A novel stress influence function (SIF) methodology for stress-constrained continuum topology optimization
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RESEARCH PAPER
A novel stress influence function (SIF) methodology for stress-constrained continuum topology optimization Haijun Xia 1 & Zhiping Qiu 1 Received: 12 October 2019 / Revised: 18 March 2020 / Accepted: 22 April 2020 # Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract This study presents a new stress influence function (SIF) methodology for continuum topology optimization under consideration of local strength failure. Firstly, the qp-relaxation criterion is involved to circumvent the stress singularity. To deal with the largescale stress constraints in topology optimization, the local stress constraint is reflected in the objective along with the material volume by multiplication, and the weight of stress is characterized by stress influence function. Meanwhile, three types of stress influence functions are proposed for comparison. By means of the study on the characteristic of high-stress elements, the rationality of the SIF methodology is illustrated, in which the proposed method may achieve the full-stress state of high-stress element. Numerical examples are given to demonstrate the applicability and validity of the proposed methodology. It is shown that the proposed methodology can obtain reasonable results. Consequently, the proposed SIF methodology provides a novel strategy with high computational efficiency for topology optimization considering local strength failure. Keywords Stress influence function . Continuum topology optimization . Local strength failure . Local stress constraint
1 Introduction In the wake of developments in science and technology, topology optimization has become a popular design tool in engineering structures since the pioneering research by Bendsøe and Kikuchi (Bendsøe and Kikuchi 1988). Over the past few decades, a large number of studies on topology optimization have been published (Zhu et al. 2015; Mei and Wang 2004; Xie and Steven 1993; Rozvany et al. 1992; Wang et al. 2019; Xia et al. 2020; Qiu et al. 2019). However, most of the developments have concentrated on minimizing structural compliance with a given amount of material despite the fact that stress constraints are important (Duysinx et al. 2009). Most likely, several challenges arise when including stress constraints in topology optimization. Responsible Editor: Xu Guo Electronic supplementary material The online version of this article (https://doi.org/10.1007/s00158-020-02615-2) contains supplementary material, which is available to authorized users. * Zhiping Qiu [email protected] 1
Institute of Solid Mechanics, School of Aeronautic Science and Engineering, Beihang University, Beijing 100083, People’s Republic of China
The first challenge is related to the so-called singular optima. Sved and Ginos (Sved and Ginos 1968) first observed it in truss topology optimization. They demonstrated on a simple three-bar truss problem that the optimum cannot necessarily be reached by gradient-based optimization as the stress constraints prevent reducing the cross-sectional area of the bar to zero. T
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