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

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.