Adjoint sensitivity analysis for nonlinear dynamic thermoelastic systems

An adjoint approach is presented to formulate explicit sensitivities for a general functional associated with a nonlinear, dynamic, thermoelastic system. Uncoupled thermoelastic response and small-deformation behavior are assumed. The formulation uses the Lagrange multiplier method to define an adjoint system, the convolution operator to incorporate transient effects, and domain parameterization to describe shape variations. Variations of the functional are expressed in explicit form with respect to perturbations of the design fields: structural shape, material properties, applied loads, prescribed boundary conditions, and initial conditions. The functional is defined in terms of the design fields and the implicit response fields: displacement, temperature, strain, temperature gradient, stress, heat flux vector, reaction force, and reaction surface flux. In an example problem, the finite element method is used to evaluate the real and adjoint responses and the shape sensitivities for a tank design problem. The tank is modeled as a nonlinear, quasistatic, uncoupled, thermoelastic system.