Transverse stress profiles reconstruction for finite element analysis of laminated plates

Miranda, Stefano de; Patruno, L.; Ubertini, Francesco

doi:10.1016/j.compstruct.2012.03.026

Cited by 13 publications

(4 citation statements)

References 17 publications

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“…As a last remark, it is worth noticing that the proposed approach can be easily extended to high‐order schemes. In particular, the polynomial representation of the homogeneous part of the stress field P can be enriched to become a complete representation base of equilibrated stress fields up to an arbitrary degree (see, for instance, the work of de Miranda et al). Numerous variants of the presented techniques can be developed by varying the underlying VEM formulation, P , the size of the patch (ie, the number of hems around the central element used to identify the patch) and their construction procedure (eg, node patches might be considered).…”

Section: Recovery By Compatibility In Patchesmentioning

confidence: 99%

“…Moreover, it has been already successfully applied to a posteriori error estimation as well as to drive adaptive mesh refinement . Moreover, it has been shown to be particularly well suited for transverse stresses profile reconstruction in plate bending problems for which, thanks to its equilibrating nature, it leads to the automatic fulfillment of the pointwise equilibrium at the plate top and bottom surfaces …”

Section: Introductionmentioning

confidence: 99%

“…38 Moreover, it has been shown to be particularly well suited for transverse stresses profile reconstruction in plate bending problems for which, thanks to its equilibrating nature, it leads to the automatic fulfillment of the pointwise equilibrium at the plate top and bottom surfaces. 39 The key idea underlying RCP is to minimize the complementary energy associated to a patch of elements treated as an isolated system among a set of equilibrated stress fields. In particular, on each patch, stresses are approximated as a linear combination of self-equilibrated stress modes enriched by an appropriate particular solution.…”

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confidence: 99%

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An equilibrium‐based stress recovery procedure for the VEM

Artioli

Miranda

Lovadina

et al. 2018

Numerical Meth Engineering

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Summary Within the framework of the displacement‐based virtual element method (VEM), namely, for plane elasticity, an important topic is the development of optimal techniques for the evaluation of the stress field. In fact, in the classical VEM formulation, the same projection operator used to approximate the strain field (and then evaluate the stiffness matrix) is employed to recover, via constitutive law, the stress field. Considering a first‐order formulation, strains are locally mapped onto constant functions, and stresses are piecewise constant. However, the virtual displacements might engender more complex strain fields for polygons, which are not triangles. This leads to an undesirable loss of information with respect to the underlying virtual stress field. The recovery by compatibility in patches, originally proposed for finite element schemes, is here extended to VEM, aiming at mitigating such an effect. Stresses are recovered by minimizing the complementary energy of patches of elements over an assumed set of equilibrated stress modes. The procedure is simple, efficient, and can be readily implemented in existing codes. Numerical tests confirm the good performance of the proposed technique in terms of accuracy and indicate an increase of convergence rate with respect to the classical approach in many cases.

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Section: Recovery By Compatibility In Patchesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

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An equilibrium‐based stress recovery procedure for the VEM

Artioli

Miranda

Lovadina

et al. 2018

Numerical Meth Engineering

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“…The key idea of RCP is to minimise the complementary energy associated to a patch of elements treated as an isolated system [19]. Such operation allows to enforce equilibrium, which might be desirable in some applications (see for instance [36]), as well as to increase the accuracy of the obtained stress field. In this work, RCP is presented for degenerate patches composed of a single virtual element.…”

Section: Recovery By Compatibility In Patchesmentioning

confidence: 99%

Virtual Element Method: an equilibrium-based stress recovery procedure

Artioli,

de Miranda,

Lovadina

et al. 2018

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Within the framework of the displacement-based Virtual Element Method (VEM) for plane elasticity a significant problem is represented by an accurate evaluation of the stress field. In particular, in the classical VEM formulation, a suitable operator which maps to the strain field is introduced in order to allow the calculation of the stiffness matrix. The stress field is then computed using that strian field, by using the constitutive law. Considering for example a first-order formulation for a homogeneous material, strains are locally mapped onto constant functions, and stresses are accordingly piecewise constant. However, the virtual displacements might engender more complex strain fields for polygons which are not triangles. In this paper, Recovery by Compatibility in Patches is used in order to mitigate such an effect and, thus, enhance the accuracy of the recovered stress field. The procedure is simple, efficient and can be readily implemented in existing codes. Numerical tests confirm the soundness of the proposed approach.

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