Topological shape optimization of geometrically nonlinear structures using level set method

Using the level set method, a topological shape optimization method is developed for geometrically nonlinear structures in total Lagrangian formulation. The structural boundaries are implicitly represented by the level set function, obtainable from “Hamilton–Jacobi type” equation with “up-wind scheme,” embedded into a fixed initial domain. The method minimizes the compliance through the variations of implicit boundary, satisfying an allowable volume requirement. The required velocity field to solve the Hamilton–Jacobi equation is determined by the descent direction of Lagrangian derived from an optimality condition. Since the homogeneous material property and implicit boundary are utilized, the convergence difficulty is significantly relieved.