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

For con"guration design of non-linear dynamic structures, such as crashworthiness design, a continuumbased con"guration 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 "nite strain and rotation e!ect are considered. The "rst-order variations of the energy forms, load form and kinematic and structural responses with respect to con"guration design variables are derived. For the con"guration design, both the shape and orientation variations contribute to the "rst-order variation of the equations of motion. The angular design velocity "eld 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 di!erentiation method are used for DSA for the path-dependent problem. For the updated Lagrangian formulation, the design velocity "eld that de"nes the mapping between the initial and perturbed designs should also be updated at each con"guration. Numerical implementation of con"guration DSA and optimization is carried out for "xed time steps using DYNA3D and the modi"ed feasible direction (MFD) method. It is observed that the proposed DSA method yields better sensitivity results than the "nite di!erence method for the highly non-linear problem. Design optimization is carried out using the design sensitivity information