In-plane mesh regularization for node-based shape optimization problems

• A mesh regularization method for shape optimization is presented.
• Both size and shape of individual elements can be controlled.
• Solution of one linear equation system defined on the design surface is required.
• The method is inspired by form-finding which is a method to determine the free-form equilibrium shape of membrane and shell structures subjected to a certain stress field.

In this contribution a global and linear method for controlling the surface mesh quality during node-based shape optimization is presented. In this method, an artificial stress is applied on the surface mesh and the global linear system of equations is solved for the equilibrium state by finite elements. The applied stress adapts each element towards a desired predefined template geometry and at the end a globally smooth mesh is achieved. In this way both the shape and the size of each element is controlled. Some examples, as well as possible fields of application are shown. At the end, the strength of the method in shape optimization of computational fluid dynamics problems is described.