Topology optimization for maximizing linear buckling load based on level set method

Stability and buckling have attracted extensive attention in the design of structural elements, especially in the design of thin-walled structures since they may naturally have poor stability and be prone to buckling failure. This paper proposes a level-set based topology optimization (TO) method that can maximize the lowest linear buckling load under a mean compliance constraint. First, we conduct the linearized buckling analysis and formulate the optimum design problem. Second, we derive the design sensitivity and revisit the reaction-diffusion equation-based level-set topology optimization. Finally, we solve several two-dimensional benchmark problems and the design results are presented to validate the proposed method

Optimum design method for structural configuration and fiber arrangement for fiber-reinforced composites

Fiber-reinforced composite materials, exemplified by CFRP, offer the possibility of achieving lightweight, high-stiffness, and high-strength structures by continuously and evenly distributing fibers. While topology and orientation optimization methods have been developed for anisotropic materials in the past, there remains a gap in design methods that consider manufacturability, especially for continuous fiber materials. In this study, we propose a design method that takes into account manufacturability, focusing on the aspects of continuity and uniformity in fiber-reinforced composite optimum design. Specifically, we introduce a two-stage optimization approach. In the first stage, we conduct concurrent optimization of topology and fiber orientation. We utilize a level-set function to represent topological configuration, while for orientation, we introduce a “double angle vector”, which enables us to consider fiber properties such as angular periodicity. These design variables are updated by solving partial differential equations based on reaction–diffusion equations. In the second stage, leveraging the optimal orientations obtained in the first stage, we optimize the path-line generation for the manufacture of continuous fiber materials. We introduce a scalar function representing path lines and formulate an optimization problem to ensure that the path lines are both evenly spaced and continuous. The update of design variables in this state is also achieved via solving the partial differential equation. Through the development of this two-stage optimization method, we aim to create an optimal structure with manufacturable continuous fiber materials, incorporating both the topology and fiber orientation that satisfy the requirements of continuity and uniformity