Sensitivity analysis for coupled thermoelastic systems

This paper presents an adjoint approach, derived from the reciprocal theorem, for the sensitivity analysis of linear dynamic thermoelastic systems. The variation of a general response functional is expressed in explicit form with respect to variations of the design fields which consist of the material properties, applied loads, prescribed boundary, initial conditions, and the structural shape. The functional is dependent on these design quantities as well as the following implicity defined response fields: displacement, temperature, stress, strain, heat flux, temperature gradient, reaction forces, and reaction surface flux. The formulation incorporates the reciprocal relation between variations of the real system design and response fields and an adjoint state. Here, convolution is employed in lieu of time mappings used in other transient adjoint sensitivity derivations. Specializations of the formulation to uncoupled, combined quasi-static uncoupled, and steady-state thermoelasticity are also presented. The finite element method is used to demonstrate the application of the formulation to a problem in automobile engine design.