Approximate response sensitivities for nonlinear problems in explicit dynamic formulation

Abstract

Explicit and implicit time integration schemes are discussed in the context of sensitivity analysis of dynamic problems. The application of the fully explicit central difference method (CDM) proves to be efficient for many nonlinear problems. In the case of the corresponding dynamic sensitivity problem the CDM is less advantageous both from efficiency and accuracy points of view. Approximate sensitivity expressions are derived in the paper for nonlinear path-dependent problems allowing the application of an unconditionally stable implicit time integration scheme with the time step much larger than the time step of the explicit CDM scheme of the direct problem. The method seems to be particularly suitable for problems of quasi-static nature in which the dynamic terms are artificially introduced to allow explicit CDM solution of highly nonlinear equations.