Automated elasto-plastic design of truss structures based on residual plastic deformations using a geometrical nonlinear optimization framework

Abstract

This paper introduces a novel automated framework for the optimal design of steel truss structures, incorporating plastic deformations through the complementary strain energy of residual forces while minimizing weight. The presented methodology is equally applicable to purely elastic scenarios, ensuring zero plastic deformations and further reducing material usage. To achieve this, a nonlinear finite element (FE) program was developed, capable of accounting for large deformations and initial geometric imperfections. A genetic algorithm (GA) was integrated to iteratively optimize the objective function, enabling a fully automated design process. The efficiency and versatility of the framework were validated through four numerical examples. The first two comprise benchmark cases: a 9-bar planar truss and a 25-bar space truss. The remaining two examples were selected to be more representative of practical applications, involving a prestressed arched truss and a double-layer space truss. Analyses of various configurations were performed to demonstrate the robustness of the approach. Using the proposed methodology, significant improvements in plastic performance and material efficiency were achieved, underscoring its potential, adaptability, and effectiveness in advancing truss design techniques.