Topological Shape Optimization of Geometrically Nonlinear Structures using Level Set Method

摘要

A level set method is employed as an alternative approach to conventional topology optimization methods. Using the level set function and adjoint sensitivity, we develop a gradient-based topology optimization method applicable to geometrically nonlinear structures. Structural boundaries are implicitly represented by the level set function obtained from the "Hamilton-Jacobi (H-J) type" equation with an up-wind scheme. The implicit function is embedded into a fixed initial domain to obtain the response and sensitivity of structures under total Lagrangian formulation. The developed method defines a Lagrangian function for constrained optimization. It minimizes the compliance, satisfying the constraint of allowable volume, through implicit boundary variations. The required boundary velocity to integrate the H-J equation is obtained from the optimality condition for the Lagrangian function. Using the homogeneous material distribution and the implicit boundary, we significantly relieve the convergence difficulty mainly caused by the intermediate material distribution in the conventional topology optimization methods.