Abstract
This paper presents an adaptive continuation method for buckling topology optimization of continuum structures using the Solid Isotropic Material with Penalization (SIMP) model. For optimization problems of minimizing structural compliance subject to constraints on material volume and buckling load factors, it has been found that the conflict between the requirements for structural stiffness and stability may have an adverse impact on the performance of existing optimization algorithms. An automatic scheme for adjusting the penalization parameter is introduced to deal with this conflict and thus achieves better designs. Based on an investigation on the effect of the penalization parameter on design evolution during the optimization process, a rule is established to determine the appropriate penalization parameter values. Using this rule, an effective scheme is developed for determining the penalization parameter values such that the buckling constraints are appropriately considered throughout the optimization process. Numerical examples are presented to illustrate the effectiveness of the proposed method.
Highlights
Topology optimization has significantly progressed since the fundamental work of Bendsøe and Kikuchi [1988] and is an effective tool for structural design in different engineering fields [Chen et al, 2015; Cai et al, 2016; Solovyev and Duong, 2016]
To overcome deficiencies in the existing methods, the present study develops an adaptive continuation method based upon the continuation method [Rozvany, 2009] and the previous studies by the authors [Gao and Ma, 2015]
A novel adaptive continuation method has been developed for compliance minimization of continuum structures subject to constraints on material volume and buckling load factors
Summary
Topology optimization has significantly progressed since the fundamental work of Bendsøe and Kikuchi [1988] and is an effective tool for structural design in different engineering fields [Chen et al, 2015; Cai et al, 2016; Solovyev and Duong, 2016]. The compliance minimization problem with volume constraint has been widely studied [He et al, 2015] and various methods have been proposed to maximize structural stiffness. The Solid Isotropic Material with Penalization (SIMP) material model has been widely applied to solve various topology optimization problems and is reasonably effective in a majority of situations When this model is used for eigenvalue optimization problems, pseudo eigenmodes may appear in low-density regions during the optimization process, causing numerical difficulties [Neves et al, 1995, 2002]. In an earlier work of Gao and Ma [2015], the authors have shown that a conventional algorithm with a fixed penalization parameter might not work well for a topology optimization problem with buckling constraints and proposed two-phase algorithms.
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