Hollow structural topology optimization considering geometrical nonlinearity using three-dimensional moving morphable bars

Hollow structures show higher performance and more easily satisfy lightweight requirements than solid structures in engineering. However, hollow optimized results obtained by topology optimization are currently under the assumption of the small deformation rather than the large deformation. Therefore, this paper proposes a hollow structural topology optimization method considering geometrical nonlinearity using three-dimensional moving morphable bars. This proposed method is innovative in bridging topology optimization and the hollow design under the large deformation assumption. The three-dimensional moving morphable bars have the hollow characteristic, and their corresponding geometrical parameters are regarded as the design variables to obtain the hollow optimized result. The density function established by hollow moving morphable bars is incorporated into the three-dimensional geometrical nonlinear finite element analysis. The explicit optimization model is established and the corresponding sensitivities are also derived. Numerical examples demonstrate that whether the geometrical nonlinearity is considered has a great influence on the hollow optimized results. The cross sections of the optimized results for the same structure cause different hollow shapes according to different magnitudes of external forces. Moreover, these hollow cross-sectional shapes are significantly specific under certain loading conditions involving the buckling effects, such as the bending and torsional conditions.

Automated summary

This paper proposes a hollow structural topology optimization method considering geometrical nonlinearity using three-dimensional moving morphable bars. Numerical examples demonstrate the effectiveness of this method under large deformation conditions.