Isogeometric configuration design optimization of heat conduction problems using boundary integral equation

The shape variation of a domain naturally results in both shape and orientation variations, so called configuration variation, when employing a boundary integral equation (BIE) method. A configuration design sensitivity analysis (DSA) method is developed for steady state heat conduction problems using the boundary integral equations in an isogeometric approach, where NURBS basis functions in a CAD system are directly utilized in the response analysis. Thus, we can accomplish a seamless incorporation of exact geometry and the higher continuity into a computational framework. To enhance the accuracy of configuration design sensitivity, the CAD-based higher-order geometric information such as normal and tangent vectors is exactly embedded in the design sensitivity expressions. The necessary velocity field for configuration design obtained from the NURBS is analytically decomposed into shape and orientation velocity fields. It is shown to be essential to consider orientation variations and significant for accurate configuration sensitivity through comparison with finite differencing conventional BIE method. The developed isogeometric configuration DSA method turns out to be accurate compared with the analytic solution and the conventional DSA method. During the optimization, a mesh regularization scheme is employed to avoid excessive mesh distortion, which comes from significant design changes.