Shape optimization in three-dimensional linear elasticity by the boundary contour method
A variant of the usual boundary element method (BEM), called the boundary contour method (BCM), has been presented in the literature in recent years. In the three-dimensional BCM, surface integrals on boundary elements of the usual BEM are transformed, through the application of Stokes theorem, into line integrals along the bounding contours of these elements. The BCM employs linear combinations of global weighted shape functions, being defined piecewise on the boundary elements. A useful consequence of this approach is that stresses, at suitable boundary points, can be easily obtained from a post-processing step of the standard BCM. The subject of this paper is the shape optimization in three-dimensional (3D) linear elasticity by the use of BCM. This is achieved by coupling the 3D BCM code with a mathematical programming code based on a successive quadratic programming algorithm. Numerical results are presented for several interesting illustrative examples, like shape optimization of a fillet, optimal shape of an ellipsoidal cavity inside a cube, etc.
scientific article; zbMATH DE number 1452642
scientific article