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This work presents a new method for efficiently designing loads and supports simultaneously with material distribution in density-based topology optimization. We use a higher-order or super-Gaussian function to parameterize the shapes, locations, and orientations of mechanical loads and supports. With a distance function as an input, the super-Gaussian function projects smooth geometric shapes which can be used to model various types of boundary conditions using minimal numbers of additional design variables. As examples, we use the proposed formulation to model both concentrated and distributed loads and supports. We also model movable non-design regions of predetermined solid shapes using the same distance functions and design variables as the variable boundary conditions. Computing the design sensitivities using the adjoint sensitivity analysis method, we implement the technique in a 2D topology optimization algorithm with linear elasticity and demonstrate the improvements that the super-Gaussian projection method makes to some common benchmark problems. By allowing the optimizer to move the loads and supports throughout the design domain, the method produces significant enhancements to structures such as compliant mechanisms where the locations of the input load and fixed supports have a large effect on the magnitude of the output displacements.
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This content will become publicly available on January 15, 2026
Compliant Mechanism Synthesis Using Nonlinear Elastic Topology Optimization With Variable Boundary Conditions
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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- Award ID(s):
- 2311078
- PAR ID:
- 10568818
- Publisher / Repository:
- Wiley
- Date Published:
- Journal Name:
- International Journal for Numerical Methods in Engineering
- Volume:
- 126
- Issue:
- 1
- ISSN:
- 0029-5981
- Subject(s) / Keyword(s):
- bistability large displacements morphing wing design path generation variable loads variable supports
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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