Design sensitivity analysis for nonlinear thermal systems

The Lagrange multiplier method and convolution theory are used to formulate design sensitivities for nonlinear transient thermal systems. Variations of a general design functional are expressed in explicit form with respect to variations in structural shape and the conventional design quantities, i.e., material properties, applied loads, prescribed boundary conditions and initial conditions. The design functional depends on these explicit quantities and the implicit repsonse fields: temperature, temperature gradient, heat flux vector and reaction surface flux. A finite element implementation of the methodology illustrates the formulation.