Design smoothing in shape optimization of shells

Shape description and control techniques are crucial in shape optimization, since they determine to a large extent the optimum from a geometrical point of view. The most popular shape description techniques are CAD based and FE based design parametrization. Both have advantages and disadvantages, being the first more suitable for manufacture purposes and the second one for preliminary designs and free-formed shapes. In shape optimization of shells, an important shortcoming of the FE design based parametrization technique is the proliferation of local optima which may be wiggly shapes. These designs are usually not desired because of esthetics, utilization reasons and, most important, because they entail high mesh distortion and, consequently, unreliable structural and sensitivity analysis. For these reasons, shape control techniques to enforce and influence design smoothness are required. In the present paper a technique to control smoothness of surfaces in shape optimization is studied. This approach is based on regularization of the surface based on intrinsic curvature measures. The objective function of the original optimization problem is penalized with a regularization term. Intrinsic curvature measures of the surface approximated by a polygonal mesh are computed from the nodal positions, nodal normals to the surface and mesh topology information. Smoothness can be controlled by designer through a regularization parameter and a prescribed curvature function. Numerical experiments show the good performance of the approach.