Bi-directional evolutionary topology optimization of geometrically nonlinear 3D continuum structures with an additional displacement constraint

This paper addresses the volume minimization topology optimization problem for geometrically nonlinear structures with displacement constraint. Displacement constraints are essential in structural design, limiting specific parts of a structure from moving beyond a predefined boundary. To tackle this challenge, an enhanced bi-directional evolutionary structural optimization (BESO) method is proposed. The sensitivity information required for design updates is derived through the adjoint method. This approach leverages the linear perturbation function in ABAQUS, which eliminates the need to compute the inverse of the global tangential stiffness matrix, thereby significantly improving computational efficiency. Python is employed to manage the optimization process, while ABAQUS serves as the finite element solver. Numerical experiments demonstrate the effectiveness and accuracy of the method in optimizing complex 3D structures. The adaptive volume change algorithm stabilizes the optimization process by automatically adjusting volume changes, resulting in a smooth convergence to the optimal solution. Additionally, the method reduces displacement fluctuations by applying constraints on maximum volume addition rates and incorporating historical sensitivity data.