Shape design optimization of thermoelasticity problems using isogeometric boundary element method

An integrated geometric design sensitivity (DSA) method for weakly coupled thermoelastic problems is developed in this study using boundary integral equations with an isogeometric approach that directly utilizes a CAD system's NURBS basis functions in response analysis. Thermomechanical coupling frequently creates thermoelastic behaviors in plants and nuclear systems and requires a structural optimization process that minimizes the overall weight and maximizes the system performance. To incorporate accurate geometries and higher continuities into the optimization process, we derive a shape design sensitivity equation using thermoelastic boundary integral equations within the isogeometric framework. In the boundary integral formulation, the shape design velocity field is decomposed into normal and tangential components, which significantly affects the accuracy of shape design sensitivity. Consequently, the developed isogeometric shape DSA method using thermoelastic boundary integral equations is more accurate compared with the analytic solution and the conventional DSA method. Utilizing the formulated isogeometric shape sensitivity as the gradient information of the objective function, isogeometric shape optimization examples for thermoelastic problems are presented. It is demonstrated that the derived isogeometric shape DSA using boundary integral equations are efficient and applicable.