Configuration design sensitivity analyss of nonlinear transient dynamics
by Seonho Cho, Kyu-Yeul Lee
International Journal of Vehicle Design (IJVD), Vol. 28, No. 4, 2002

Abstract: A continuum-based configuration design sensitivity analysis (DSA) method is developed for the transient dynamic response of nonlinear structural systems. The first-order variations of energy forms, load form, and kinematic and structural responses with respect to the configuration design variables are derived. For the configuration design, both shape and orientation variations contribute to the first-order variation of the governing equation. A material derivative approach is employed to represent the shape variation. The shape and orientation design variations usually defined in element local coordinates are expressed in terms of global coordinates in this paper. A direct differentiation method is used since it is more appropriate for both path independent and path dependent problems than the adjoint variable method. For the structural domain, updated Lagrangian formulation is used so that the design velocity field that defines the mapping between initial and perturbed design velocity field that defines the mapping between initial and perturbed designs is updated at each updated configuration. The Hughes-Liu truss/beam element based on the degeneration of an 8-node isoparametric solid is selected to discretise the struuctural domain. The objective stress and strain measures and Jaumann rate-based incrementally objective stress integration scheme are employed to handle large rotation effects. In temporal domain, an explicitly central difference method is used for time integration. For accurate numerical implementation, a fixed time step, sufficiently smaller than the critical time step that is determined by element geometry and material properties, is selected to remove the effect of time step sensitivity on the sensitivity of the performance measures. The developed DSA method is implemented to validate the accuracy and efficiency of the proposed method, which yields very good agreement with the central finite difference results.

Online publication date: Fri, 15-Aug-2003

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