TIMP method for topology optimization of plate structures with displacement constraints under multiple loading cases

This paper utilizes the TIMP (Transplanting ICM Ideas into Material with Penalization) method to solve topology optimization problems of plate structures with displacement constraints under multiple loading cases. Two basic perspectives embedded within the TIMP method are that, (1) one more penalty function is added besides the Young's modulus penalty function by transplanting the ICM ideas and progresses into the SIMP (Solid Isotropic Material with Penalization) method, and (2) the definition of the artificial material design variables, as well as the idea of penalization on materials, is inherited from the SIMP method. Based on the TIMP method, complex topology optimization problems with displacement constraints are expressed explicitly by using the element weight and Young's modulus penalty functions, and the nonlinear programming algorithm is used to get solutions. Displacement filtering is employed to eliminate the mesh-dependency and checkerboard issues, and the coarse selection of quasi-active constraint strategy is adopted to select active constraints and improve the computing efficiency. The whole solution development process is implemented into a secondary development software based on the Abaqus software by its script language Python. Two problems with a single loading case and two problems with multiple loading cases are addressed on this secondary development software. The effects of using linear and nonlinear element weight penalty functions on the convergence speed are observed through these numerical problems. The results demonstrate that the TIMP method is effective to undertake complex topology optimization problems with displacement constraints under multiple loading cases.