An isoparametric approach to level set topology optimization using a body-fitted finite-element mesh

We present a new method for performing level set topology optimization of structures confined to irregularly-shaped physical domains. The shape sensitivities are computed in physical space using a body-fitted, non-uniform finite-element mesh. These values are then mapped to the Euclidean computational space using the Jacobian matrix of the isoparametric transformation taking place within each cell. The method is demonstrated on a three-dimensional problem in which we minimize the compliance of a contoured wingbox structure. Results show that the method converges consistently, and generates solutions comparable to those obtained using the SIMP method.