Shape design sensitivity analysis for non-linear anisotropic heat conducting solids and shape optimization by the BEM

Shape design sensitivity analysis (SDSA) expressions have been derived for non-linear anisotropic heat conducting solid bodies by following the material derivative concept and adjoint variable method of optimal shape design given in the literature. The variation of a general integral functional has been described in terms of primary and adjoint quantities evaluated at the varying boundaries. As an example problem in shape optimization, optimal outer boundary profiles of an orthotropic solid body are obtained by the boundary element method (BEM), after reformulating the SDSA equations in a form which is most suitable for the BEM.