Minimal compliance topologies for maximal buckling load of columns

Abstract

This paper presents a new approach to the topology optimization of columns exposed to a loss of stability. The idea is to replace a conventional maximization of a buckling load by a locally formulated topology optimization problem based on compliance minimization. In order to do this, the standard instability analysis of a compressed column is performed first and the buckling mode is determined. Then the compressive loading is replaced by a transverse one which is selected so as to generate a bending moment, the distribution of which coincides with the one representing the considered buckling mode. Minimization of compliance is performed for the bent structure and optimal topology is generated. Finally, the critical load for the optimal column is calculated. The selected numerical results obtained with the use of the above technique, under the assumption that the buckling load is unimodal, are presented. The above approach allows generating optimal topologies using Cellular Automata (CA) method, which by nature requires local formulation of the design problem.

Revisiting topology optimization with buckling constraints

“…Recently, Thomsen et al (2018) introduced a method for the design of periodic microstructures with respect to multi-scale buckling conditions, laying the foundations for plenty of future applications within multi-scale structural and material design. Other recent works and applications can be found where we wish to mention Zhou (2004); Lund (2009) ;Bochenek and Tajs-Zielińska (2015); Cheng and Xu (2016); Chin and Kennedy (2016).…”

Topology optimization of steering knuckle structure

“…By drawing a preliminary structure on the top of base topology, the actual shape optimization model is developed. Bochenek et al [8] used a minimal compliance objective approach to optimize extruded columns with different support constraints (pinned and fixed) and subjected to a transverse distributed load representing buckling in one or two planes. Optimal topologies and their corresponding critical buckling loads were obtained.…”

An Adaptive Continuation Method for Topology Optimization of Continuum Structures Considering Buckling Constraints

“…Luo and Tong [2015] investigated the topology design optimization to maximize critical buckling loads of thin-walled structures using a moving iso-surface threshold method. Furthermore, Bochenek and Tajs-Zielińska [2015] achieved topology optimization of columns against buckling by replacing the conventional maximization of a buckling load with a locally formulated topology optimization problem based on compliance minimization. Recently, Cheng and Xu [2016] studied the maximum out-of-plane buckling load design of thin bending plated with volume constraints.…”