Design sensitivity analysis and optimization of non-linear transient dynamics. Part II?configuration design

Abstract

For configuration design of non-linear dynamic structures, such as crashworthiness design, a continuum-based configuration design sensitivity analysis (DSA) and optimization methods are developed. The same transient dynamic analysis method used in Part I of this paper is employed here. The elastic–plastic material and finite strain and rotation effect are considered. The first-order variations of the energy forms, load form and kinematic and structural responses with respect to configuration design variables are derived. For the configuration design, both the shape and orientation variations contribute to the first-order variation of the equations of motion. The angular design velocity field associated with Euler angles is used to represent the orientation variation to obtain accurate design sensitivity results. Like Part I of the paper, the updated Lagrangian formulation and direct differentiation method are used for DSA for the path-dependent problem. For the updated Lagrangian formulation, the design velocity field that defines the mapping between the initial and perturbed designs should also be updated at each configuration. Numerical implementation of configuration DSA and optimization is carried out for fixed time steps using DYNA3D and the modified feasible direction (MFD) method. It is observed that the proposed DSA method yields better sensitivity results than the finite difference method for the highly non-linear problem. Design optimization is carried out using the design sensitivity information.Copyright © 2000 John Wiley & Sons, Ltd.