Abstract
Soft materials are finding widespread implementation in a variety of applications, and it is necessary for the structural design of such soft materials to consider the large nonlinear deformations and hyperelastic material models to accurately predict their mechanical behavior. In this paper, we present an effective modified evolutionary topology optimization (M-ETO) method for the design of hyperelastic structures that undergo large deformations. The proposed M-ETO method is implemented by introducing the projection scheme into the evolutionary topology optimization (ETO) method. This improvement allows nonlinear topology optimization problems to be solved with a relatively big evolution rate, which significantly enhances the robustness. The minimal length scale is achieved as well. Numerical examples show that the proposed M-ETO method can stably obtain a series of optimized structures under different volume fractions with smooth boundaries. Moreover, compared with other smooth boundary methods, another merit of M-ETO is that the problem of the dependency on initial layout can be eliminated naturally due to the inherent characteristic of ETO.
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This work was supported in part by the National Natural Science Foundation of China under Grant Nos. 51675525 and 11725211.
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The proposed framework is built on the projection scheme and the original evolutionary topology optimization method; the combination of which has been fully expounded in this work. The results can be easily reproduced. Moreover, the opening of the source code of the proposed method is banned by a project.
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Appendix
Appendix
The matrices BN BL BNL G used in (21) and (25) are defined as follows, here take the four-node element as an example:
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Zhang, Z., Zhao, Y., Du, B. et al. Topology optimization of hyperelastic structures using a modified evolutionary topology optimization method. Struct Multidisc Optim 62, 3071–3088 (2020). https://doi.org/10.1007/s00158-020-02654-9
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DOI: https://doi.org/10.1007/s00158-020-02654-9