Multi-objective structural optimization of ground stuctures considering dynamic and stability behaviors and automatic member grouping

Resumo

This paper aims to formulate the many-objective structural optimization problem to find the optimal design of ground-structure systems. The objective functions are the weight of the topologically optimized ground structure (to be minimized), the compliance (to be minimized), the different number of discrete cross-sectional areas (to be minimized), the first natural frequency of vibration (to be maximized), and the first load factor concerning the global stability of the structure (to be maximized).
It is worthwhile to emphasize that minimizing the number of distinct cross-sectional areas of the optimized ground structure makes finding the best member grouping possible. As a result, the smaller the number of different groups, the greater the weight of the structure, and the greater the number of groups, the smaller the structures weight. Also, minimizing compliance, maximizing the first natural frequency of vibration, and maximizing the critical load factor directly impact the structures mass. The constraints are defined as the maximum allowable stress in the bars, and when the natural frequency of vibration or the critical load factor is not set as one of the objectives, they become part of the set of constraints. DE-based multi-objective algorithms are adopted to solve the proposed optimization problem. Benchmark problems are analyzed, and Pareto fronts are obtained, showing the non-dominated solutions. Multi-criteria decision-making (MCDM) is adopted to extract solutions from the Pareto front according to the preferences of the decision-maker (DM) used in the ground-structure system. The complete data for each extracted non-dominated solution, including its optimized topology, is provided.