Topological optimization of structures subject to Von Mises stress constraints

Amstutz, Samuel; Novotny, Antônio André

doi:10.1007/s00158-009-0425-x

Cited by 133 publications

(86 citation statements)

References 23 publications

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“…where W eb are the filter weights defined in (2). We note that the gradient of the mass is affected by neighboring design variables through the filter.…”

Section: Sensitivity Analysismentioning

confidence: 99%

“…The L-shaped beam is a popular test example for stress constrained topology optimization, see [13], [14], [20], [21] among others and also [1], [2] and [16] for the Lshaped beam optimized using the level set method. The design domain of the L-shaped beam contains an internal corner with an initial geometric stress singularity, see Figure 4.…”

Section: The L-shaped Beammentioning

confidence: 99%

“…Allaire and Jouve [1], Amstutz and Novoty [2] and Guo et al [16]. In the level set approach two phases, typically representing solid material or voids, are used and as the stress constraints only are applied to the solid phase, no singularity problems occur.…”

Section: Introductionmentioning

confidence: 99%

“…The final designs are also free from the transition layer of intermediate design variable values between solid and voids that remain for filtered SIMP-based formulations. How-ever, the large number of design variables remain and a global stress measure that approximates local stresses [1], [2], or an active set strategy [16] is used in order to reduce the computational cost.…”

Section: Introductionmentioning

confidence: 99%

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Stress constrained topology optimization

Holmberg

Torstenfelt

Klarbring

2013

Struct Multidisc Optim

336

167

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This paper develops and evaluates a method for handling stress constraints in topology optimization. The stress constraints are used together with an objective function that minimizes mass or maximizes stiffness, and in addition, the traditional stiffness based formulation is discussed for comparison. We use a clustering technique, where stresses for several stress evaluation points are clustered into groups using a modified P-norm to decrease the number of stress constraints and thus the computational cost. We give a detailed description of the formulations and the sensitivity analysis. This is done in a general manner, so that different element types and 2D as well as 3D structures can be treated. However, we restrict the numerical examples to 2D structures with bilinear quadrilateral elements.The three formulations and different approaches to stress constraints are compared using two well known test examples in topology optimization: the L-shaped beam and the MBB-beam. In contrast to some other papers on stress constrained topology optimization, we find that our formulation gives topologies that are significantly different from traditionally optimized designs, in that it actually manage to avoid stress concentrations. It can therefore be used to generate conceptual designs for industrial applications.

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“…where W eb are the filter weights defined in (2). We note that the gradient of the mass is affected by neighboring design variables through the filter.…”

Section: Sensitivity Analysismentioning

confidence: 99%

Section: The L-shaped Beammentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Stress constrained topology optimization

Holmberg

Torstenfelt

Klarbring

2013

Struct Multidisc Optim

336

167

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show abstract

“…Duysinx and Sigmund (1998); Svanberg and Werme (2007); Bruggi and Venini (2008); Le et al (2010); Cheng and Jiang (1992); Allaire and Jouve (2008); Allaire et al (2011Allaire et al ( , 2014; Ha and Cho (2008); Yamasaki et al (2011)) and a number of other papers. In the work of (Amstutz and Novotny 2010) the authors present a topology optimization method which utilizes a p-norm stress measure with very high p's such that the locality of stresses is resolved. Common for the aforementioned topology optimization methods is that they all use implicit representation of boundaries and a smoothed von Mises stress measure for the objectives and/or constraints.…”

Section: Introductionmentioning

confidence: 99%

Combined shape and topology optimization for minimization of maximal von Mises stress

Lian

Christiansen

Tortorelli

et al. 2017

Struct Multidisc Optim

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Optimal topology design of continuum structures with stress concentration alleviation via level set method

Zhang

Guo

Wang

et al. 2012

Numerical Meth Engineering

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SUMMARY Although the phenomenon of stress concentration is of paramount importance to engineers when they are designing load‐carrying structures, stiffness is often used as the solely concerned objective or constraint functional in the studies of optimal topology design of continuum structures. Sometimes this will lead to optimal designs with severe stress concentrations that may be highly responsible for the fracture, creep, and fatigue of structures. The aim of the present work is to develop some effective numerical techniques for designing stiff structures with less stress concentrations. This is achieved by introducing some specific stress measures, which are sensitive to the existence of high local stresses, in the problem formulation and resolving the corresponding optimization problem numerically in a level set framework. Our study indicates that with use of the proposed numerical schemes, some intrinsic difficulties in stress‐related topology optimization of continuum structures can be overcome in a natural way. Copyright © 2012 John Wiley & Sons, Ltd.

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Topological optimization of structures subject to Von Mises stress constraints

Cited by 133 publications

References 23 publications

Stress constrained topology optimization

Stress constrained topology optimization

Combined shape and topology optimization for minimization of maximal von Mises stress

Optimal topology design of continuum structures with stress concentration alleviation via level set method

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