Accuracy Analysis of the Semi-Analytical Method for Shape Sensitivity Calculation∗

Barthelemy, Bruno; Haftka, Raphael T.

doi:10.1080/08905459008915677

Cited by 70 publications

(9 citation statements)

References 6 publications

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“…In that case, it is desirable to look for simpler examples with similar characteristics. For example, Barthelemy and Haftka (1990) became aware of the accuracy problems of the semi-analytical method for shape sensitivity of static response when calculating derivatives of car finite element models. They looked for a simple problem that would illustrate the difficulty and found that it could be reproduced with a cantilever beam.…”

Section: Structuring Research So That It Is Easily Reproducedmentioning

confidence: 99%

Replication of results

Haftka

Zhou

Queipo

2019

Struct Multidisc Optim

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Section: Structuring Research So That It Is Easily Reproducedmentioning

confidence: 99%

Replication of results

Haftka

Zhou

Queipo

2019

Struct Multidisc Optim

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“…This is addressed in the work of Wang et al [Wang and Poh (2018)]. Despite the fact that SA approach is computationally efficient and popular, the accuracy of the sensitivity analysis can be relatively unsatisfactory for some special cases [Barthelemy and Haftka (1990)].…”

Section: Semi-analytical (Sa) Approachesmentioning

confidence: 99%

Structural Design Optimization Using Isogeometric Analysis: A Comprehensive Review

Wang¹,

Wang²,

Xia³

et al. 2018

CMES

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Isogeometric analysis (IGA), an approach that integrates CAE into conventional CAD design tools, has been used in structural optimization for 10 years, with plenty of excellent research results. This paper provides a comprehensive review on isogeometric shape and topology optimization, with a brief coverage of size optimization. For isogeometric shape optimization, attention is focused on the parametrization methods, mesh updating schemes and shape sensitivity analyses. Some interesting observations, e.g. the popularity of using direct (differential) method for shape sensitivity analysis and the possibility of developing a large scale, seamlessly integrated analysis-design platform, are discussed in the framework of isogeometric shape optimization. For isogeometric topology optimization (ITO), we discuss different types of ITOs, e.g. ITO using SIMP (Solid Isotropic Material with Penalization) method, ITO using level set method, ITO using moving morphable components (MMC), ITO with phase field model, etc., their technical details and applications such as the spline filter, multi-resolution approach, multi-material problems and stress constrained problems. In addition to the review in the last 10 years, the current developmental trend of isogeometric structural optimization is discussed.

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“…Mahnken and Stein (1996) and Cooreman et al (2007) applied such procedure in the case of viscoplastic and elastice plastic constitutive models, respectively. Some authors proposed other determination schemes such as the mixed technique based on the semi-analytical method using the finite differentiation and analytical derivatives (Massoni et al, 2002;Barthelemy and Haftka, 1990), or adjoint methods (Bonnet, 1999;Tortorelli and Michaleris, 1994).…”

Section: Selection Of the Parameter Identification Strategy For Supermentioning

confidence: 99%

Parameter identification of a thermodynamic model for superelastic shape memory alloys using analytical calculation of the sensitivity matrix

Meraghni

Chemisky

Piotrowski

et al. 2014

European Journal of Mechanics - A/Solids

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IThis paper presents an identification procedure for the parameters of a thermodynamically based constitutive model for Shape memory Alloys (SMAs). The proposed approach is a gradient-based method and utilizes an analytical computation of the sensitivity matrix. For several loading cases, including superelasticity, that are commonly utilized for the model parameters identification of such a constitutivemodel, a closed-form of the total infinitesimal strain is derived. The partial derivatives of this state variable are developed to find the components of the sensitivity matrix. A LevenbergeMarquardt algorithm is utilized to solve the inverse problem and find the best set of model parameters for specific SMA materials. Moreover, a pre-identification method, based on the second derivative of the total strain components is proposed. This provides a suitable initial set of model parameters, which increases theefficiency of the inverse method. The proposed approach is applied for the simultaneous identification of the non-linear constitutive parameters for two superelastic SMAs. The comparison between experimental and numerical curves obtained for different temperatures shows the capabilities of the developedidentification approach. The robustness and the efficiency of the developed approach are then experimentally validatedInternational audienceThis paper presents an identification procedure for the parameters of a thermodynamically based constitutive model for Shape memory Alloys (SMAs). The proposed approach is a gradient-based method and utilizes an analytical computation of the sensitivity matrix. For several loading cases, including superelasticity, that are commonly utilized for the model parameters identification of such a constitutivemodel, a closed-form of the total infinitesimal strain is derived. The partial derivatives of this state variable are developed to find the components of the sensitivity matrix. A LevenbergeMarquardt algorithm is utilized to solve the inverse problem and find the best set of model parameters for specific SMA materials. Moreover, a pre-identification method, based on the second derivative of the total strain components is proposed. This provides a suitable initial set of model parameters, which increases theefficiency of the inverse method. The proposed approach is applied for the simultaneous identification of the non-linear constitutive parameters for two superelastic SMAs. The comparison between experimental and numerical curves obtained for different temperatures shows the capabilities of the developedidentification approach. The robustness and the efficiency of the developed approach are then experimentally validate

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Accuracy Analysis of the Semi-Analytical Method for Shape Sensitivity Calculation∗

Cited by 70 publications

References 6 publications

Replication of results

Replication of results

Structural Design Optimization Using Isogeometric Analysis: A Comprehensive Review

Parameter identification of a thermodynamic model for superelastic shape memory alloys using analytical calculation of the sensitivity matrix

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