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ABSTRACT In topology optimization of compliant mechanisms, the specific placement of boundary conditions strongly affects the resulting material distribution and performance of the design. At the same time, the most effective locations of the loads and supports are often difficult to find manually. This substantially limits topology optimization's effectiveness for many mechanism design problems. We remove this limitation by developing a method which automatically determines optimal positioning of a prescribed input displacement and a set of supports simultaneously with an optimal material layout. Using nonlinear elastic physics, we synthesize a variety of compliant mechanisms with large output displacements, snap‐through responses, and prescribed output paths, producing designs with significantly improved performance in every case tested. Compared to optimal designs generated using manually designed boundary conditions used in previous studies, the mechanisms presented in this paper see performance increases ranging from 47% to 380%. The results show that nonlinear mechanism responses may be particularly sensitive to boundary condition locations and that effective placements can be difficult to find without an automated method.
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This content will become publicly available on August 17, 2026
Level-Set Nonlinear Topology Optimization for Large-Deformation Compliant Mechanisms with Hyperelastic Materials
The level set method has been widely applied in topology optimization of mechanical structures, primarily for linear materials, but its application to nonlinear hyperelastic materials, particularly for compliant mechanisms, remains largely unexplored. This paper addresses this gap by developing a comprehensive level set-based topology optimization framework specifically for designing compliant mechanisms using neo-Hookean hyperelastic materials. A key advantage of hyperelastic materials is their ability to undergo large, reversible deformations, making them well-suited for soft robotics and biomedical applications. However, existing nonlinear topology optimization studies using the level set method mainly focus on stiffness optimization and often rely on linear results as preliminary approximations. Our framework rigorously derives the shape sensitivity analysis using the adjoint method, including crucial higher-order displacement gradient terms often neglected in simplified approaches. By retaining these terms, we achieve more accurate boundary evolution during optimization, leading to improved convergence behavior and more effective structural designs. The proposed approach is first validated with a mean compliance problem as a benchmark, demonstrating its ability to generate optimized structural configurations while addressing the nonlinear behavior of hyperelastic materials. Subsequently, we extend the method to design a displacement inverter compliant mechanism that fully exploits the advantages of hyperelastic materials in achieving controlled large deformations. The resulting designs feature smooth boundaries and clear structural features that effectively leverage the material's nonlinear properties. This work provides a robust foundation for designing advanced compliant mechanisms with large deformation capabilities, extending the reach of topology optimization into new application domains where traditional linear approaches are insufficient. The developed methodology is expected to provide a timely solution to computational design for soft robotics, flexible mechanisms, and other emerging technologies that benefit from hyperelastic material properties.
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- Award ID(s):
- 2213852
- PAR ID:
- 10634612
- Publisher / Repository:
- American Society of Mechanical Engineers (ASME)
- Date Published:
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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