Optimization Methods for Structural Engineering

In this chapter, a review of the optimum design of passive and active tuned mass dampers for structures is presented. Metaheuristics have been often used in the optimum design of tuned mass dampers. As an example, an improved harmony search algorithm is presented for the optimum design of active tuned mass dampers (ATMDs) using proportional integral derivative type controllers. The ATMD was also compared via passive tuned mass damper (TMD) and the optimum design results are presented for a 10-story structure with multiple cases of the time delay of the controller and stroke capacity of ATMD. ATMD is better than TMD in the reduction of displacements up to 32.01%.

Structural analysis is important as it provides the basis for structural design and assesses whether a particular structure design will be able to withstand external and internal pressures and forces. While solving the structural problems, we find that such problems are quite complex in solving and the number of iterations taken to find the optimal solution is quite high. Various techniques were used to solve such types of problems such as the artificial bee colony algorithm (ABC), fuzzy-controlled genetic algorithm (FCGA), approximation method algorithm, harmony search algorithm (HS), constrained mean–variance mapping algorithm, buckling restrained sizing, and shaping algorithm. The following paper uses the CI-SAPF approach to find the size optimization of truss structure using buckling and natural frequency constraints along with discrete variables. In this paper, two separate problems of 18-bar truss structure are considered. The solutions obtained from CI-SAPF algorithm are compared with other contemporary techniques.

The metaheuristic optimization methods are non-gradient-based search techniques that wildly utilized for solving various optimization cases in the different disciplines. Drosophila food-search algorithm (DFO) is a metaheuristic search approach that models the food-search mechanism of the Drosophila Melanogaster incest in the nature. It applies a three-phase search pattern to explore the desired problem’s search domain. To provide a proper level of population diversity during the optimization process, it applied the quadratic approximation search approach. In this chapter, an improved version of the DFO is utilized for solving structural optimization problems. The attained outcomes are reported and compared with five other well-stablished methods as differential evolution (DE), firefly algorithm (FA), teaching and learning-based optimization (TLBO), Drosophila food-search optimization (DFO), and integrated particle swarm optimization (iPSO). The acquired results demonstrate that the proposed IDFO, specially compared with the standard DFO, provides an appropriate dynamic balance between exploration and exploitation search behaviors during the optimization process. Also, the proposed method in comparison with all other selected methods has the most stable behavior with the lowest standard deviation value.

An especially significant class of structurally constrained optimization problems is truss design. This study presents a constrained version of two variations of the Cohort Intelligence (CI) algorithm. In this work, discrete variable truss structures with six bars and two cases with ten bars are studied using follow-best and follow-better approaches, as well as the self-adaptive penalty function (SAPF). These problems are associated with two linear constraints: tensile/compressive stress and deflection. Algorithm efficiency is evaluated by counting the function evaluations, computing CPU time, and determining the total weight of the truss structure. Compared to follow-better and other contemporary optimizers from literature, follow-best performs significantly better.

Several nature-based optimization methods have been developed by the researchers to solve the real-world problems. There are certain characteristics of the inherent approaches associated with the algorithms which could be combined with other algorithm to enhance the exploration and exploitation quality of the algorithm. Cohort Intelligence (CI) is one of the socio-inspired optimization algorithms which is inspired from self-supervised learning of the candidates in a cohort. To further increase the performance of CI, it is hybridized with fuzzy logic (FL). FL is an approach that allows multiple possible truth values to be processed through variables. FL was used to solve problems with an open, imprecise data, and heuristics that make it possible to obtain accurate results. In this current work, a new combination of CI and FL named as CIFL is introduced for solving truss structure optimization problem. The validity of the algorithm is verified using two cases of three-bar truss design optimization problem. CIFL is applied to both discrete and continuous variable-constrained problems. The self-adaptive penalty function (SAPF) approach is used to handle the constraints. The results obtained from CIFL are compared with other nature-inspired optimization techniques and discussed in details.

Buckling-restrained braces (BRBs) are one of the popular seismic-resistant structural systems. The cross-sectional area and length of the BRB is one of the most important characteristics of these braces that directly affect their cost. Since columns, beams, and connections are designed for the maximum force delivered by the brace, the decrease in cross-sectional area of the BRB causes a decrease in dimensions of the columns and beams. On the other hand, drift uniformity over the height of the structure is accounted as a structural health index and would lead in efficiency of BRB system in a seismic event. The aim of this study is then to optimize three objectives including weight of the BRB, weight of the structure, and uniformity of the drift profile over the height of structure by changing the cross-sectional area and the length of the BRB at the height of the structure using genetic algorithms and other multi-objective optimization algorithms. Optimization is based on the results of nonlinear time history analysis of 2D frames. Seven earthquake records are selected to conduct nonlinear time history analysis using OpenSees software. To this end, the desired functions and constraints were defined in the genetic algorithms, i.e., NSGA_II, MOPSO, MOEA_D, PESA_II, SPEA_II, and the initial created population was entered as the initial cross-sectional area and length of the braces in the OpenSees software. The optimization results showed that for all three objective functions, the weight of the structure, the weight of the BRB brace, and the uniformity of drift in the height of the structure can be optimized largely using a nonlinear time history analysis.

This chapter presents the theoretical and the numerical study of shape and topology optimization for linear elasticity, plasticity and fracture using the level-set method. The governing equation of linear elasticity is theoretically shape-differentiable, while that of plasticity and damage is not shape-differentiable. To overcome the non-differentiability issue for the latter, we construct an approximation by penalization and regularization. For the three physics, the shape sensitivity analysis is performed using Céa’s technique. The shape optimization is implemented numerically using a level-set method with body-fitted remeshing, which captures the boundary of the shapes while allowing for topology changes. Numerical results are presented in 2D and 3D.

Quarter car model can be used to approximate a response of the suspension systems to obtain a behavioral relationship between the suspension and the body. The major aim of the quarter is to obtain a stable working control system for achieving three major control states. The three states include the passenger’s comfort design, the road handling design, and a balanced design. The objective is to obtain the three control systems by using the H-infinity synthesis and designing a controller based on the defined states and control inputs of the car. The designed controller can therefore be optimized for the account of uncertainty. The use of µ-synthesis for the optimization of the designed controller and the balanced design is considered for the optimization. For the analysis of the control system, initially the system is given a disturbance of 7 cm. For the optimization, the input was increased and a bump of 10 cm was considered for achieving a greater disturbance and gains in the measurements. The bode plots recorded for the calculation would verify the performance of the control system which would take the quarter car model as a state space and the controller for the feedback module for the control of the suspension system.