Incorporating buckling effect into the topology design of 2D continuum structures using isolines

Isolines Topology Design (ITD) is an iterative algorithm for use in the topological design of two-dimensional (2D) continuum structures using isolines. This paper presents an extension to this algorithm for topology design of 2D continuum structures under the influence of buckling. Topology design has been used to obtain the lightest structure that can support the loading conditions without failure, with optimal designs typically consisting of slender members. In many cases, instability (or buckling) of the slender compressive members may occur at load levels below those predicted using a stress-based failure criteria. Although topology optimization is often used in the conceptual phase of the design, the influence of buckling has a significant impact on the features and performance of the final structure. This article presents an alternative approach to incorporate the buckling effect into the ITD algorithm for the design of 2D continuum structures. The concept consists of transforming the buckling topology optimization problem into a conventional von Mises stress-based topology design problem at each iteration using the shape of the buckling mode of the structure obtained by the eigenvalue analysis. Three examples are presented to show the viability and effectiveness of the alternative approach implemented into the ITD algorithm. The effect of the displacement factor ratio value on the first critical load of a resulting designs was studied. The resulting designs presented are in good agreement with those from the literature. The main conclusion is that the alternative approach can maximize the first critical load of a design subject to final volume constraints if the associated stiffness loss can be assumed.