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## Über dieses Buch

This book comprises select proceedings of the 63rd Congress of the Indian Society of Theoretical and Applied Mechanics (ISTAM) held in Bangalore, in December 2018. Latest research in computational, experimental, and applied mechanics is presented in the book. The chapters are broadly classified into two sections - (i) fluid mechanics and (ii) solid mechanics. Each section covers computational and experimental studies on various contemporary topics such as aerospace dynamics and propulsion, atmospheric sciences, boundary layers, compressible flow, environmental fluid dynamics, control structures, fracture and crack, viscoelasticity, and mechanics of composites. The contents of this book will serve as a useful reference to students, researchers, and practitioners interested in the broad field of mechanics.

## Inhaltsverzeichnis

### Sun Gravity-Assist to Trans-Lunar Injection Orbits

Abstract
Solar gravity propelled highly elliptical resident Earth orbits have been utilized to improve lunar mission performance. A regularized orbit propagator has been used to perform linear search for initial conditions that produce energy-saving pre-trans-lunar injection exo-atmospheric highly elliptical orbits. Additional propellant mass margin or smaller piggyback payloads to the Moon/high altitude orbits may be enabled by such transfers.
Harishkumar Sellamuthu, Subramanian Arumugam, Ram Krishan Sharma

### On the Recurrence Signatures of Flapping Wings Exposed to Gusty Simple Shear Flow

Abstract
The primary aim of the research reported in this paper was to understand the effect of change of gusty simple shear inflow’s gradient on the force and moment patterns of a flapping wing in the 3D reference frame. A wing undergoing one degree of freedom asymmetric flapping and rectangular planform shape was considered. The gradient of the gusty simple shear inflow profile, Vgrad, was varied from –10 to +10 in steps of 5 and corresponding vertical and horizontal forces and moment about the flapping axis were computed. Time series of these forces and moment were used to plot the global recurrence plots and were compared. Quantitative analysis of the findings was carried out by the windowed recurrence quantification analysis of the force and moment patterns. Eight recurrence parameters, viz. recurrence rate, determinism, laminarity, trapping time, ratio, entropy, maximum line and trend were calculated and compared. Numerical investigations revealed that negative gusty shear gradient induced a considerable increase in vertical force and moment and marginally decreased the horizontal forces. Positive gusty shear gradient induced a marginal increase in horizontal forces but caused a substantial decrement in vertical force and moment.
Manabendra M. De, J. S. Mathur, S. Vengadesan

### Unsteady Heat Transfer from a Non-isothermal Axisymmetric Body Immersed in Porous Media Saturated by Nanofluid

Abstract
The intent of this paper is to present the numerical results for transient heat transfer across an axisymmetric non-isothermal body embedded in porous media saturated by nanofluid. A non-linear coupled PDE is reduced using dimensionless similarity variables and is solved using Keller Box method. Buoyancy ratio Nr, Brownian motion Nb and thermophoresis Nt are the parameters considered in this study. The effect of Lewis number Le and non-Newtonian parameter N on reduced Nusselt number and reduced Sherwood number is recorded in tabular form for isothermal as well as for non-isothermal bodies. The heat flux for different values of non-Newtonian parameter N is plotted in the case of sphere and cylinder at different time levels.
Shobha Bagai, Mridu Sharma

### Nevanlinna Theory for Finding Meromorphic Solutions of Cubic-Quintic Ginzburg–Landau Equation Arising in Nonlinear Dynamics

Abstract
Research on meromorphic solution of complex differential equations using Nevanlinna theory has become a subject of great interest. This paper is devoted to finding meromorphic solutions of the cubic-quintic Ginzburg–Landau equation which arises in problems of dynamics, especially fluid dynamics. We consider the complex differential equation corresponding to cubic-quintic Ginzburg–Landau equation with coefficients being small functions of meromorphic functions. The problem has been mainly studied under the condition that meromorphic function and its first derivative share one value of the type counting multiplicity or ignoring multiplicity.

### Geometry of Variably Inclined Inviscid MHD Flows

Abstract
A steady plane variably inclined magnetohydrodynamic flow of an inviscid incompressible fluid of infinite electrical conductivity studied. Introducing the vorticity, magnetic flux density, and energy functions along with the variable angle between magnetic field and velocity vector, governing equations are reformulated. The resulting equations are solved to analyze the geometry of the fluid flow. Considering streamlines to be parallel, stream function approach is applied to obtain the pattern for magnetic lines and the complete solution to the flow variables. Next considering parallel magnetic lines, magnetic flux function approach is applied to obtain streamlines and the complete solution of the flow. A graphical analysis of pressure variation is made in all the cases.

### Kinematic Analysis of Theo Jansen Mechanism-Based Eight-Leg Robot

Abstract
This paper presents the design analysis of an intellectual model of an autonomous surveillance robot. The principle objective is to do surveillance in the muddy or desert area or on that region where the surface is less grippy. This spider is having EIGHT legs controlled by two DC servo motors. The mechanism which is used to make those legs is THEO JANSEN MECHANISM, which is one of the animal walking patterns. To do the surveillance, a 360° rotating camera is used which is having its own working module. All the electronics are controlled by Arduino and that Arduino takes power to run itself as well as all other systems by 12 V DC battery. As this is the first spider robot which is made by Polylactic Acid (PLA) material, it gives comparison between Conventional Theo Jansen Mechanism and Modified Theo Jansen Mechanism.
Keval Bhavsar, Dharmik Gohel, Pranav Darji, Jitendra Modi, Umang Parmar

### Wave Trapping by Trapezoidal Porous Breakwater

Abstract
The trapping of normally incident free surface water waves by a porous trapezoidal breakwater is studied in the context of two-dimensional linearized and potential water wave theory. The trapezoidal porous breakwater is situated at a finite distance away from the leeward rigid wall. The mathematical solution of the related boundary value problem is obtained using the well-known boundary element method. The flow of the water through the porous medium is modeled using Sollitt and Cross model for thick porous structure (see [13]). A number of important physical parameters such as wave loads on the rigid wall, reflection coefficient, and free surface elevations are calculated and discussed in detail.
Santanu Koley

### Heat and Mass Transfer Due to Double-Diffusion Convection in a Square Porous Enclosure Occupied by Casson Fluid

Abstract
Heat and mass transfer in a porous cavity filled with Casson fluid are analyzed. The flow behavior of Casson fluid in a porous cavity is investigated due to the realization that most of the fluids exhibiting non-Newtonian behavior come in contact with porous media, particularly, in ceramic processing, enhanced oil recovery, production of glass float, and processing of nuclear waste. The mathematical model of the physical problem consisting of continuity, momentum, energy, and concentration equations is converted into finite element equations and solved by penalty finite element method. The bottom wall of the cavity is hotter than the side walls (Th > Tc). The top wall of the cavity is adiabatic. On the other hand, concentration is more on the top wall compared to the bottom (Ch > Cc) wall. The side walls are taken to be impermeable to concentration flux. The physical parameters governing the fluid flow are Rayleigh number $$\left( {Ra} \right),$$ Prandtl number $$(Pr)$$, Darcy number $$\left( {Da} \right)$$, Lewis number $$(Le )$$, buoyancy ratio parameter (N), and Casson fluid parameter $$(\gamma )$$. It is observed from the obtained results that with the rise in Casson fluid parameter in porous medium leads to enhancement in heat transfer rate, mass transfer rate, and fluid flow intensification.

### Convergence of Eigenfunction Expansions for Membrane Coupled Gravity Waves

Abstract
In the present paper, some characteristics of eigenfunctions associated with membrane coupled gravity waves and its convergence are provided for finite water depth. Expansion formulae for velocity potentials and related orthogonal mode coupling relations for Laplace equation subject to the higher order boundary conditions are studied. The spectral representation of eigenfunctions is obtained in terms of Dirac delta function through the Green’s function technique. Finally, the convergence of eigenfunction expansion to velocity potential is obtained with the help of spectral representations.
Santanu Koley, K. Panduranga, Dipak K. Satpathi

### Numerical Analysis of Variations on Design Modifications of Train and Tunnel Geometries to Reduce Aerodynamic Drag on Train

Abstract
The flow of air around the train in a confined space, i.e., tunnel is different than that of the train moving in an open air. As the train passes through a tunnel, there is a large amount of aerodynamic drag force exerted on the body of the train. There is a compression of the air ahead of the train inside a tunnel due to which large pressure is produced ahead of a train while just behind the tail there is a suction of air due to low pressure at the tail end of the train. The train inside a confined space in a tunnel behaves just like a loosely fitted piston inside a cylinder. Thus, in order to reduce the drag force, train head and tail geometries are modified. This analysis has been done on ANSYS Fluent 14.0 and steady Navier–Stokes (N-S) equations for two-dimensional, axi-symmetric, incompressible flow using standard k-ε turbulence modeling was solved with the help of Fluent 14.0 software to simulate the flow around the train passing inside a tunnel. In this analysis, two observations are done: first, tunnel width, i.e., blockage ratio has been changed from 0.25 to 0.36 (tunnel width from 6 to 5 m) and variation of drag force with the blockage ratio is analyzed. Second, train head and tail geometries are changed to see the variation of drag force on blunt and hemispherical head and tail of the train. This paper suggests that a less blockage ratio is responsible for less drag force on the train. A similar investigation has been performed by taking different shapes of head and tail of the train keeping the blockage ratio same.
Vaibhav Rastogi, Nityananda Nandi

### Analysis of Exact Solutions of Electromagnetohydrodynamic Flow and Heat Transfer of Non-Newtonian Casson Fluid in Microchannel with Viscous Dissipation and Joule Heating

Abstract
A theoretical investigation is done to study the analytical solutions for the velocity and temperature distribution of non-Newtonian Casson fluid in microchannel associated with combined effects of electromagnetohydrodynamics forces and electrokinematics forces. Heat transfer and flow characteristic of non-newtonian Casson fluid are controlled by the combination of imposed pressure gradients, applied magnetic field, and electrokinematic forces. The interesting features of the electromagnetohydrodynamics flow along with heat transfer characteristic are examined by variation in the nondimensional physical parameter on the velocity and temperate profiles. The effect of Casson parameter on the velocity and temperature distribution has been analyzed. Variation of Nusselt number with applied magnetic field and also Casson parameter has been studied.
Motahar Reza, Amalendu Rana

### Pre-clinical Analysis of Implanted Ankle Joint Using Finite Element Method

Abstract
Slacken off of the implant component, dislocation, misalignment, fracture, wear in meniscal bearing, etc. are the most important reasons behind the failure of ankle arthroplasty. The study on the effects of implant material on tibia bone stress due to total ankle replacement (TAR) is the prime goal of this paper. Computed tomography (CT) scan data was used to develop the bones, and other soft tissues for the intact and implanted ankle joint. Three implanted FE models were generated having a different combination of implant material. The implanted FE model 1 is having the implant material combination of metal and ultra-high molecular weight polyethylene (UHMWPE). The combination of implant material in FE model 2 was ceramic and UHMWPE, whereas FE model 3 consists of the implant material combination of ceramic and carbon-fiber-reinforced polyetheretherketone (CFR-PEEK), respectively. Three positions during gait such as dorsiflexion, neutral, and plantar flexion positions were considered as applied loading condition, along with muscle force and ligaments. Stress shielding was found in the proximal region of the tibia (i.e., away from the implant neighborhood) due to implantation. Implant material combinations have less impact on tibia bone stress. The present outcome recommended that ceramic can be used as a substitute for metal and CFR-PEEK as an alternate to UHMWPE owing to the high metal release of metal and UHMWPE for long-standing attainment of the prosthetic components.
Subrata Mondal, Rajesh Ghosh

### Dynamic Problem of Fractional Thermoelasticity in Bounded Cylindrical Domain with Relaxation Time

Abstract
A fractional heat conduction model of a solid heat conductor is designed in the bounded cylindrical domain. The solid heat conductor under consideration is assumed to be in the form of a thick circular plate. The boundaries of the thick circular plate are traction free and subjected to externally applied axisymmetric heat source. Governing heat conduction equation of this model has been designed in the context of time fractional derivative with one-relaxation time. The solution of fractional heat conduction equation in association with Caputo time fractional derivative has been found by transforming the original boundary value problem into eigenvalue problem through the integral transforms. The inversion of Laplace transforms in terms of infinite series approximations has been achieved numerically using Gaver–Stehfest algorithm. The convergence of infinite series solutions has been discussed. Illustratively, the numerical scheme has been employed to partially distributed heat flux and thermal behavior of a heat conductor has been discussed numerically and studied graphically. Results obtained are compared with coupled thermoelasticity, fractional thermoelasticity, and generalized thermoelasticity.
Gaurav Mittal, V. S. Kulkarni

### A Study on Free Vibration Behavior of Microbeam Under Large Static Deflection Using Modified Couple Stress Theory

Abstract
The free vibration behavior of a statically deflected Timoshenko microbeam under uniformly distributed static load is studied based on modified couple stress theory. In the first step of the analysis, the beam configuration under large static deflection is obtained through a nonlinear static analysis in which the governing equations are derived employing minimum potential energy principle and incorporating von Karman geometric nonlinearity. In the subsequent step, the free vibration behavior of the statically deflected microbeam is investigated employing Hamilton’s principle and incorporating the tangent stiffness of the statically deflected beam configuration. The solutions of the governing equations for both the steps are obtained by approximating the displacement fields following Ritz method. The model is validated using the available results in the literature for some reduced problems. The results for the first two vibration modes are presented in nondimensional frequency–amplitude plane for clamped, simply supported, and clamped–simply supported beams.
Sujash Bhattacharya, Debabrata Das

### Fatigue Life Estimation of a Box Girder Bridge Using Coupled and Uncoupled Bridge–Vehicle Dynamics

Abstract
In the present paper, fatigue life of a steel box girder bridge has been evaluated by two approaches and the influencing parameters on fatigue life have been studied. In the first approach, the box girder bridge has been idealized as a Euler–Bernoulli beam and the coupled bridge–vehicle equations are developed. In the second approach, vehicle equations are first solved taking bridge as rigid. The pavement force found from the vehicle response and road roughness has been given as input in 3-D FEM model created in CSI Bridge. Fatigue life of the bridge component at the critical location has been found out using Miner approach and the stress time history from coupled and uncoupled schemes has been used for comparison purpose. The parameters which affect the fatigue life, i.e., velocity of the vehicle and road surface roughness are varied to observe the effect on fatigue life.
Anjaly J. Pillai, Suvendu Parida, Sudip Talukdar

### Size-Dependent Responses of Timoshenko Beam Incorporating the Strain Gradient Theories of Elasticity

Abstract
This paper is concerned with the study of size effects over elastic response due to strain gradient elasticity (SGE). The general form of SGE with higher order gradients is simplified and either modified couple stress theory (MCST) or modified strain gradient theory (MSGT) models the size effects. An element-free Galerkin (EFG) model of the SGE response is obtained, and the algebraic governing equations of motion are derived here from the variational principles. Following validation, a comparison of the size effects exhibited by MCST and MSGT is carried out. The effect of each component of the higher gradients over the stiffness of the beam is also studied.
Sai Sidhardh

### Dynamic Response of Axisymmetric Functionally Graded Viscothermoelastic Hollow Cylinder Due to Heat Sources by Using Series Solution

Abstract
This paper represents the exact analysis of functionally graded viscothermoelastic hollow cylinder subjected to dynamic heat sources. The viscothermoelastic material is considered to be inhomogeneous due to easy power law. The outer and inner surfaces of cylinder are kept traction free and time-dependent heat flux is supplied on inner part of the body and outer part may be isothermal. The governing equations have been changed into ordinary differential equations due to time harmonics. Series solution for regular singular points has been applied to ordinary differential equations to represent deformation, temperature change, and traction analytically. Numerical computations have been applied to field functions and represented graphically for radial stress, temperature change, and displacement against time and thickness of cylinder. The present work has been deliberated for some special applications in the thermal environment as it controls the variations of tractions and deformations.
Himani Mittal, Dinesh Kumar Sharma

### Modeling of a Novel Lower Limb Exoskeleton System for Paraplegic Patients

Abstract
This paper presents the design of a novel low-cost motorized wheelchair exoskeleton device to provide locomotive assistance and physical rehabilitation to paraplegic patients in the age group of 20–75 years. CAD modeling of different parts of the device has been completed using SOLIDWORKS software. Mathematical calculations are performed to estimate the torque requirements to drive rear wheels, and maximum torque requirement at knees in static condition. Static structural analysis of different parts of the mechanism is performed using ANSYS software for optimization and validation of the proposed design. The reduction in the overall mass of the mechanism is achieved by multi-use of actuators, where a single motor has been used for motion at more than one joints in the device. A mechanism is also designed to allow easy switching of power for the motors from one joint to the other. Further, to make the device eligible for use by people of different heights, adjustability in height of the mechanism has been achieved via the use of telescoping link mechanisms for legs of the device. The aim is to come up with a low-cost device which along with fulfilling the mobility requirements stays light, without compromising the strength and motion capabilities of the device.
Mrinal Gupta, Jyotindra Narayan, S. K. Dwivedy

### Characterization of Banana and Bagasse Fiber-Reinforced Hybrid Epoxy Composites

Abstract
In this work, banana and bagasse fibers have been taken as reinforcement material because of its ease of availability and low cost. Initially, the density of the fibers are found using water displacement method. The fibers were treated by NaOH and NaCl solution of 5% concentration for good adhesion property. These are reinforced with the epoxy with Hardener—HY 951. The 20 and 30% of volume fraction of banana and bagasse fibers of equal proportions are taken for fabrication using hand lay-up method for the dimension 300 * 300 mm2. Change in the volume fraction of FRC’s changes the value of young’s modulus by making the material more stiffer. The testing was carried out by the computer-integrated universal testing machine (UTM), which has the capacity of 100KN Kalpak software is used for the data acquisition the testing. The specimen is cut into as per ASTM D-3039 and ASTM D-790 standards for tensile test and flexural bending test, respectively. Tensile test and flexural bending tests are conducted on 20 and 30% of volume fraction of fibers (banana and bagasse). Results of tensile test and flexural bending test are obtained experimentally and compared each other, results reveal that fibers of 30% volume fraction make material stiffer and in turn increases the elasticity and UTS.
R. Prem Chand, Y. P. Ravitej, J. V. Shiva Mani Kanta

### Crack Growth Simulation in Quasi-brittle Materials Using a Localizing Gradient Damage Model

Abstract
Failure in quasi-brittle materials comes under an intermediate category of fracture failure, which includes different stages, i.e., micro-cracks nucleation, growth, and coalescence into a macroscopic crack. The different stages of failure result in a tension-softening structural response, which can be accurately modeled using the conventional gradient damage models. However, due to a constant interacting domain throughout the load history, conventional gradient damage models suffer from various drawbacks which limits their application to simulate the final stages of quasi-brittle failure process. In this contribution, the present work illustrates a thermodynamically consistent localizing gradient damage model, which successfully overcomes the drawbacks of conventional gradient damage models. The localizing gradient damage model uses an interaction function definition in the constitutive framework to take into account the diminishing nonlocal interactions, thus attaining a macroscopic crack in the form of a localized damage profile during the last stages of failure. The numerical accuracy of the model is tested against both mode-I and mode-II types of failure problems and compared with the experimental results.
Alok Negi, Sachin Kumar

### Delamination Damage Analyses of Lap Shear Joints Made with Flat Fibre-Reinforced Polymer Composite Laminates Subjected to Transverse Load

Abstract
In this work, initiation and growth of pre-embedded delamination in the adhesive-bonded lap shear joint (LSJ) made out of laminated fibre-reinforced polymer (FRP) considering flat geometry subjected to transverse load have been investigated. 3D nonlinear finite element technique has been employed to monitor the damage mechanism. The critical location to place the delamination has been obtained from the Tsai-Wu failure criterion. It is found to occur between the first and second layers of the bottom adherend of the Lap shear joint. Proper contact elements have been employed to avoid any interpenetration of delaminated surfaces. Interlaminar peel and shear stresses are obtained and found to be three dimensional in behavior. Virtual crack closure technique (VCCT) is used to determine the three components of strain energy release rates (SERR) with respect to sliding (Mode I), opening (Mode II) and cross sliding (Mode III) modes of failure. These values are found to be different along two delamination fronts which show the dissimilar nature of propagation of delamination.
Sumeet Kumar Pati, A. K. Pradhan, M. K. Pandit

### Dynamic Characteristics of Twisted Composite Panels—A Finite Element Study

Abstract
This paper presents the details of the dynamic analysis of Laminated Composite Twisted Panels. The effects of different parameters such as the angle of twist, lamination angle, aspect ratio (plate width to thickness ratio) on the natural frequencies and mode shapes are considered. The FEM analysis was carried out using the front-end commercial software ANSYS (Ver: 10.0) (ANSYS(R) Help System, 2006 [1]) with its modal analysis capabilities. The Block Lanczos algorithm with subspace iteration technique was used in the extraction of natural frequencies and corresponding mode shapes. The first few natural frequencies and corresponding mode shapes were extracted for different combinations of angles of twist, lamination angles, and aspect ratios. The frequencies extracted are in good agreement with reported analytical solutions (Qatu and Leissa in Int J Mech Sci 33:927–940, 1991 [2]).
K. S. Shivakumar Aradhya, S. Moorthi

### Analytical Solution for Two-Dimensional Axisymmetric Thermoelastic Behavior in the Multilayer Composite Hollow Sphere

Abstract
This article deals with an analytic solution of temperature distribution, displacement and stress distribution function for two-dimensional multilayered hollow spheres. The solution is obtained by using the separation of the variable method. Homogenous boundary conditions of the first or second kind can be applied on surfaces of θ = constant. However, homogeneous boundary conditions of the third kind (convection) are used in the r-direction. Under prescribed conditions, the temperature distribution, displacement and thermal stresses in the sphere are to be analyzed under the steady-state temperature field. The layers of the multilayer sphere are homogeneous and isotropic.
N. J. Wange, S. P. Pawar, M. N. Gaikwad

### Investigation of Torsional Stability and Camber Test on a Meter Gauge Flat Wagon

Abstract
This paper presents the experimental study of the torsion test and camber test of a flat freight wagon. The freight wagon considered as open-type 40 ft. gauge flat wagon. The flat freight wagon comprises flat body structure and two bogies, where the flat surface used to transport containers, goods, wood logs, etc. HBM load cell of 50 T capacity is used to measure the force and deflection for experimental determination of the torsional and camber values. The test methodology and setup are established freight wagon testing. It is seen that the camber values are within the safe zone as per designed payload. The average torsional stiffness is 3.45 × 1010 KN mm2/rad are seen considering the worst-case elevation with one side 20 mm and other three side elevations are zero.
Apurba Das, Gopal Agarwal

### Nonlinear Dynamic Buckling and Failure Study of Laminated Composite Plates Subjected to Axial Impulse Loads

Abstract
In this paper, the nonlinear dynamic buckling of laminated composite plate is studied along with the failure of the plates. The balanced and symmetric cross-ply laminated composite plates are subjected to in-plane impulse compressive loads. The dynamic buckling load is calculated using Volmir’s criterion. The nonlinear dynamic equations are solved using the finite element method. Imperfections are incorporated in the plate in order to simulate the actual behavior. The effect of imperfection, loading function, and duration of loading is studied. The first ply failure load for the plate is calculated to check the precedence of dynamic buckling and first ply failure. It is observed that the first ply failure for balanced and symmetric cross-ply laminated composite plates occurs after the plate has buckled due to dynamic impulse loads.
Vasanth Keshav, S. N. Patel, Rajesh Kumar

Abstract
Functionally Graded Materials (FGMs) are the variation of composition and structure over a volume which results in improvement of mechanical properties. Damage in adhesive-bonded FGM composite joints may generate in various forms like cohesive failure, adhesion failure, etc. This article deals with the loss of structural integrity of the Lap Shear Joint (LSJ) made with curved FGM adherends of $$Al_{2} O_{3}$$ and Nickel by quantifying adhesion failure propagation. This is performed by evaluation of the interfacial stresses and the three modes of Strain Energy Release Rate (SERR). The rate of propagation of the adhesion failure in the LSJ made with FGM panels subjected to transverse loading is evaluated by employing a three-dimensional nonlinear finite element analysis. The effect of overlap length on the LSJ made with curved adherends on the interfacial stresses and the three modes of SERR is computed. The use of FGM as adherend materials is found to be effective in reducing the peak values of interfacial stresses and the three modes of SERR.
Pritam Kumar Kundu, Arun Kumar Pradhan, Mihir Kumar Pandit

### A Gradient-Damage Model for Cyclic Behavior of Concrete

Abstract
The present paper elaborates a continuum formulation using a single loading surface that relates a unified equivalent strain with a history deformation parameter to characterize both the softening and hardening behaviors of the material. The history parameter governs the growth of damage. Two additional history parameters capture the crack-opening/closure effectively. The model further incorporates an implicit-gradient regularization to avoid numerical difficulties such as localization of deformation into a vanishing size and ill-posedness of the boundary value problem. Numerical results exhibit good agreement with experimental data under several tests. Finally, the paper demonstrates the localization of deformation due to a gradient-enhanced variable.
A. H. Monnamitheen Abdul Gafoor, D. Dinkler

### Reductions of Bending Stresses and Wear in an Aerodynamic Involute Spur Gear Profile

Abstract
Gears are widely used in automobile and aerospace sectors. The most important duty of an engineer to design and manufacture of the transmission system of it. Gears normally fail stress concentrations and fatigue resulting in wear and tear of transmission elements like gears, pulleys, etc. This paper clears that by changing properties of material used for manufacturing of gears, by optimizing the gear, the stresses induced in the gears can be decreased modeling and analysis is carried out by CATIA and ANSYS workbench, respectively. It is seen that reduction in bending stresses is found in the above cases, are compared and correlated with each other.
Y. P. Ravitej, O. Abhilash, Naveen kumar

### Probability of Failure of a Beam Subjected to Randomly Moving Loads

Abstract
In the present paper, an analytical approach to study the deflection and dynamic stresses in a simply supported beam when traversed by randomly moving loads at a uniform speed whose inter-arrival time follows Poisson distribution has been developed. The magnitude of payloads has been assumed to follow a uniform distribution. Initially, the expression for deflection and dynamic stresses in a simply supported beam traversed by a constant force is developed by application of Fourier sine integral transformation followed by the method of Laplace–Carson integral transformation and further followed by Inverse Fourier transformation. The analytical expressions are found to obtain the deflection due to a set of loads which follow the Poisson distribution. The inter-arrival time between the payload is an important factor for the probability of failure as revealed from the analysis. The probability of failure increases when the interval of arrival time is decreased.
Alben Jose Kezhiyur, S. Talukdar, Anjaly J. Pillai

### Numerical Simulation and Wind Tunnel Experiment on Pressure and Velocity Distribution Around the NACA0012 Airfoil for Optimising an Aerodynamic Model

Abstract
Airfoil design is a significant facet of aerodynamics. In this paper, optimise aerodynamic model for the NACA0012 airfoil shape has been studied based the wind tunnel experiment and numerical simulation using ANSYS. The velocity and pressure distribution around the NACA0012 airfoil has found by tests results which are compared with numerical simulation. Based on this experiment result, optimisations shape of the airfoil has been investigated.
Motahar Reza, Anindita M. Bhattacharyya, Deepak K. Sadangi, Aman Kumar
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