Topology optimization procedure for ship structures having irregular design domain

Abstract

A systematic approach of topology optimization of any irregular design domain having unstructured mesh is developed by implementing the features of Object-Oriented Programming (OOP). This research focuses on two-dimensional problems. In solving the topology optimization mathematical problem, the formulation of Solid Isotropic Material with Penalization (SIMP) is used. The objective is to minimize the compliance of the structural domain for a given volume fraction. To evaluate the element stiffness matrixes of quadrilateral plane stress elements, the four-point Gaussian quadrature integration rule is applied as a part of Finite Element Analysis (FEA). The element stiffness matrixes are then accumulated into a global stiffness matrix with some modifications for the SIMP approach. After that, a system of linear equations is solved to get the nodal displacements. The resulting displacements are later used to calculate compliance and compliance sensitivity. Compliance sensitivity weighted averaging modifies compliance sensitivities to avoid the checkerboard problem. Optimality criteria optimizer finds out individual element’s relative material densities using the compliance sensitivities. The optimality criteria optimizer solves the Lagrange multiplier using bi-sectioning algorithm which satisfies the volume fraction constraint. Maximum element relative material density change is tracked in each optimization iteration to mark the convergence.

A computer program is developed with Graphical User Interface (GUI) in Python programming language as a general tool to solve the above formulation. The software can optimize both structured and unstructured mesh. The design domain needs not to be regular shaped. The mesh can be imported from some professional meshing software like Abaqus, Ansys, Gmsh etc. Specific elements can be set to freeze so that they cannot be removed during the optimization. There is also an option to set the wall elements (elements adjacent to design domain walls) to freeze. Each optimization iteration can be graphically viewed in the software. The resulting optimized mesh can be exported to Abaqus (INP) format to perform further structural analysis. There is also an option to export the optimized mesh to STL format which can be used for 3D printing. Some examples are shown in this thesis to verify the effectiveness of the research.