On a constraint-based regularization technique for configurational r-adaptivity and 3D shape optimization

This contribution deals with a numerical regularization technique for con-figurational r-adaptivity and shape optimization based on a fictitious energy con-straint. The notion configurational refers to the fact that both r-adaptivity and shape optimization rely on an optimization of the potential energy with respect to changes of the (discrete) reference configuration. In the case of r-adaptivity, the minimization of the total potential energy optimizes the mesh and thus improves the accuracy of the finite element solution, whereas the maximization of the total potential energy by varying the initial shape increases the stiffness of the structure. In the context of r-adaptivity, the energy constraint sets the distortion of the mesh to a reasonable limit and improves the solvability of the problem. The application of the energy constraint to a node-based shape optimization is a remedy for well-known problems of node-based shape optimization methods with maintaining a smooth and regular boundary