Reduced Basis Technique for Evaluating Sensitivity Derivatives of the Nonlinear Response of the Space Shuttle Orbiter Nose-Gear Tire

Abstract

Abstract A study is made of the sensitivity of the nonlinear tire response to variations in the design variables. The tire is discretized by using three-field mixed finite element models. An efficient reduced basis technique is used for calculating the nonlinear tire response as well as the first-order and second-order sensitivity coefficients (derivatives with respect to design variables). In this technique the vector of structural response and its first-order and second-order sensitivity coefficients are each expressed as a linear combination of a small number of basis (or global approximation) vectors. The Bubnov-Galerkin technique is then used to approximate each of the finite element equations governing the response and the sensitivity coefficients by a small number of algebraic equations in the amplitudes of the vectors. Extensive numerical results are presented for the sensitivity coefficients of the Space Shuttle orbiter nose-gear tire, when subjected to uniform inflation pressure.