SHAPE OPTIMIZATION OF 2-DIMENSIONAL THERMOELASTIC STRUCTURES USING BOUNDARY INTEGRAL-EQUATION FORMULATION

A general method for shape design sensitivity analysis as applied to two-dimensional uncoupled thermoelasticity problem is developed using the material derivative concept and adjoint variable method. The method for deriving sensitivity formula is based on standard direct thermal and elastic boundary integral equation formulation. The sensitivity of a general functional is considered which depends on thermal and mechanical quantities such as temperature, heat flux, displacement, stress and surface traction. The method is then applied to obtain the sensitivity formula for a general stress constraint imposed over a small part of the boundary. The accuracy of the sensitivity is studied with two thermoelastic shape optimization problems of a fillet and a hole. Optimal shapes for the two problems of weight minimization are presented to show numerical applications. It is shown through the fillet design problem that optimal shape under stress constraint is highly dependent on thermal boundary conditions, indicating that the shape optimization based on thermoelasticity is crucial when thermal field is sensitive to boundary shape.