Explicit and efficient topology optimization for three-dimensional structures considering geometrical nonlinearity

Abstract

In this paper, a geometrically nonlinear topology optimization method is presented for three-dimensional structures using moving morphable bars. The explicit geometrical shapes of moving morphable bars reduce the design variables, so the computational efficiency of the method can be enhanced by accelerating the convergence process. The element density function with respect to moving morphable bars is obtained by a Heaviside approximation of distance functions, which is modified without the coordinate transformation. Afterwards, the density function is skillfully applied to derive the geometrically nonlinear finite element analysis for three-dimensional structures. Besides, the topology optimization model is established, whose sensitivities are derived by the adjoint method. Numerical examples demonstrate the effectiveness of the proposed method, and show that for some symmetric design domains, the optimized results tend towards slightly nonsymmetric due to the buckling effects.