Stress-constrained level set topology optimization for compliant mechanisms

Abstract

This work presents a level set-based topology optimization procedure to design compliant mechanisms subject to local stress constraints. A classical technical difficulty related to the design of compliant mechanisms is the emergence of non-realistic flexible joints (hinges) subject to unfeasible strain and stresses. A natural way to overcome this occurrence is the inclusion of stress constraints within the formulation. This approach brings, on the other hand, particular difficulties associated with the local nature of stress constraints. To deal with this issue, stress constraints are included in the present work using an augmented Lagrangian mathematical programming technique. A level set approach defines the design of the mechanical part and a reaction–diffusion equation is used to update the level set function towards the optimized state. A natural extension of the velocity field provided for the reaction–diffusion equation allows for hole nucleation during the design updating. The joining of an augmented Lagrangian approach and level set implicit boundaries to handle local stress constraints in order to obtain hinge-free compliant mechanisms is the novelty of this paper. Several two-dimensional numerical examples show the efficacy of the proposed procedure. In particular, an example analyzes the influence of the weak material in the design of compliant mechanisms. Level set designs enable that final solutions are validated in commercial finite element codes without any post-processing procedure.