Local continuum shape sensitivity with spatial gradient reconstruction for nonlinear analysis

Abstract

Gradient-based optimization for large-scale, multidisciplinary design problems requires accurate and efficient sensitivity analysis to compute design derivatives. Presented here is a nonintrusive analytic sensitivity method, that is relatively easy to implement. Furthermore, it can be as accurate as conventional analytic sensitivity methods, which are intrusive and tend to be difficult, if not infeasible, to implement. The nonintrusive local continuum shape sensitivity method with spatial gradient reconstruction (SGR) is formulated for nonlinear systems. This is an extension of the formulation previously published for linear systems. SGR, a numerical technique used to approximate spatial derivatives, can be leveraged to implement the sensitivity method in a nonintrusive manner. The method is used to compute design derivatives for a variety of applications, including nonlinear static beam bending, nonlinear transient gust response of a 2-D beam structure, and nonlinear static bending of rectangular plates. To demonstrate that the method is nonintrusive, all analyses are conducted using black box solvers. One limiting requirement of the method is that it requires the converged Jacobian or tangent stiffness matrix as output from the analysis tool. For each example the design derivatives of the structural displacement response are verified with finite difference calculations.