A mesh-shape sensitivity synthesis for boundary-formulated shape optimal design

This paper presents a sequential mesh-shape sensitivity synthesis with which only the structural boundary information is required during the shape optimization process. Large structural shape reformation as well as the minimum mesh distortion can be obtained. This method avoids the repetitive remeshing procedure by employing an optimization driven mesh smoothing algorithm proposed by Hwang and Fleury. It eliminates the need to explicitly define the grid point peturbations for the shape sensitivity by extracting the mesh sensitivity from the optimized mesh. Since only the structural boundary is involved in the shape optimization scheme, the method used to create the finite element mesh is not important as long as the element topology for the model is valid. Examples are provided to show the effectiveness of this approach.