A fidelity equivalence computation method for topology optimization of geometrically nonlinear structures

Abstract

The application of geometrically nonlinear topology optimization under large deformations in engineering is seriously hindered by its excessive time consumption. To this end, a fidelity equivalent computation method (FECM) with double optimization loops is proposed, in which the topology optimization (TO) model of linear elastic structure is regarded as the low-fidelity TO model of a geometrically nonlinear structure. Then, the geometrically nonlinear TO model is approached in a piecewise manner by a linear TO model using the equivalent factor. Accordingly, the sensitivities of geometrically nonlinear TO are transformed into the sensitivities of linear TO to capture the layouts of the geometrically nonlinear TO model. Moreover, computational accuracy is demonstrated. The validity and feasibility of the proposed FECM are verified through five numerical examples, and the results demonstrate that the FECM can provide sufficient accuracy for solving the TO problem of geometrically nonlinear structures with a relatively small computational cost.

KEYWORDS:

• Topology optimization
• geometric nonlinearity
• fidelity equivalence calculation method
• equivalent factor
• efficiency

Acknowledgement

The authors are grateful to Professor Krister Svanberg for providing the MMA code.

Disclosure statement

No potential conflict of interest was reported by the authors.

Data availability

The data that support the findings of this study are available from the corresponding author, Zeng Meng, upon reasonable request.

Additional information

Funding

This work is supported by the National Natural Science Foundation of China [grant number 11972143]; Key Laboratory of High-Efficiency and Clean Mechanical Manufacture at Shandong University, Ministry of Education, and Fundamental Research Funds for the Central Universities of China [grant numbers JZ2020HGPA0112, JZ2020HGTA0080].