Abstract
In this work, a density-based method is applied for synthesizing compliant mechanisms using topology optimization. This kind of mechanisms uses the elastic strain as the basis for kinematic actuation and it is widely used in precision mechanical devices, in biomedical engineering, and recently in MicroElectroMechanical Systems (MEMS). Geometrical and material (compressible hyperelasticity) nonlinearities are taken into account to obtain mechanisms near real-world applications. A strength criterion for the optimization problem is applied, to design compliant mechanisms that fulfill the desired kinematic tasks while complying with a stress threshold. The addition of a stress constraint to the formulation also aims to alleviate the appearance of hinges in the optimized design. Employing benchmark examples, we investigate the influence of a nonlinear formulation with a stress constraint in the final designs. It is shown that material nonlinearity plays an important role for stress constraint problems. The use of a projection scheme helps to obtain optimized topologies with a high level of discreteness. The Method of Moving Asymptotes (MMA) is applied for design variables updating and the required derivatives are calculated analytically by the adjoint method.
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Acknowledgments
The authors would like to thanks Prof. Jun Sergio Ono Fonseca (in memoriam) for the initial idea. Also we would like to acknowledge Niels Aage, from the Technical University of Denmark, for a C version of MMA.
Funding
This research was partially supported by the Brazilian National Council for Scientific and Technological Development (CNPq). J. F. Gonçalves received support from the RCGI (Research Centre for Gas Innovation) hosted by the University of São Paulo (USP) and sponsored by FAPESP (São Paulo Research Fundation (2014/50279-4)) and Shell Brasil.
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Replication of results
All necessary data to reproduce results presented in this paper are described in the results section. Derivatives necessary to replicate optimized topologies are developed in the sensitivity analysis subsection. Methods applied to perform equilibrium equations for the FEM analysis are available in the cited literature.
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De Leon, D.M., Gonçalves, J.F. & de Souza, C.E. Stress-based topology optimization of compliant mechanisms design using geometrical and material nonlinearities. Struct Multidisc Optim 62, 231–248 (2020). https://doi.org/10.1007/s00158-019-02484-4
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DOI: https://doi.org/10.1007/s00158-019-02484-4