Structural optimization using adaptive level set method

A novel structural optimization method that utilizes both explicit and implicit geometric representations is presented. In this method, an octree grid is adopted to accommodate the free structural interface of an implicit level set model and a corresponding 2-manifold triangle mesh model. Within each iteration of optimization, the interface is evolved implicitly by using a semi-Lagrange level set method, during which the signed distance field is evaluated directly and accurately from the current surface model other than interpolation. After that, another mesh model is extracted from the updated field and serves as the input of subsequent design process. This hybrid and adaptive representation scheme not only achieves "narrow band computation", but also facilitates the structural analysis by using a geometry-aware mesh-free approach. Moreover, a feature preserving and topological errorless mesh simplification algorithm can also be leveraged to enhance the computational efficiency. A three dimensional benchmark example is provided to demonstrate the capability and potential of this method.