Implementation of design sensitivity analysis for nonlinear elastic structures

Abstract

Implementation of design sensitivity analysis into MARC, a general nonlinear finite element code, is described. Follower forces and constraints treated via Lagrange multipliers are also included in the implementation. The sensitivity analysis is implemented in the most general way; i.e., arbitrary design criteria and design parameters including shape, sizing, and material property variables can be defined through special user-supplied subroutines. Local derivatives of all of the quantities needed for sensitivity analysis are calculated using the central differences allowing a very general implementation without sacrificing the accuracy. Design sensitivities to multiple parameters are implemented, even though an option for multiple loading does not apply to nonlinear finite element analysis. Also, design sensitivities can be calculated at any load level, whereas the analysis calculations march on as if there was no interruption. Derivation of design sensitivities with constraints such as incompressibility or unilateral frictionless contact indicates that the same steps, as in the implementation of regular displacement based nonlinear finite element method, can be followed without any modifications. A numerical example using the modified finite element code is presented to demonstrate the new capability.