Topology Optimization of Elastoplastic Behavior Conditions by Selectively Suppressing Plastic Work

Eun-Ho Lee,Tae-Hyun Kim

doi:10.3390/math8112062

Abstract

This work conducted topology optimization with an implicit analysis of elastoplastic constitutive equation in order to design supporting structures for unexpected heavy loading conditions. In this topology optimization model, plastic work was extracted from strain energy and selectively employed in the objective function according to deformation mode. While strain energy was minimized in elastic deformation areas, in elastoplastic deformation areas, the plastic work was minimized for the purpose of suppressing plastic deformation. This method can focus on suppressing plastic strain in the plastic deformation zone with maintaining elastic stiffness in the elastic deformation zone. These formulations were implemented into MATLAB and applied to three optimization problems. The elastoplastic optimization results were compared to pure elastic design results. The comparison showed that structures designed with accounting for plastic deformation had a reinforced area where plastic deformation occurs. Finally, a finite element analysis was conducted to compare the mechanical performances of structures with respect to the design method.

Highlights

Topology optimization is a scheme used to obtain a design with an optimized shape for a specific purpose, and is widely used in engineering problems [1,2,3,4,5,6,7,8,9,10,11]
(1) The element optimization algorithm was combined with the nonlinear weak form of the finite element
In elastic deformation areas, (2) In the objective function, plastic work was separated from stain energy and the separated plastic strain energy was minimized, as in general cases

Summary

Introduction

Topology optimization is a scheme used to obtain a design with an optimized shape for a specific purpose, and is widely used in engineering problems [1,2,3,4,5,6,7,8,9,10,11]. Under elastic deformation, calculating the strain energy is simple since stress and strain have a simple linear relation. When a part of a material undergoes elastoplastic deformation, its material properties change according to the level of plastic strain, resulting in a nonlinear relation between stress and strain. This nonlinear relation leads to difficulties when attempting to determine stress and the material property matrix. The majority of topology optimization applications are based on the assumption of elastic deformation [12,13,14,15,16,17,18]. A few researchers have tried to consider plastic deformation in topology optimization. Blachowski et al [22] recently proposed a stress intensity-driven elastoplastic topology optimization method to find a minimum weight structure that is able to carry a given load

Methods

Results

Discussion

Conclusion