Improved semi-analytical sensitivity analysis using a secant stiffness matrix for geometric nonlinear shape optimization
Exact semi-analytical sensitivity analysis method is extended to geometric nonlinear case. A correction term is constructed in the product spaces of two different sets of zero-eigenvectors. The analytical formulas of these vectors are presented with respect to the secant stiffness matrix. Numerical results show that the method eliminates semi-analytical sensitivity errors significantly.
secant stiffness matrix geometric nonlinearity exact semi-analytical sensitivity analysis correction term finite difference approximation nonparametric shape optimization