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In this paper, optimal design of arch dams is performed under frequency limitations. Colliding Bodies Optimization (CBO), a recently developed meta-heuristic optimization method, which has been successfully applied to several structural problems, is revised and utilized for finding the best feasible shape of arch dams. The formulation of CBO is derived from one-dimensional collisions between bodies, where each agent solution is considered as the massed object or body. The design procedure aims to obtain minimum weight of arch dams subjected to natural frequencies, stability and geometrical limitations. Two arch dam examples from the literature are examined to verify the suitability of the design procedure and to demonstrate the effectiveness and robustness of the CBO in creating optimal design for arch dams. The results of the examples show that CBO is a powerful method for optimal design of arch dams.

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The Isogeometric Analysis (IA) is utilized for structural topology optimization  considering minimization of weight and local stress constraints. For this purpose, material density of the structure  is  assumed  as  a  continuous  function  throughout  the  design  domain  and approximated using the Non-Uniform Rational B-Spline (NURBS) basis functions. Control points of the density surface are considered as design variables of the optimization problem that can change the topology during the optimization process. For initial design, weight and stresses of the structure are obtained based on full material density over the design domain. The  Method  of  Moving  Asymptotes  (MMA)  is  employed  for  optimization  algorithm. Derivatives of the objective function and constraints with respect to the design variables are determined  through  a  direct  sensitivity  analysis.  In  order  to  avoid  singularity  a  relaxation technique  is  used  for  calculating  stress  constraints.  A  few  examples  are  presented  to demonstrate the performance of the method. It is shown that using the IA method and an appropriate stress relaxation technique can lead to reasonable optimum layouts.

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The first step in the design of plate girder is to estimate the self-weight of it. Although empirical formulae for the same are available, the level of their accuracy (underestimate or overestimate) with respect to actual self-weight is not known. In this paper, optimized sections are obtained for different spans subjected to different live load carrying capacities and self-weights are estimated. EXCEL solver, which adopts Reduced Gradient Method (RGM) was applied for optimization. The objective function was chosen as Cross-sectional area with twelve constraints based on LRFD (IS 800: 2007) design specification for safety and serviceability. Simply supported (laterally restrained) plastic symmetric cross section without stiffeners is adopted for study. A mathematical model was developed based on best-fit curves between self-weight, span and live load carrying capacity and their trend line equations are obtained. The study revealed that, the ratio of self-weight to load carrying capacity was parabolic for a given span. The results from this equation are compared with the conventional formula and the standard deviation of the proposed model with respect to actual self-weight is in the range of -0.03 to 2.29 while that from the conventional model is in the range of -0.04 to 9.18.

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Due to the favorable performance of structural topology optimization to create a proper understanding in the early stages of design, this issue is taken into consideration from the standpoint of research or industrial application in recent decades. Over the last three decades, several methods have been proposed for topology optimization. One of the methods that has been effectively used in structural topology optimization is level set method. Since in the level set method, the boundary of design domain is displayed implicitly, this method can easily modify the shape and topology of structure. Topological design with multiple constraints is of great importance in practical engineering design problems. Most recent topology optimization methods have used only the volume constraint; so in this paper, in addition to current volume constraint, the level set method combines with other constraints such as displacement and frequency. To demonstrate the effectiveness of the proposed level set approach, several examples are presented.

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Jellyfish Search (JS) is a recently developed population-based metaheuristic inspired by the food-finding behavior of jellyfish in the ocean. The purpose of this paper is to propose a quantum-based Jellyfish Search algorithm, named Quantum JS (QJS), for solving structural optimization problems. Compared to the classical JS, three main improvements are made in the proposed QJS: (1) a quantum-based update rule is adopted to encourage the diversification in the search space, (2) a new boundary handling mechanism is used to avoid getting trapped in local optima, and (3) modifications of the time control mechanism are added to strike a better balance between global and local searches. The proposed QJS is applied to solve frequency-constrained large-scale cyclic symmetric dome optimization problems. To the best of our knowledge, this is the first time that JS is applied in frequency-constrained optimization problems. An efficient eigensolution method for free vibration analysis of rotationally repetitive structures is employed to perform structural analyses required in the optimization process. The efficient eigensolution method leads to a considerable saving in computational time as compared to the existing classical eigensolution method. Numerical results confirm that the proposed QJS considerably outperforms the classical JS and has superior or comparable performance to other state-of-the-art optimization algorithms. Moreover, it is shown that the present eigensolution method significantly reduces the required computational time of the optimization process compared to the classical eigensolution method.

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Natural frequencies of a structure give useful information about the structural response to dynamic loading. These frequencies should be far enough from the critical frequency range of dynamic excitations like earthquakes in order to prevent the resonance phenomenon sufficiently. Although there are many investigations on optimization of truss structures subjected to frequency constraints, just a few studies have been considered for optimal design of frame structures under these constraints. In this paper, a recently proposed metaheuristic algorithm called Adaptive Charged System Search (ACSS) is applied to optimal design of steel frame structures considering the frequency constraints. Benchmark design examples are solved with the ACSS, and optimization results are illustrated in terms of some statistical indices, convergence history and solution quality. The design examples include three planar steel frames with small to large number of design variables. Results show that the ACSS outperforms the charged system search algorithm in this sizing optimization problem.

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The arithmetic optimization algorithm (AOA) is a recently developed metaheuristic optimization algorithm that simulates the distribution characteristics of the four basic arithmetic operations (i.e., addition, subtraction, multiplication, and division) and has been successfully applied to solve some optimization problems. However, the AOA suffers from poor exploration and prematurely converges to non-optimal solutions, especially when dealing with multi-dimensional optimization problems. More recently, in order to overcome the shortcomings of the original AOA, an improved version of AOA, named IAOA, has been proposed and successfully applied to discrete structural optimization problems. Compared to the original AOA, two major improvements have been made in IAOA: (1) The original formulation of the AOA is modified to enhance the exploration and exploitation capabilities; (2) The IAOA requires fewer algorithm-specific parameters compared with the original AOA, which makes it easy to be implemented. In this paper, IAOA is applied to the optimal design of large-scale dome-like truss structures with multiple frequency constraints. To the best of our knowledge, this is the first time that IAOA is applied to structural optimization problems with frequency constraints. Three benchmark dome-shaped truss optimization problems with frequency constraints are investigated to demonstrate the efficiency and robustness of the IAOA. Experimental results indicate that IAOA significantly outperforms the original AOA and achieves results comparable or superior to other state-of-the-art algorithms.

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In recent years many researchers prefer to use metaheuristic algorithms to reach the optimum design of structures. In this study, an Enhanced Vibrating Particle System (EVPS) is applied to get the minimum weight of large-scale dome trusses under frequency constraints. Vibration frequencies are important parameters, which can be used to control the responses of a structure that is subjected to dynamic excitation. The truss structures were analyzed by finite element method and optimization processes were implemented by the computer program coded in MATLAB. The effectiveness and efficiency of the Enhanced Vibrating Particle System (EVPS) is investigated in three large-scale dome trusses 600-, 1180-, and 1410-bar to obtain the weight optimization with frequency constraints.

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Metaheuristics are considered the first choice in addressing structural optimization problems. One of the complicated structural optimization problems is the highly nonlinear dynamic truss shape and size optimization with multiple natural frequency constraints. On the other hand, natural frequency constraints are useful to control the responses of a dynamically exciting structure. In this regard, this study uses for the first time the water evaporation optimization (WEO) algorithm to address this problem. Four benchmark trusses are considered for experimental investigation of the WEO. Obtained results indicate the comparative performance of WEO to the best-known algorithms in this problem, high performance in comparison to those of different optimization techniques, and high performance in comparison to all algorithms in terms of robustness. The simulation results clearly show a good balance between the global and local exploration abilities of WEO and its potential robust efficiency for other complicated constrained engineering optimization problems.

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In this paper, the improved shuffled-based Jaya algorithm (IS-Jaya) is applied to the size optimization of the braced dome with the frequency constraints. IS-Jaya is the enhanced version of the Jaya algorithm that the shuffling process and escaping from local optima are added for it. These two modifications increase the population diversity and ability the escape from the local optima of the Jaya. The robustness and performance of the IS-Jaya are evaluated by the three design examples. The results show that the IS-Jaya algorithm outperforms other state-of-the-art optimization techniques considered in the literature.