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.