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The present study attempts to apply an efficient yet simple optimization (SOPT) algorithm to optimum design of truss structures under stress and displacement constraints. The computational efficiency of the technique is improved through avoiding unnecessary analyses during the course of optimization using the so-called upper bound strategy (UBS). The efficiency of the UBS integrated SOPT algorithm is evaluated through benchmark sizing optimization problems of truss structures and the numerical results are reported. A comparison of the numerical results attained using the SOPT algorithm with those of modern metaheuristic techniques demonstrates that the employed algorithm is capable of locating promising designs with considerably less computational effort.

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This paper attempts to improve the computational efficiency of the well known particle swarm optimization (PSO) algorithm for tackling discrete sizing optimization problems of steel frame structures. It is generally known that, in structural design optimization applications, PSO entails enormously time-consuming structural analyses to locate an optimum solution. Hence, in the present study it is attempted to lessen the computational effort of the algorithm, using the so called upper bound strategy (UBS), which is a recently proposed strategy for reducing the total number of structural analyses involved in the course of design optimization. In the UBS, the key issue is to identify those candidate solutions which have no chance to improve the search during the optimum design process. After identifying those non-improving solutions, they are directly excluded from the structural analysis stage, diminishing the total computational cost. The performance of the UBS integrated PSO algorithm (UPSO) is evaluated in discrete sizing optimization of a real scale steel frame to AISC-LRFD specifications. The numerical results demonstrate that the UPSO outperforms the original PSO algorithm in terms of the computational efficiency.

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Computational cost of metaheuristic based optimum design algorithms grows excessively with structure size. This results in computational inefficiency of modern metaheuristic algorithms in tackling optimum design problems of large scale structural systems. This paper attempts to provide a computationally efficient optimization tool for optimum design of large scale steel frame structures to AISC-LRFD specifications. To this end an upper bound strategy (UBS), which is a recently proposed strategy for reducing the total number of structural analyses in metaheuristic optimization algorithms, is used in conjunction with an exponential variant of the well-known big bang-big crunch optimization algorithm. The performance of the UBS integrated algorithm is investigated in the optimum design of two large-scale steel frame structures with 3860 and 11540 structural members. The obtained numerical results clearly reveal the usefulness of the employed technique in practical optimum design of large-scale structural systems even using regular computers.

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Calculation of lateral earth pressure on retaining walls is one of the main issues in geotechnics. The upper and lower bound theorems of plasticity are used to analyze the stability of geotechnical structures include bearing capacity of foundations, lateral earth pressure on retaining walls and factor of safety of slopes. In this paper formulation of finite element limit analysis is introduced to determine plastic limit load in the perfect plastic materials. Elements with linear strain rates, which are used in the formulation, cause to eliminate the necessity of velocity discontinuities between the elements. Using non-linear programming based on second order cone programming (SOCP), which has good conformity with cone yield functions such as Mohr-Coulomb and Drucker-Prager, is another important advantage that remove the problem of using ordinary linear programming algorithms for yield functions such as divergent in the apexes. Finally, the optimization problem will be solved by mathematical method. The proposed method is used for calculating active earth pressure on retaining walls in cohesive-frictional soils. According to results of analysis, active earth force on retaining wall is decreased by increasing soil cohesion, wall inclination friction angle between backfill and wall and friction angle of soil wherein the force is increased by increasing surcharge on the backfill and the backfill slope. Mathematical method is used for obtaining accurate results in this research, however, heuristic methods are used when approximate solutions are sufficient.