Topology Optimization of Cracked Structures With Manufacturing Constraints

Abstract

Abstract Topology optimization (TO) is a tool used in the design process to improve the structure’s performance, e.g. increasing the stiffness. However, the final topologies typically include complex shapes making them impractical or unrealizable from a fabrication point-of-view. This issue stems from the limitations that the currently available manufacturing methods have, such as milling. Hence, considering these limits as the manufacturing constraints into the optimization problem would shorten the post-processing time. Moreover, the existence of initial damage such as cracks is another common issue of engineering structures, resulting in unreliable topologies if neglected. These two challenges are the main motivations of this study. A projection method is utilized to restrict the range of solutions to a manufacturable design domain by projecting the design variable into a pseudo-density field. The main advantage of this approach is that the manufacturing restrictions are achieved naturally, without adding constraints to the TO problem, which leads to a straightforward calculation of sensitivities. This technique allows the designer to define, for instance, a minimum member size as well as a minimum hole size as geometrical constraints. In order to penalize the intermediate phases, the popular Solid Isotropic Material with Penalty method (SIMP) is employed. The Peri-dynamics theory is used to study the structure’s behaviour because of its ability to introduce discontinuities without requiring complicated mathematical expressions as opposed to its counterpart mesh-based approaches. The robustness of the proposed method is demonstrated through some compliance minimization problems.