cylindrical bending explicate on the far-reaching implications of the proposed shell model and its possible spin-offs.

Bensingh Dhas, Debasish Roy

### 3-Dimensional Analysis of Fixed-Headed Single Pile and 2 × 2 Pile Group in Multilayered Soil

Apart from vertical loads from the supporting superstructure, pile foundations are often subjected to lateral loads and moments owing to the actions of wind, traffic, earth pressure, water wave, seismic forces or their combined action. The analysis and design of piles, subjected to such lateral forces, are very important for ensuring the serviceability of the supported structure. This article reports the lateral load behavior of a fixed-headed floating tip single pile and 2 × 2 pile group embedded in layered soil. For this purpose, nonlinear 3-dimensional Finite Element analysis is conducted using PLAXIS 3D. The multilayered soils are represented by Mohr–Coulomb models, while the pile is represented by the elastic embedded beam model. The 3D analysis provides detailed insight into the characteristic development of 3D stress-strain features surrounding the pile that governs its flexural response. The outcomes of the present study are compared to the results from simplified numerical approaches available in the literature, thereby highlighting the efficacy of the developed finite element model. The study revealed that the soil stratigraphy largely influences the flexural response of the pile. The influence of the pile group on the stress-strain behavior of the soil, flexural response of the pile, and the pile–soil interaction is also revealed.

Arindam Dey, Somenath Mukherjee

### Significance of Interface Modeling in the Analysis of Laterally Loaded Deep Foundations

Interface modeling is one of the important components in the numerical modeling of soil–structure interaction problem. It is equally important as material and geometrical modeling. Inaccurate modeling of the interface between the soil and the structure may lead to unreliable results. However, in many cases, interface modeling is overlooked and the interface between the soil and the structure is generally modeled as a rigid connection. In the present paper, we have shown the influence of interface modeling in the analysis of laterally loaded deep foundations. A finite element model of laterally loaded foundation–soil system is developed wherein the foundation is modeled as a linear elastic system and the soil as nonlinear which is defined by the multi-yield surface plasticity model. The interface between the soil and the foundation is modeled using zero thickness contact element, which is defined, by constitutive relationships capable to define sliding and separation mechanisms at the interface. The results obtained from the proposed finite element model are then compared with the conventional approach of interface modeling. The present study indicates that the conventional approach overestimates the lateral load capacity of deep foundation as well as it is unable to explain the mechanisms of the deformation of laterally loaded foundation–soil system.

### Micromechanical Modeling of Material Cross-anisotropy

Micromechanical behavior of granular materials is an important aspect for various engineering fields like soil mechanics, powder technology and mineral processing. The anisotropic material structure of the granular deposits is generally represented by a fabric tensor which takes into account the distribution of normal vectors at the interparticle contacts. In this regard, a truncated spherical harmonic function, restricted up to second-order terms, is often used to define the fabric tensor; however, this constrains the generic description of material anisotropy. While getting deposited under gravity, granular solids often exhibit a cross-anisotropic fabric structure with a preferential particle contact orientation favored by the direction of deposition. In the present study, the stiffness tensor of a cross-anisotropic fabric structure has been explored taking into account both the second and fourth order truncation of the spherical harmonic function. It has been noticed that the fourth order truncation gives a better control in capturing the cross-anisotropic nature of the granular fabric. Further, the bounds on fabric parameters are examined along with the influence of their respective magnitudes on the elastic stiffness moduli of the granular packing.

Geethesh Naiyyalga, Mousumi Mukherjee

### Stability of an Unsupported Elliptical Tunnel Subjected to Surcharge Loading in Cohesive-Frictional Soil

This study investigates the stability of an unsupported elliptical tunnel subjected to surcharge loading in cohesive-frictional soil. Non-circular tunnels, like an elliptical tunnel, provide more space and structural stability due to their smooth tunnel profile. The analysis has been performed assuming a plane strain condition by using lower bound limit analysis in conjunction with finite elements and second-order conic programming (SOCP). Limit analysis determines the collapse load at which the soil mass undergoes an unrestricted plastic deformation. The soil medium around the tunnel has been modelled as a homogenous and isotropic Mohr–Coulomb material obeying an associative flow rule. SOCP enables the usage of the non-linear Mohr–Coulomb yield criteria, which is expressed as a set of second-order cones and overcomes the difficulty of singular apex point of the Mohr–Coulomb yield function and is robust and efficient in solving a huge number of variables. In this study, a uniform surcharge loading is applied to the ground surface, and the stability is determined for smooth interface condition between the loading surface and the underlying soil. The results are presented in the form of dimensionless stability charts. The stability number in this analysis is indicated as σs/c obtained for different combinations of soil cover ratio H/B, aspect ratio of tunnel D/B, γB/c and ϕ where H is soil cover depth of tunnel, B and D are width and height of tunnel, respectively, and c, γ and ϕ are cohesion, unit weight and peak friction angle of soil. It has been noted that the stability number increases with increase in the peak friction angle of soil and soil cover depth ratio and decreases with an increase in D/B and γB/c. The size of the plastic zone increases as H/B keeps increasing and extends downwards enclosing the entire tunnel.

Puja Dutta, Paramita Bhattacharya

### PFC3D Modeling of Rock Fragmentation by Pressure Pulse

Unconventional hydrocarbon resources like tight oil make up a large fraction of the global hydrocarbon reserve. Tight oil exists in low permeability formations that require permeability enhancement for economic production. Chemically induced pressure pulses are being investigated as an alternative to hydraulic fracturing to enhance the permeability of these reservoirs. A numerical investigation of rock damage and fragmentation due to a chemically induced pressure pulse around a well is carried out using Itasca’s discrete element code PFC3D. Itasca’s material-modeling support package is used to create synthetic rock specimens that are subject to explosive loading. Python scripting, which is embedded in PFC Furtney et al.(Proceedings of the fourth Itasca symposium on applied numerical modeling (Lima, Peru). Minneapolis, Itasca International, Inc, [1]), is used to apply the gas pressure and generate the visualization. Qualitative features of the laboratory experiments matched with PFC3D results. Fragmentation of a block specimen expected at a range of peak pressure and pressure rise time values was analyzed. As expected, and as observed in the experiments, the number of radial fractures increases as the rise time decreases. The intensity of the fracturing and near hole crushing increase as the peak pressure increases. Permeability change is estimated from the predicted fracturing. Insights gained from numerical modeling have helped the development of the chemical stimulation methodology.

Jason Furtney, Jay Aglawe

### Modeling of Seismic Actions on Earth Retaining Structures

Present work deals with numerical modeling of seismic actions on earth retaining structures. Finite element (FE) analyses have been carried out on scaled-down retaining wall models. The capability of finite element models has been evaluated for the replication of shaking table experiment results. It was observed that FE models are highly sensitive to assigned nonlinear material models, especially for hardening and softening behavior of backfill soil. A detailed and simplified FE modeling procedure is explained for the simulation of seismic actions on earth retaining structures.

Rohit Tiwari, Nelson Lam, Elisa Lumantarna

### Detection of Damages in Structures Using Changes in Stiffness and Damping

Structural damage identification has been gaining a lot of importance for almost two decades. In this paper, a fibre-reinforced plastic (FRP) plate has been considered under the free–free support condition. Damage is assumed to be confined within a small area of the plate locally. Experimental data has been numerically simulated for both damaged and undamaged plate. Both stiffness and damping changes are considered in the present study. Rayleigh’s proportional damping has been used for modelling the damping in the plate. For the model updating process, Inverse Eigen sensitivity Method (IEM) has been implemented. The objective function is based on the variation between frequency response function (FRF) values. The damaged area is modelled with degraded values of elastic moduli. Further, the global modal damping factors of the damaged model have been increased to account for the increase in damping due to damage. A two-stage damage identification approach has been adopted. Damage site is located first using a damage index based on mode shape curvature difference. Subsequently, in the second stage, the damage is quantified employing model updating technique. The estimated reduced stiffness and increased damping parameters are found to be converging to actual values in these numerically simulated examples.

Uday Sinha, Sushanta Chakraborty

### A Data-Based Technique for Damage Detection Handling Environmental Variability During Online Structural Health Monitoring

The success of data-based online damage detection techniques depends upon the ability to detect the deviation from the previous measurements of the healthy system, changes in the material and/or geometric properties, boundary conditions, and system connectivity. Most of the data-based techniques extract features like frequencies, mode shapes, etc., for further processing. However, the random excitation, the varied environmental conditions, and the undesired measurement noise, often bring in the stochasticity in the features extracted from the vibration data. Also, the environmental variability due to temperature alters the material property of the structure, and creates an effect which is similar to that of the real damage. This fact emphasizes the need for techniques to differentiate the effects of environmental variability from damage, during diagnosis, using the output-only vibration data. In this paper, a data-based technique, which can effectively handle the environmental variability, as well as capable of locating the region of damage in the structure, using the acceleration time-history data, is presented. In this paper, Mahalanobis Squared Distance (MSD), which is popularly used in novelty detection, is used to handle the effect of environmental or operational variability (EOV) and simultaneously perform the damage detection, by treating the acceleration time-history of sensor nodes as feature vectors. With the confirmation of the presence of damage, subsequently, the spatial domain of damage is identified, by performing a sequential elimination approach, while forming the feature vectors for MSD evaluation. The results of the numerical studies using a synthetic data and benchmark data show that the proposed data-based technique using MSD is efficient in eliminating the variability and precisely locating the damage region, spatially on the structure.

K. Lakshmi, Junia Blessy

### Damage Detection in Presence of Varying Temperature Using Mode Shape and a Two-Step Neural Network

The dynamic characteristics of any structural system get affected not only due to damage but also from variations in ambient uncertainty. Thus, false positive or negative alarm may be signalled if temperature effects are not taken care off. The difficulty lies in correlating response measurements to corresponding damage patterns in the presence of varying temperature. This study employs machine learning algorithm to filter out the temperature effect from the measured mode shapes. A two-stage data-driven approach has been developed in which damage detection and localization are performed in consequence. For detection, a model to correlate mode shapes and temperature is formulated using an Auto-Associative Neural Network (AANN) and a temperature-invariant prediction error is defined as Novelty Index (NI). NIs are further classified to corresponding damage cases employing a fully connected layer network. With numerical experiments, the algorithm presented excellent efficiency and robustness against varying temperature in detecting damage.

Smriti Sharma, Subhamoy Sen

### Breathing Crack Localization Using Nonlinear Intermodulation Based Exponential Weighting Function Augmented Spatial Curvature Approach

Localization of breathing crack using vibration-based measurements is a highly challenging inverse problem. In this paper, we present the conventional spatial curvature-based damage detection approach augmented with specially formulated exponential weighting functions for breathing crack identification using the vibration responses obtained spatially across the structure under bitone harmonic excitation. The proposed exponential weighting function provides an enhanced damage diagnosis as it exploits nonlinear sensitive damage features such as superharmonics and intermodulations, induced by the opening and closing behaviour of the breathing crack. The robustness and effectiveness of the proposed damage diagnostic scheme is validated through both numerical and laboratory-level investigations.

J. Prawin

### Error in Constitutive Equation based Approach for Isotropic Material Parameter Estimation in Frequency-Domain Elastodynamics

A new version of error in constitutive equation (ECE)-based material parameter identification technique for linear elastic structure in frequency-domain elastodynamics has been proposed in this article. The inverse identification problem is solved by minimizing the ECE cost functional. The ECE functional measures the error in constitutive equation due to two incompatible stress and strain fields. This incompatibility is produced due to the generation of these two fields following dissimilar constraints. The stress field is dynamically admissible and the strain field is kinematically admissible with the measured displacement data. First, the strain field is generated by using a simple penalization technique with weak incorporation of full or partial noisy measured displacement data. This penalization technique also acts as a regularization to tackle the ill-posedness of the inverse problem. Then the stress field is generated by solving a linear system of equations. Thus, in the proposed methodology, the generation of incompatible stress and strain field is uncoupled in nature which reduces the numerical computational cost in contrast to standard modified error in constitutive equation (MECE)-based method. Afterward, explicit linear update formulas are formed for isotropic material model. In numerical examples, identification of heterogeneous isotropic material parameters is performed for 3D structures. The numerical experimentation shows that the proposed method can effectively identify the elastic material parameter distribution in a few number of iterations. The present method can be utilized in large-scale elastic parameter estimation problem because of its low computational cost.

Shyamal Guchhait, Biswanath Banerjee

### A Novel Sloshing Damper for Vibration Control of Short Period Structures

Tuned sloshing damper is a well-established and popular passive control device for vibration mitigation of structures subjected to excitations such as wind, earthquake, wave, etc. However, being a long period system, the applicability of this type of control device is restricted to flexible structures. To overcome this, a new kind of translational spring-connected sloshing damper is introduced in the present research paper and its applicability to short period structures is explored. First, a time-domain formulation of a linear single-degree-of-freedom (SDOF) structure with spring-connected sloshing damper system is developed. A nonlinear model based on the shallow water wave theory is utilized for modelling the liquid motion in the sloshing damper. Further, a numerical study on the performance of the damper system attached to a short period structure subjected to harmonic input is carried out. The performance of the damper system is examined on the basis of reduction in the peak value of the structural displacement. The performance of the proposed damper system indicates that the spring-connected sloshing damper has great potential as a vibration mitigation device for short period structures.

Anuja Roy, Atanu Sahu, Debasish Bandyopadhyay

### Fracture Mechanics Based Unilateral and Bilateral Earthquake Simulations: Application to Cable-Stayed Bridge Response

The phenomena of forward-directivity effects cause pulse-type earthquake ground motions that result in significant damage to structures. Forward directivity ground motions can be facilitated by typically simulating unilateral ruptures and occasionally by bilateral ruptures. Traditional analysis methods do not employ the dynamics of fault rupture hence are inadequate to capture the full effects of these pulse-type ground motions. Computational seismology overcomes this limitation and plays an important role to simulate dynamic earthquake ruptures. The objective of this paper is to use an open-source code SPECFEM3D to generate synthetic field vector data to improve the understanding of pulse-type ground motions generated using dynamic simulations. The software was used to generate synthetic earthquakes of moment magnitude, Mw = 7 with a strike-slip mechanism. Two cases were considered with nucleation at the end and in the center of the fault to generate unilateral and bilateral ruptures. The generated ground motions are then interpreted to comprehend the concept of directivity. Later, the seismic response of the bridge is evaluated for selected stations around the fault. The behavior of the bridge in terms of displacement field is evaluated which showed a similar response for stations located at a distance of 2 and 10 km in front of the fault. Further inference of bridge response is drawn by comparing the Fourier amplitude spectrum of velocities at these particular stations. The peak amplitude frequencies of the velocity fields at these stations lie in the regime of natural frequencies of the bridge which caused it to resonate in turn exhibiting high displacements at stations in front of the fault.

K. S. K. Karthik Reddy, Surendra Nadh Somala

### Broadband Ground Motion in Indo-Gangetic Basin for Hypothetical Earthquakes in Himalaya

Indo-Gangetic (IG) Basin, formed between the Indian shield and Himalayas, is the largest sedimentary basin in India. The region also constitutes many metropolitan cities, including the capital city New Delhi. The seismic risk in the region is attributed due to the proximity to seismically active Himalayan faults, the possible seismic wave amplification due to huge sedimentary layers, and the vulnerability due to urban agglomerations. However, the region lacks a dense set of recorded data curbing the direct assessment of ground motion intensities. Hence, seismic hazard needs to be estimated based on synthetic ground motions for possible scenario earthquakes. These ground motion simulations require a proper understanding of the spatial variation of material properties, viz., density and wave velocities in the region of interest. Hence, the present work focuses on developing the 3D regional velocity model for ground motion simulations in IG Basin spanning between longitude 74.5–82.5 E and latitude 24.5–32.5 N. The spatially varying material properties of the region are derived by suitably interpreting the available velocity models constrained according to geological features reported in the literature. The 3D velocity model derived from the study is first employed in a finite element platform to obtain low-frequency ground motion. These ground motions rich in low-frequency content are further combined with the high-frequency ground motion simulated using the Zeng-scattering method on a hybrid broadband ground motion generation platform. Hence, the simulated time histories comprise of energy in the period between 0 and 10 s, thus complying to engineering interest. The 3D velocity model developed from the study is validated using the strong motion data available for an event in the Main Boundary Thrust. The simulated time histories are observed to match the phase and energy content of recorded data. The model is further employed to simulate time histories for Mw 8.5 hypothetical earthquake in the Himalayas. The obtained response spectra are compared with the IS1893 code recommendations.

J. Dhanya, S. Jayalakshmi, S. T. G. Raghukanth

### Earthquake Engineering in Areas Away from Tectonic Plate Boundaries

This article presents findings on many facets of research into engineering for mitigating earthquake hazards in regions remote from tectonic plate boundaries. Topics covered include seismic activities in intraplate regions, ground motion behaviour of intraplate earthquakes, considerations of site modification behaviour, structural design and detailing of reinforced concrete and structural analysis in regions of low-to-moderate seismicity. Much of the materials presented were generated from collaborative research involving the author and numerous esteemed collaborators over many years. The challenges that are being attended to are distinctive to those addressed in mainstream earthquake engineering research which is applicable to areas in proximity to tectonic plate boundaries.

Nelson Lam

### Floor Response Spectra Generation Considering Nonlinearity of Reinforced Concrete Shear Walls

Many devastating earthquakes exceeding the design basis levels have occurred in the past. Safety assessment of system and component like equipment and piping systems of industrial/nuclear safety-related structures subjected to earthquakes beyond design basis levels necessitates consideration of the structural nonlinearity. The evaluation of the seismic performance of nuclear power plant structures requires the assessment of shear walls, which are its main structural members and for qualification of secondary systems, in-structure or floor response spectra [FRS] is the input required. Hence, it is essential to generate nonlinear FRS considering structural nonlinearity in shear walls. Earlier shake table experiments were performed on two numbers of RC shear walls of aspect ratio 1.98 till failure by Parulekar et al. (Struct Eng Mech 59:291–312, 2016 [1]). This paper addresses the numerical work carried out on generation of FRS for the shear wall considering structural nonlinearity. A stiffness and strength degrading damage-based model given by Sucuoǧlu and Erberik (Earthq Eng Struct Dyn 33:69–88, 2004 [2]) is used for modeling strength degradation for concrete hinges in dynamic analysis. The shear wall is modeled with hinge characteristics using pivot hysteretic law. Finally, the floor spectra obtained by numerical simulation of the shear wall are compared with those obtained from the tests.

Paresh Kothari, Y. M. Parulekar, G. V. Ramarao, G. V. Shenai

### Efficient Arrangement of Friction Damped Bracing System (FDBS) for Multi-storey Steel Frame

The Friction Damped Bracing System (FDBS) is able to significantly control the vibration of framed structure without dissipating energy through the inelastic yielding of its structural components. Therefore, it is a useful tool to design the structural system by isolating the energy dissipation components at some specific as well as desired locations. This purposeful isolation of the critical components helps, in turn, to monitor the health of the system efficiently, especially for the large and complicated systems such as process plant structures, offshore structure, etc. Therefore, effective placement of the energy dissipation devices in terms of their numbers as well as locations is essential to meet the optimum requirement of serviceability, safety, and stability. In this article, FDBS is modelled numerically following standard Friction Damper guideline. The 2D building frames with FDBS at various locations are used to study the responses of multi-storey building frames having different vertical bracing configurations. Locations of the energy dissipation devices are altered for each of the structures to study the effect of load flow through the desired load path. It is intended to isolate the FDBS in such a way so that the operational constraints do not interfere with the monitoring and maintenance of the critical dissipating system, which is the lifeline for the structural stability. Nonlinear time history analysis is performed for each of the frames for a scaled ground motion obtained using Conditional Mean Spectra for the city of Vancouver. Energy dissipation behavior of the structures is compared in order to comprehend the effect of damper arrangement. Load versus deflection behaviour of the structures at different levels indicate that structures with regular configurations show better behaviour in comparison to the customized structures with special configurations. Therefore, it is concluded that FDBS enabled structural systems are suitable as well as necessary for the complicated structures where the horizontal load transfer system is expected to be flexible to meet the process requirements.

Saikat Bagchi, Avirup Sarkar, Ashutosh Bagchi

### Bidirectional Pushover Analysis considering the Effect of Angle of Seismic Incidence

The general practice in structural assessment or design using 3D seismic analysis of inelastic structures is to obtain the responses (such as storey displacement, inter-storey drift, etc.) by applying the bidirectional components along any arbitrarily chosen structural axes. However, such response quantities may not remain the same when the bidirectional components are rotated with respect to the structural axes. It becomes relevant to identify the angle of seismic loading which maximizes the response quantity in the structure, and that angle would be called as critical angle of incidence (CAI), and the associated response as critical response. Nevertheless, a single CAI which can simultaneously maximize all the responses of the structure does not exist, rather the critical angle varies according to the type of response and earthquake loading. Therefore, any structural assessment or design of buildings based on the responses obtained from applying the earthquake loading along user defined structural axes may not be always conservative. To avoid such scenarios the critical responses should be estimated considering the effect of angle of seismic incidence. To address such an issue, pertaining to inelastic structures, this study presents a new approach which essentially combines bidirectional pushover analysis with an already existing non-linear static procedure called the Extended-N2 method.

Prabakaran Kesavan, Arun Menon

### Seismic Energy Loss in Semi-rigid Steel Frames Under Near-Field Earthquakes

A comparative study is carried out to estimate the seismic energy losses between the semi-rigid steel frames, modeled in two different approaches and rigid frames. For this purpose, three variant of earthquakes is considered, namely, far-field and near-field with forward directivity and fling step effect. These earthquakes are scaled to a peak ground acceleration (PGA) level of 0.4 and 0.6 g. The seismic energy loss is evaluated along with other seismic response parameters. The responses parameters of interest are maximum roof displacement, base shear, the total number of formation of plastic hinges with their square root of the sum of square (SRSS) values of maximum hinge rotations, and the energy dissipation in the form of modal damping and link hysteretic energy. For this numerical simulation study, a five-story rigid frame is designed as per Indian standard provisions as an illustrative problem. A nonlinear response history analysis is performed using the SAP2000 platform to evaluate the desired responses. The results of present work reveal that (i) the seismic energy dissipation significantly more in semi-rigid connected frame with plastic link as compared to elastic link; (ii) the energy dissipation in the form of plastic hinges are substantial in rigid frames as compared to semi-rigid frames with plastic and elastic link, plastic link model provides comparable loss in seismic energy with rigid frames; and (iii) the significance of seismic energy loss depends on earthquakes type, PGA level, degree of semi-rigidity and connection type.

Vijay Sharma, M. K. Shrimali, S. D. Bharti, T. K. Datta

### Seismic Behavior of Baffled Liquid Storage Tank Under Far-Field and Near-Field Earthquake

The liquid storage tanks (LST) are one of the essential civil structures. The inter-action of LSTs with an earthquake during its service life is a critical and crucial factor that cannot be ignored. The present study describes effect of the earthquake on the response parameters of LSTs. Depending on the nature of the earthquake these responses can increase or decrease. The study is further extended by implementing the passive control device. A vertical baffle plate is placed at the base of the tank. The non-linear dynamic analysis of the LST is performed on the ABAQUS. The response quantities of interest include top board displacement, Von-Mises stress, shear force, overturning moment, wave height, and hydrodynamic pressure in the tank. The results show that wave height for the different earthquakes can yield a difference of about four times. The baffle plate can significantly impact the sloshing height. The maximum reduction of 77% in wave height for far-field earthquake is present. However, the presence of the baffle increases the shear force response of the tank.

Sourabh Vern, M. K. Shrimali, S. D. Bharti, T. K. Datta

### Seismic Response of Asymmetric Structure with Soil Structure Interaction Using Semi-Active MR Damper

The seismic response of a four-storey asymmetric building with SSI using MR damper with semi-active damping with friction type damping algorithm is studied. The effect of SSI is assessed by comparing the seismic response of a four-storey one-way asymmetric building resting on stiff soil and soft soil with that of the same building considering fixed base case. The optimal damper parameters considering four different ground motions are obtained. The controlled response of the building resting on soft soil is also compared with that of the corresponding uncontrolled symmetric structure to assess the effects of lateral torsional coupling. It is observed from the present study that MR damper with friction type damping scheme could significantly reduce the detrimental effects of SSI and lateral torsional coupling but the reduction in response varies widely with the ground motion considered.

Shuvadeep Panchanan, Praveen Kumar, Swagata Basu, R. S. Jangid

### A Critical Review of TNT Equivalence Factors for Various Explosives

In the present scenario, it has been observed that terrorist attack became global issue and due to its increased frequency, it has gained attention of the researchers all over the world. Thus, it became the need of today’s era to understand the basics of explosion and factors affecting the explosion. Types of explosives are one of the important parameters which directly influences the impact of blast on any structural element. The term “TNT equivalence” is considered as the benchmark and is most commonly used to compare the performance of explosives with respect to reference explosive, i.e. trinitrotoluene (TNT). The main purpose of this study is to review TNT equivalence and the factors associated with it. The effect of charge geometry (i.e. spherical, flat, cylindrical, square etc.), confinement (close-in, intermediate or far ranges, etc.) and standoff distance on the peak overpressure and impulse are discussed in the present study as explosive energy and charge mass of the detonating material is related to equivalent weight of TNT. Moreover, effect of scaled distance of high explosives on TNT equivalent is also presented. Further, various numerical methods used to compute the TNT equivalents (TNTe) are reported for improved understanding of the TNT equivalence.

P. A. Shirbhate, M. D. Goel

### Limitations of Simplified Analysis Procedures Used for Calculation of Blast Response of Structures

The current state of practice in the blast-resistant design of structural members relies on simplified single-degree-of-freedom (SDOF) to calculate the response quantities. An equivalent SDOF representation of a structural member is obtained by assuming a deflected shape with equal deflection at the assumed degree of freedom. The blast load is approximated as a triangular pulse load. The response of an elastic and elasto-plastic SDOF system to triangular pulse is widely available in the literature. The utility of simplified SDOF procedures is mostly limited to calculating displacement response of regular-shaped members subject to far-field detonations. This paper investigates the limitations of the simplified SDOF method and role of various parameters (e.g., shape, standoff distance, boundary conditions, positive phase) on response quantities of interests (e.g., displacement, shear force). The simplified SDOF results are verified using advanced finite element model of the steel column in LS-DYNA. The findings of the study are summarized, and recommendations are provided for usage of simplified SDOF procedures for the blast-resistant design of structures.

K. K. Anjani, Manish Kumar

### A Comparative Analysis of Computation of Peak Overpressure in Near Field Scenario During High Energetic Material's Detonation

A polynomial based empirical function and chart-based techniques are available for computation of peak overpressure in the event of detonation of high energetic material. Such computations are based on experiments carried out using high mass detonative and extrapolation using scaling laws. There are mathematical tools available based on these empirical relationships but have inherent numerical approximations. These tools are observed to be insufficient for accurately predicting peak overpressure in the near field scenarios, i.e., at scaled distance lower than 0.2 m/kg1/3. Furthermore, owing to very high temperature and pressure conditions in such scenarios only limited information is captured. However, simulation techniques using MM-ALE (Multi-Material Arbitrary Lagrangian Eulerian) approach are taxing on computation resources. A comparative study is presented to compare the results obtained using commercially available simulation techniques with results from empirical relations from experiments in near field scenarios (scale distance < 0.2 m/kg1/3). The study highlights merits and challenges of using the available pre-and post-processing techniques. A comparison of results obtained by changing the mesh size and meshing techniques is also discussed.

Praveen K. Verma, Rohit Sankrityayan, Devendra K. Dubey, Anoop Chawla

### Development of Performance-Based Design Guidelines for Reinforced Concrete Columns Subject to Blast Loads

Critical civilian facilities and military infrastructure in India have been a target of several terrorist attacks in the last few decades. In order to address the risk of explosion threats, it has become critical to design and construct blast-resistant structures to save lives and protect infrastructure. The focus of this paper is to develop performance-based guidelines for the blast-resistant design of reinforced concrete (RC) columns. Columns are the most vulnerable component of a structure and are at a high risk under a detonation scenario. The paper presents a comprehensive review of the blast-resistant design procedures followed by different design documents. The gaps and challenges in the blast resistance of RC columns were identified and addressed. Specific issues in the axial, flexure, and shear design of columns are highlighted. A performance-based analysis and design approach for blast-resistant design of RC column were developed and is presented in the paper. The design approach was verified using high-fidelity numerical simulations. The performances of the design columns was assessed using nonlinear FE models developed in LS-DYNA. The ultimate capacities of the columns subject to blast loads were obtained. The numerical simulations assist in verifying the proposed design procedures and provide critical information on the failure modes, safety margin, and other parameters for blast-resistant design of RC columns. Recommendations on safe and efficient design of RC members are also provided.

Vishal Kochar, K. K. Anjani, Manish Kumar

### Numerical Damage Modelling of RC Slabs Under Blast Loading Using K&C Concrete Model

K. Akshaya Gomathi, A. Rajagopal

Occurrences of terrorist attacks using explosive have frequented in the last two decades. These attacks inflict damage to the structure and ultimately pose threat to the lives of civilians. Public transit systems have been a target of terrorism in the past resulting in casualties and property loss. Indian transit systems consist of underground tunnels mainly to connect locations which otherwise are not easily accessible. Attack on such structures can lead to inaccessibility to isolated places for indefinite period of time. Prevention of such incidents cannot be assured but measures can be adopted to mitigate the damage to these structures. This involves understanding the response of underground structures under various blast scenarios. Thereby, this work presents the response of underground tunnel subjected to surface explosion using multi-material arbitrary Lagrangian Eulerian (MM-ALE) method. The model has been validated by comparing the size of crater formed by explosion with the size calculated using empirical formulae based on the theory of model similarity. Herein, a parametric study has been carried out by varying the TNT charge weight and tunnel lining thickness. Maximum damage is observed in the tunnel with increase in charge weight and decrease in lining thickness. An intervening layer of foam is fitted directly over the tunnel to absorb shock energy generated from detonation. Optimum thickness of foam at which blast damage can effectively be mitigated has been determined by performing numerical simulations.

Jagriti Mandal, M. D. Goel, Ajay Kumar Agarwal

### Dynamic Response of Tunnel Under Blast Loading and Its Blast Mitigation Using CFRP as Protective Barrier

The terrorist activities throughout the world increasing from last decades that leads to loss of life and property. Tunnels are underground structures used for many purposes and their collapse will lead to complete hectic situation for any nation. Hence, it becomes greatest importance to safeguard such structures under extreme loading conditions such as resulting from explosion. Not as much of research had been reported on underground tunnel subjected to blast loading as compared to other structures. To minimize the loss of human life and property, it is very important to understand the response of underground tunnel under explosion. Herein, numerical investigation of underground tunnel is carried out using FE package ABAQUS/Explicit® (Dassault Systèmes Simulia Corporation. France, 2014 [1]). Complete structure is modeled using CEL (Coupled Eulerian and Lagrangian) volume fraction method as per ABAQUS/Explicit® (Dassault Systèmes Simulia Corporation. France, 2014 [1]). First of all, FE analysis is validated with the available experimental results and then parametric investigation is carried out. Herein, tunnel structure is investigated under varying charge weight for the better understand of dynamic response structure. Further, CFRP (Carbon Fiber Reinforced Polymer) is used as a protective barrier between blast waves and structure to mitigate the structure damage against blast energy. Based on this investigation, it is observed that tunnel structural damage is significantly reduced by employing CFRP as protective barrier.

V. S. Phulari, M. D. Goel

### Uncertainty Quantification of Random Heterogeneous Media Using XFEM

The macroscopic mechanical properties of two-phase heterogeneous materials, consisting of random inclusions in a solid medium, are governed by the individual material properties of the inclusions and the medium, as well as the volume fraction and spatial distribution of the inclusions. In design and analysis using such materials, the macroscopic material properties are often used. The characterization of the macroscopic properties based on the accurate micro-structure modeling may often be computationally expensive. Hence, homogenization of representative micro-structures is often used to get these macroscopic properties. In this paper too we adopt this approach for a medium with random elliptical inclusions. Monte Carlo (MC) simulations are used to obtain different micro-structure realizations, enabling the statistical modeling of macroscopic material properties. The material is modeled using the extended finite element method (XFEM), where the inclusions are modeled independent of the finite element mesh using the level set method, thereby reducing the computational cost involved in the MC simulations. The effective elastic modulus and Poisson’s ratio of the heterogeneous material are obtained using Hill’s averaging theorem, following which the failure stress is obtained using the computed homogenized elastic properties. The excellent synergy between XFEM and MC simulations gives the statistical characteristics of these effective material properties, including the variation in their estimates induced by the random micro-structure. It is shown that the uncertainty in the homogenized failure stress is much higher than the uncertainty in the elastic properties.

### Uncertainty Propagation in Estimated Structural Parameters Owing to Univariate Uncertain Parameter Using RSM and PDEM

The existence of uncertainty even in a single structural parameter may lead to random responses from the structure. This results in propagation of uncertainty in some other parameters estimated using these random responses. Therefore, to understand the behavior of any structure, investigation of the stochastic system is essential in structural health monitoring (SHM). For this purpose, response surface methodology (RSM) is applied for stiffness calculation. Probability density evolution method (PDEM) is employed for quick and efficient generation of the probability density function (PDF). In this study, the top floor mass is considered as random input parameter for PDEM. PDF of the random parameter is discretized into representative points. RSM is used to carry out inverse optimization for finding the structural properties (i.e., stiffness). PDEM is then employed for generating the PDF of stiffness. From the PDF of stiffness, it can be seen how randomness propagates from the system uncertainty into the estimated parameters.

Kumar Anjneya, Divya Grover, Koushik Roy

### Seismic Response of Liquid Storage Tank Considering Uncertain Soil Parameters

Properties of soil and structure govern the effects of soil-structure interaction on the seismic response of any structure. However, it is well known that there involves high uncertainty in the engineering properties of the soil in its natural state. The present study attempts to investigate the effects of the uncertain soil properties on the seismic responses of liquid storage tank. Critical soil parameters, such as shear wave velocity and mass density, are represented by suitable probability distribution functions and used in the analyses. The liquid storage tank is modeled using the lumped mass idealization and the soil domain is modeled utilizing the finite element approach. A sufficiently large number of coupled soil-tank models are generated with each model having a unique variation of soil parameters along the depth. Utilizing Monte Carlo simulation technique, it is observed that the uncertain soil parameters have a significant effect on the peak response quantities of the liquid storage tank.

Hitesh Kumar, Sandip Kumar Saha

### Reliability Assessment of CFRP Composite Laminate Subjected to Low Velocity Impact Damage

The stochastic behaviors of the carbon fiber reinforced plastic (CFRP) materials are investigated under the low velocity impact to consider the scatters of the material properties to predict the safety and the reliability of the structure. The probabilistic and the deterministic responses of the CFRP materials for different ply orientations are considered to obtain the optimum design for the structures. Composites have numerous applications in modern industries for the low velocity impact to predict the failure behavior of the structure. Failure of composite laminate is catastrophic in nature due to brittle nature of matrix, fiber, uncertainty in volume of constituent material, anisotropic characteristics, and in homogeneity. The stochastic continuum damage model is used for the composite materials to predict the different modes of failure such as fiber, matrix, and delamination. Modern industries prefer a material having more likelihood to perform a required function with desire life span. The stochastic finite element method is performed to account the scatter in the random fields to determine the stochastic response and reliability of the structure. The probabilistic response of the CFRP structure is determined using Gaussian process response surface method to investigate the probability of failure or reliability of composite structures.

Shivdayal Patel, Akshay Sontakke, Suhail Ahmad

### Passive Vibration Control of Tall Structures with Uncertain Parameters—A Reliability Analysis

The paper studies the reliability analysis and passive vibration control (PVC) of tall structures with uncertain parameters. A tall structure is modeled using certain parameters, Monte Carlo method is employed to create the uncertain parameters for the selected tall structure. The robust tune-able PVC (TPVC) schemes are installed to mitigate the response of the structure under earthquake excitations. Different tuned mass damper (TMD) schemes are used to mitigate the response of the structure. These schemes are single TMD (STMD), multiple TMDs (MTMDs), and distributed MTMDs (d-MTMDs). Newmark’s integration method is used to solve the equation of motion for the coupled system. It is found that ignoring the uncertainties in parameters of structure cause reduction in performances of the TPVC. Different probability distribution functions (PDF) are compared to select the most suitable one.

Said Elias, Deepika Gill, Rajesh Rupakhety, Simon Olafsson

### Dual Polynomial Response Surface-Based Robust Design Optimization of Structure Under Stochastic Blast Load

The present study deals with robust design optimization (RDO) of an underground bunker under stochastic blast-induced ground motion. Since the direct Monte Carlo Simulation (MCS) requires extensive computational time to solve an RDO problem, the polynomial response surface method (RSM) is highly appreciated as an alternative to reduce the computational burden. Thus, the present study attempts to explore the advantage of the moving least-squares method (MLSM) based dual RSM to take into account the record-to-record variation in the blast load in place of the conventional least-squares method (LSM). The blast-induced ground shock has been artificially generated by considering the Tajimi-Kanai power spectral density function (PSDF) and incorporating uncertainty in the blast parameters, viz. explosion distance and explosive charge weight. The application of the proposed dual RSM in RDO not only evades several finite element analyses runs in the simulation loop during the optimization process, but also improve the computational efficiency significantly. The RDO is formulated by simultaneously optimizing the expected value and variance of the performance function by using the weighted sum approach. The results show that the present MLSM-based RDO strategy yields more accurate and robust solutions than the conventional LSM-based approach when compared with the direct MCS results.

Gaurav Datta, Soumya Bhattacharjya

### Stochastic Modal Damping Analysis of Stiffened Laminated Composite Plate

Laminate composite plates have several significant applications in aerospace and automobile industries due to their high strength-to-weight ratio, thermal stability, etc. However, thin laminated composite plate has a tendency of buckling when subjected to some adverse loading conditions. The addition of stiffener can avoid the buckling tendency of the thin laminated composite plate. The effect of stiffener on natural frequency and random modal damping are studied herein. The effect of uncertainty in modal damping is accounted while analyzing the composite plate to evaluate the uncertainty in damped dynamic response of the stiffened composite plate. The modal damping of the composite is determined using visco-elastic damping (VED) model. The randomness in the modal damping is propagated from uncertainty in loss factor of the lamina, and stochastic finite element method (SFEM) based on generalized polynomial chaos (gPC) is applied to evaluate the uncertainty in the modal damping of the stiffened laminated composite plate. First-order shear deformation theory (FSDT), including rotary inertia, is adapted to develop collocation-based stochastic finite element formulation of the composite plate with stiffener. Addition of the stiffener increases the frequency of the composite structure. Uncertainty in the modal damping due to the varying layers of the plates and stiffener directions have been investigated.

Sourav Chandra, Kheirollah Sepahvand, Vasant Matsagar, Steffen Marburg

### Support Vector Model Based Thermal Uncertainty on Stochastic Natural Frequency of Functionally Graded Cylindrical Shells

This paper presents the effect of temperature on stochastic natural frequencies of cylindrical shells, composed of functionally graded materials (FGM) by using machine learning quadratic Support Vector Machine (SVM). An eight noded isoperimetric quadratic element is considered for the finite element formulation. The power law is employed to construct the material modelling of FGM cylindrical shells. Monte Carlo Simulation (MCS) is carried out in conjunction with stochastic eigenvalue solution. In the present study, zirconia (ceramic) and aluminium (metal) are considered to compose the FGM. The machine learning SVM model is constructed to reduce the computational iteration time and cost and validated with the traditional MCS model. The statistical analyses are conducted to portray the first three modes of frequencies. The results show that due to the increase of the temperature, the values of both deterministic as well as the stochastic mean of the first three natural frequencies decreases along with the decrease in sparsity. Sensitivity analysis is also carried out to enumerate the significant important input parameters contributing to influence the output quantity of interest (QoI). The statistical results obtained are the first known results.

Vaishali, S. Dey
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