Multi-objective shape-section optimization of free-form latticed shells using the RBF-NSGA-II algorithm

Abstract

In this study, a novel RBF-NSGA-II optimization framework based on the response surface methodology (RSM) and the constrained NSGA-II algorithm is proposed to simultaneously improve the static, nonlinear stability and economic performance of free-form latticed shells. The bending stiffness of joints is innovatively considered one of the design variables for shape-member section coupled optimization. The augmented radius basis functions (RBFs) are adopted to develop the metamodels of both the objectives and constraints. The improved minimum distance selection method (TMDSM) is used to select the optimal solution from the Pareto optimal solution set. Moreover, three alternative solutions are presented as supplements to meet various engineering requirements. The proposed RBF-NSGA-II algorithm is validated to have high accuracy for multi-objective optimization problems with high nonlinearity. Compared with those of the initial structures, the strain energy and steel consumption of the optimal structure decreased by 82.23 % and 17.97 %, respectively, while the buckling load considering both the geometric nonlinearity and material nonlinearity increased by 1.2 times. The involvement of the joint stiffness is demonstrated to have a great influence on the multi-objective optimization results. It is necessary to consider the joint stiffness as one of the design variables during shape-member section coupled optimization.