TANGENT OPERATORS, SENSITIVITY EXPRESSIONS, AND OPTIMAL-DESIGN OF NONLINEAR ELASTICA IN CONTACT WITH APPLICATIONS TO BEAMS

The tangent operator and design sensitivity expressions for non-linear elastica subject to frictionless unilateral contact are derived and c omputed via the finite element method. The sensitivity computations ar e then combined with a numerical programming package to create an opti mal design environment. To exemplify the optimal design environment, a beam's contact surface is contoured to minimize bending stress. This work combines the research on the sensitivity analysis of non-linear e lastic bodies subject to constraints, finite strain non-linear elastic beam analysis and contact analyses. The analysis is valid for any smo oth contact surface; and specialized for the case in which the surface is represented by a cubic spline. The direct differentiation method i s utilized to perform the sensitivity analysis. In an example problem, the sensitivity analysis is verified by finite difference computation s and then combined with a numerical optimization program to design th e stop profile of a valve.