Continuum Topology Optimization of Buckling-Sensitive Structures

Abstract

Two formulations for continuum topologyoptimizationof structures taking buckling considerations into account are developed, implemented, and compared. In the rst, the structure undergoing a speci ed loading is modeled as a hyperelastic continuum at nite deformations and is optimized to maximize the minimum critical buckling load. In the second, the structure under a similar loading is modeled as linear elastic, and the critical buckling load is computed with linearized buckling analysis. Speci c issues addressed include usage of suitable "mixing rules," a node-based design variable formulation, techniques for eliminating regions devoid of structural material from the analysis problem, and consistent design sensitivity analysis. The performance of the formulations is demonstrated on the design of different structures. When problems are solved with moderate loads and generous material usage constraints, designs using compression and tension members are realized. Alternatively, when fairly large loads together with very stringent material usage constraints are imposed, structures utilizing primarily tension members result. Issues that arise when designing very light structures with stringent material usage constraints are discussed along with the importance of considering potential geometrical instabilities in the concept design of structural systems.

Level‐set topology optimization with many linear buckling constraints using an efficient and robust eigensolver

“…For continuum structures, it is difficult to identify discrete structural members. Therefore, specific local buckling constraints are not used . Instead, a linear buckling analysis or a geometrically non‐linear analysis is used to compute the critical buckling load.…”

“…Therefore, specific local buckling constraints are not used . Instead, a linear buckling analysis or a geometrically non‐linear analysis is used to compute the critical buckling load. Buckling constraints have been used with several continuum topology optimization methods including simple isotropic material with penalization , evolutionary structural optimization and a nodal design variable method .…”

“…Instead, a linear buckling analysis or a geometrically non‐linear analysis is used to compute the critical buckling load. Buckling constraints have been used with several continuum topology optimization methods including simple isotropic material with penalization , evolutionary structural optimization and a nodal design variable method . The level‐set method is another approach to continuum topology optimization that has received significant attention in the last 10years .…”

Structural topology optimization for maximum linear buckling loads by using a moving iso-surface threshold method

“…In this paper, a moving iso-surface threshold method (MIST) recently developed (Tong and Lin 2011;Vasista and Tong 2012) will be used to address the following challenging issues in linear buckling optimization. Topology optimization considering structural buckling is quite complicated and convergence is often relatively poor (Neves et al 2002;Bendsoe and Sigmund 2003;Rahmatalla and Swan 2003;Bruyneel et al 2008) owing to a number of issues, e.g. : (a) omitting stress state variations in sensitivity analysis, (b) spurious local buckling, (c) multiple mode shapes, and (d) lack of effective load-path.…”

In-plane optimization of truss arch footbridges using stability and serviceability objective functions

“…The objective functions employed to improve buckling resistance either directly target buckling by maximizing the critical buckling load factor or indirectly by minimizing structural compliance (Rahmatalla and Swan 2003a). These two objective functions have been investigated using linear and nonlinear approaches and applied to traditional topology optimization problems pertaining to the conceptual designs of long span bridges (Rahmatalla and Swan 2003b), a footbridge composed of thin shell elements (Fauche et al 2010), and curved beams prone to snapthrough buckling (Lindgaard and Dahl 2013). As minimizing the nonlinear compliance and maximizing the critical nonlinear limit load can be computationally expensive, due to the incremental-iterative analysis required to generate the objective function value, it is computationally advantageous to determine whether objective functions related to the stability and serviceability performance measures of linear buckling, linear compliance, fundamental frequency, and deflection can improve the nonlinear response of truss arch footbridges.…”