Some Ideas and Progress on the Shape Optimization of Nonlinear Structures

For the sensitivity analysis of nonlinear structure with respect to the shape variation, it is formulated based on the geometrical mapping approach, rather than the material derivative approach. The shape variation is regarded as a mapping characterized by the shape variation velocity field, or a fictitious deformation of the continuum, which is not real displacement, and there are no strain and stress corresponding to such fictitious displacement field. Started from the virtual work principle, the sensitivity equations of state variables for nonlinear structure with respect to the shape variation have been formulated, and also the equation for calculating the sensitivity of performances with respect to the shape variation. To enhance the efficiency, the adjoint variable method is applied, wherein the asymmetry of the equation matrix due to the slip contacted case of the frictional contact using Lagrange multiplier method is taken into account. For the gradient-based Kriging method based on the samples determined by the orthogonal maximin Latin hypercube design, a criterion for the best likelihood spatial correlation parameter is suggested, based on the transition from insufficient to excessive control. The criterion is verified using a series of test examples.