Design sensitivity analysis and optimization of non-linear transient dynamics. Part I - sizing design

A continuum-based sizing design sensitivity analysis (DSA) method is presen ted for the transient dynamic response of non-linear structural systems wit h elastic-plastic material and large deformation. The methodology is aimed for applications in non-linear dynamic problems, such as crashworthiness de sign. The first-order variations of the energy forms, load form, and kinema tic and structural responses with respect to sizing design Variables are de rived. To obtain design sensitivities, the direct differentiation method an d updated Lagrangian formulation are used since they are more appropriate f or the path-dependent problems than the adjoint variable method and the tot al Lagrangian formulation, respectively. The central difference method and the finite element method are used to discretize the temporal and spatial d omains, respectively. The Hughes-Liu truss/beam element, Jaumann rate of Ca uchy stress, rate of deformation tensor, and Jaumann rate-based incremental ly objective stress integration scheme are used to handle the finite strain and rotation. An elastic-plastic material model with combined isotropic/ki nematic hardening rule is employed. A key development is to use the radial return algorithm along with the secant iteration method to enforce the cons istency condition that prevents the discontinuity of stress sensitivities a t the yield point. Numerical results of sizing DSA using DYNA3D yield very good agreement with the finite difference results. Design optimization is c arried out using the design sensitivity information. Copyright (C) 2000 Joh n Wiley & Sons, Ltd.