Sensitivity analysis in thermoelasticity problems

In many problems of structural mechanics there is a need to assess the effect of variation of one or several design functions or parameters /such as material properties, cross-sectional dimensions, shape or support conditions/ on the thermal and mechanical state fields within a structure. The methods of such sensitivity analysis have been explored in various fields of science and engineering. Numerous publications reveal the growing interest in the optimum design of structures subject to both mechanical and temperature constraints. When mathematical optimization techniques are used to design structures subjected to temperature, stress and/or displacement constraints, derivatives of these constraints with respect to design variables are usually required. The present paper extends the previous works [1–2] and is concerned with such class of problems for which the first and second variations of any functional that depends on displacements, strains, stresses and temperature can be explicitly expressed in terms of variations of design variables.