A simple and versatile topology optimization formulation for flexure synthesis

TL;DR

This paper introduces a simple, versatile topology optimization method for designing flexures based on strain energy, offering ease of use, computational efficiency, and broad applicability for precise manipulation devices.

Contribution

A novel topology optimization formulation for flexure synthesis based on strain energy measures, with simplicity, efficiency, and extendability compared to existing methods.

Findings

Demonstrates versatility across different flexure types

Shows extendability with additional design constraints

Provides source code for practical application

Abstract

High-tech equipment critically relies on flexures for precise manipulation and measurement. Through elastic deformation, flexures offer extreme position repeatability within a limited range of motion in their degrees of freedom, while constraining motion in the degrees of constraint. Topology optimization proves a prospective tool for the design of short-stroke flexures, providing maximum design freedom and allowing for application-specific requirements. State-of-the-art topology optimization formulations for flexure synthesis are subject to challenges like ease of use, versatility, implementation complexity, and computational cost, leaving a generally accepted formulation absent. This study proposes a novel topology optimization formulation for the synthesis of short-stroke flexures uniquely based on strain energy measures under prescribed displacement scenarios. The resulting self-adjoint optimization problem resembles great similarity to classic compliance minimization and inherits similar implementation simplicity, computational efficiency, and convergence properties. Numerical examples demonstrate the versatility in flexure types and the extendability of additional design requirements. The provided source code encourages the formulation to be explored and applied in academia and industry.