Design sensitivity analysis of nonlinear structures subjected to thermal loads

Abstract

This work presents a simple and efficient methodology for sensitivity analysis of geometrically nonlinear structures subjected to thermo-mechanical loading in regular and critical states. Using the effective strain approach, the path-following methods and the algorithms for critical point computation developed originally for finite element analysis of mechanically loaded structures are modified to include the thermal effects. The general expressions for sensitivity computation of displacements, stresses and nonlinear critical loads are obtained through the differentiation of the finite element equations. The practical implementation of the sensitivity analysis in a finite element code employing the Analytical, Semi-Analytical and Refined Semi-Analytical approaches is discussed in detail. Finally, a set of numerical examples is used to validate the proposed methodology.