Multiresolution Topology Optimization of Large-Deformation Path-Generation Compliant Mechanisms with Stress Constraints

Joseph Reinisch,Johannes Achleitner,Erich Wehrle

doi:10.3390/app11062479

Abstract

Topology optimization is a powerful numerical tool in the synthesis of lightweight structures and compliant mechanisms. Compliant mechanisms present challenges for topology optimization, as they typically exhibit large displacements and rotations. Path-generation mechanisms are a class of mechanisms that are designed to follow an exact path. The characteristics of compliant mechanisms therefore exclude the validity of linear finite-element analysis to ensure the proper modeling of deformation and stresses. As stresses can exceed the limit when neglected, stress constraints are needed in the synthesis of compliant mechanisms. Both nonlinear finite-element analysis as well as the consideration of stress constraints significantly increase computational cost of topology optimization. Multiresolution topology optimization, which employs different levels of discretization for the finite-element analysis and the representation of the material distribution, allows an important reduction of computational effort. A multiresolution topology optimization methodology is proposed integrating stress constraints based on nonlinear finite-element analysis for path-generation mechanisms. Two objective formulations are used to motivate and validate this methodology: maximum-displacement mechanisms and path-generation mechanisms. The formulation of the stress constraints and their sensitivities within nonlinear finite-element analysis and multiresolution topology optimization are explained. We introduce two academic benchmark examples to demonstrate the results for each of the objective formulations. To show the practical, large-scale application of this method, results for the compliant mechanism structure of a droop-nose morphing wing concept are shown.

Highlights

Engineers are constantly pursuing the design of lighter, faster and more efficient structures and mechanisms
We propose a method for the synthesis of both maximum-displacement and path-generating compliant mechanisms with multilevel stress-constrained topology optimization based on geometrically nonlinear finite-element analysis
This review highlights the lack of literature in the field of topology optimization for compliant mechanisms with large deformation and stress constraints, which we address here

Summary

Introduction

Engineers are constantly pursuing the design of lighter, faster and more efficient structures and mechanisms. We use structural design optimization—and topology optimization—to design optimal lightweight compliant mechanisms. These flexible structures have the same design goals as more traditional mechanisms, though without joints. The motion of the mechanism is achieved by elastic deformation. This characteristic presents a number of advantages including no frictional loss, scalability and precision due to lack of backlash [1]. The optimal designs achieved via topology optimization have traditionally undergone toilsome derivation of geometries to ensure manufacturability. This can be (partially) avoided with additive manufacturing techniques in which the optimal results are directly fabricated

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Results

Conclusion