Multiobjective optimization approach to shape and topology optimization of plane trusses with various aspect ratios

TL;DR

This paper presents a multiobjective optimization method for designing plane trusses with various aspect ratios, optimizing shape and topology simultaneously to minimize compliance and structural volume in a single process.

Contribution

It introduces a novel multiobjective approach that efficiently generates Pareto optimal solutions for different aspect ratios in one optimization run.

Findings

Accurate optimal solutions obtained compared to weighted sum method.

Single optimization process effectively handles multiple aspect ratios.

Force density method improves handling of coalescent or melting nodes.

Abstract

A multiobjective optimization method is proposed for obtaining the optimal plane trusses simultaneously for various aspect ratios of the initial ground structure as a set of Pareto optimal solutions generated through a single optimization process. The shape and topology are optimized simultaneously to minimize the compliance under constraint on the total structural volume. The strain energy of each member is divided into components of two coordinate directions on the plane. The force density method is used for alleviating difficulties due to existence of coalescent or melting nodes. It is shown in the numerical example that sufficiently accurate optimal solutions are obtained by comparison with those obtained by the linear weighted sum approach that requires solving a single-objective optimization problem many times.