Reliability-based topology optimization

Kharmanda, Ghias; Olhoff, Niels; Mohamed, Alaa; Lemaire, Maurice

doi:10.1007/s00158-003-0322-7

Cited by 354 publications

(157 citation statements)

References 21 publications

Supporting

Mentioning

153

Contrasting

Unclassified

Order By: Relevance

“…Since mid-2000 there has been increasing research on reliability based topology optimization (RBTO) considering uncertainties in loads, material, boundary geometry or fabrication. Since this work doesn't directly build on earlier RBTO contributions, we simply refer to Deaton and Grandhi (2014) for literature survey, and to select papers for further reading: Maute and Frangopol (2003), Kharmanda et al (2004), Jung and Cho (2004), Guest and Igusa (2008), Silva et al (2010), Chen et al (2010), Chen and Chen (2011), Lazarov et al (2012), Nguyen et al (2011), Rozvany and Maute (2011), Tootkaboni et al (2012), Wang et al (2006). However, as also pointed out by Jansen et al (2014), due to the binary nature of failure definition it is difficult to treat failsafe requirement within statistics based RBTO framework.…”

Section: Introductionmentioning

confidence: 99%

Fail-safe topology optimization

Zhou

Fleury

2016

Struct Multidisc Optim

View full text Add to dashboard Cite

Fail-safe robustness of critical load carrying structures is an important design philosophy for aerospace industry. The basic idea is that a structure should be designed to survive normal loading conditions when partial damage occurred. Such damage is quantified as complete failure of a structural member, or a partial damage of a larger structural part. In the context of topology optimization fail-safe consideration was first proposed by Jansen et al. Struct Multidiscip Optim 49(4):657-666, (2014). While their approach captures the essence of fail-safe requirement, it has two major shortcomings: (1) it involves analysis of a very large number of FEA models at the scale equal to the number of elements; (2) failure was introduced in generic terms and therefore the fundamental aspects of failure test of discrete members was not discussed. This paper aims at establishing a rigorous framework for failsafe topology optimization of general 3D structures, with the goal to develop a computationally viable solution for industrial applications. We demonstrate the effectiveness of the proposed approach on several examples including a 3D example with over three hundred thousand elements.

show abstract

Section: Introductionmentioning

confidence: 99%

Fail-safe topology optimization

Zhou

Fleury

2016

Struct Multidisc Optim

View full text Add to dashboard Cite

show abstract

“…Reliability-based structural design methods have been investigated extensively based on the framework of probabilistic uncertainty models [Kharmanda et al 2004;Zang et al 2005]. Nonprobabilistic Keywords: data uncertainty, linear program, plastic limit analysis, robust optimization, info-gap analysis.…”

Section: Introductionmentioning

confidence: 99%

Robustness analysis of structures based on plastic limit analysis with uncertain loads

Matsuda

Kanno

2008

JOMMS

View full text Add to dashboard Cite

This paper presents a method for computing an info-gap robustness function of structures, which is regarded as one measure of structural robustness, under uncertainties associated with the limit load factor. We assume that the external load in the plastic limit analysis is uncertain around its nominal value. Various uncertainties are considered for the live, dead, and reference disturbance loads based on the nonstochastic info-gap uncertainty model. Although the robustness function is originally defined by using the optimization problem with infinitely many constraints, we show that the robustness function is obtained as an optimal value of a linear programming (LP) problem. Hence, we can easily compute the info-gap robustness function associated with the limit load factor by solving an LP problem. As the second contribution, we show that the robust structural optimization problems of trusses and frames can also be reduced to LP problems. In numerical examples, the robustness functions, as well as the robust optimal designs, are computed for trusses and framed structures by solving LP problems.

show abstract

Section: Introductionmentioning

confidence: 99%

Untitled

2008

JOMMS

View full text Add to dashboard Cite

See inside back cover or http://www.jomms.org for submission guidelines.Regular subscription rate: $500 a year.Subscriptions, requests for back issues, and changes of address should be sent to Mathematical Sciences Publishers, 798 Evans Hall, Department of Mathematics, University of California, Berkeley, CA 94720-3840. ELASTIC CONSTANTS AND THERMAL EXPANSION AVERAGES OF A NONTEXTURED POLYCRYSTAL ROLAND DEWITThis paper gives expressions for the overall average elastic constants and thermal expansion coefficients of a polycrystal in terms of its single crystal components. The polycrystal is assumed to be statistically homogeneous, isotropic, and perfectly disordered. Upper and lower bounds for the averages are easily found by assuming a uniform strain or stress. The upper bound follows from Voigt's assumption that the total strain is uniform within the polycrystal while the lower bound follows from Reuss' original assumption that the stress is uniform. A self-consistent estimate for the averages can be found if it is assumed that the overall response of the polycrystal is the same as the average response of each crystallite. The derivation method is based on Eshelby's theory of inclusions and inhomogeneities. We define an equivalent inclusion, which gives an expression for the strain disturbance of the inhomogeneity when external fields are applied. The equivalent inclusion is then used to represent the crystallites. For the self-consistent model the average response of the grains has to be the same as the overall response of the material, or the average strain disturbance must vanish. The result is an implicit equation for the average polycrystal elastic constants and an explicit equation for the average thermal expansion coefficients. For the particular case of cubic symmetry the results can be reduced to a cubic equation for the selfconsistent shear modulus. For lower symmetry crystals it is best to calculate the self-consistent bulk and shear modulus numerically. IntroductionA polycrystal, whose properties vary in a complicated fashion from point to point over a small microscopic length scale, may appear on average to be uniform or perhaps, more generally, its properties appear to vary smoothly. The determination of such overall properties from the properties and geometrical arrangement of the constituent monocrystal grains is our aim. In the simplest case the polycrystal is assumed to be statistically homogeneous, isotropic, and perfectly disordered. General expressions for averages can then be derived. Many different properties can be averaged, such as dielectric constants, diffusivity, elastic constants, electrical conductivity, magnetic permeability, magnetostriction, piezoelectric constants, thermal conductivity, or thermal expansion. In this paper we treat the elastic constants, which have already received more attention than most other physical properties, and the thermal expansion. Elastic constants are fundamental physical data needed for the characterization of materials. In addition to their fundam...

show abstract

Reliability-based topology optimization

Cited by 354 publications

References 21 publications

Fail-safe topology optimization

Fail-safe topology optimization

Robustness analysis of structures based on plastic limit analysis with uncertain loads

Untitled

Contact Info

Product

Resources

About