Topology optimization of three-dimensional structures subject to self-weight loading

IF 1.5 4区 工程技术 Q3 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS
Jorge Morvan Marotte Luz Filho, Antonio Andre Novotny
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引用次数: 0

Abstract

PurposeTopology optimization of structures under self-weight loading is a challenging problem which has received increasing attention in the past years. The use of standard formulations based on compliance minimization under volume constraint suffers from numerous difficulties for self-weight dominant scenarios, such as non-monotonic behaviour of the compliance, possible unconstrained character of the optimum and parasitic effects for low densities in density-based approaches. This paper aims to propose an alternative approach for dealing with topology design optimization of structures into three spatial dimensions subject to self-weight loading.Design/methodology/approachIn order to overcome the above first two issues, a regularized formulation of the classical compliance minimization problem under volume constraint is adopted, which enjoys two important features: (a) it allows for imposing any feasible volume constraint and (b) the standard (original) formulation is recovered once the regularizing parameter vanishes. The resulting topology optimization problem is solved with the help of the topological derivative method, which naturally overcomes the above last issue since no intermediate densities (grey-scale) approach is necessary.FindingsA novel and simple approach for dealing with topology design optimization of structures into three spatial dimensions subject to self-weight loading is proposed. A set of benchmark examples is presented, showing not only the effectiveness of the proposed approach but also highlighting the role of the self-weight loading in the final design, which are: (1) a bridge structure is subject to pure self-weight loading; (2) a truss-like structure is submitted to an external horizontal force (free of self-weight loading) and also to the combination of self-weight and the external horizontal loading; and (3) a tower structure is under dominant self-weight loading.Originality/valueAn alternative regularized formulation of the compliance minimization problem that naturally overcomes the difficulties of dealing with self-weight dominant scenarios; a rigorous derivation of the associated topological derivative; computational aspects of a simple FreeFEM implementation; and three-dimensional numerical benchmarks of bridge, truss-like and tower structures.
承受自重荷载的三维结构拓扑优化
目的 自重荷载下的结构拓扑优化是一个具有挑战性的问题,近年来受到越来越多的关注。对于自重占主导地位的情况,使用基于体积约束下顺应性最小化的标准公式存在诸多困难,例如顺应性的非单调行为、最佳值可能不受约束的特点以及基于密度的方法中低密度的寄生效应。为了克服上述前两个问题,本文采用了体积约束下经典顺应性最小化问题的正则化表述,该表述有两个重要特点:(a) 它允许施加任何可行的体积约束;(b) 一旦正则化参数消失,就能恢复标准(原始)公式。在拓扑导数法的帮助下,拓扑优化问题得以解决,由于不需要采用中间密度(灰度)方法,因此自然而然地克服了上述最后一个问题。本文介绍了一组基准实例,不仅显示了所提方法的有效性,而且突出了自重荷载在最终设计中的作用,这些实例是(1) 桥梁结构承受纯自重荷载;(2) 类桁架结构承受外部水平力(无自重荷载)以及自重和外部水平荷载的组合;(3) 塔式结构承受主要自重荷载。独创性/价值 对顺应性最小化问题的另一种正则化表述,自然地克服了处理自重主导情况的困难;相关拓扑导数的严格推导;简单的 FreeFEM 实现的计算方面;以及桥梁、类桁架和塔式结构的三维数值基准。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Engineering Computations
Engineering Computations 工程技术-工程:综合
CiteScore
3.40
自引率
6.20%
发文量
61
审稿时长
5 months
期刊介绍: The journal presents its readers with broad coverage across all branches of engineering and science of the latest development and application of new solution algorithms, innovative numerical methods and/or solution techniques directed at the utilization of computational methods in engineering analysis, engineering design and practice. For more information visit: http://www.emeraldgrouppublishing.com/ec.htm
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