Parameter sensitivity for large deformation inelastic problems

Abstract

The algorithm for parametric sensitivity assessment for both materially and geometrically nonlinear static problems is presented. Similarly to its geometrically linear version presented elsewhere, the sensitivity analysis is shown to reduce to a linear problem with the same operator matrix that has been used in just completed equilibrium iteration, which makes the computations very efficient. Both total and updated Lagrangian approaches are analysed, including design differentiation of the configuration update transformation. Sensitivity with respect to constitutive parameters is discussed in detail. Possible extensions towards cross-sectional geometry or general shape parameters are pointed out.