A Thermo-elastic Analogy for High-order Curvilinear Meshing with Control of Mesh Validity and Quality

Moxey, David; Ekelschot, Dirk; Keskin, Ümit; Sherwin, Spencer J.; Peiró, Joaquim

doi:10.1016/j.proeng.2014.10.378

Cited by 25 publications

(21 citation statements)

References 10 publications

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“…Alternative solid mechanics methodologies have been developed in the past, based on a variety of linearised elasticity approaches [1,56,77]. It is worth emphasising that, to guarantee and/or maintain previously mentioned mathematical requirements for the linearised strain energy density, a linearised solid mechanics approach must emanate from an underlying non-linear variational principle, as the notion of objectivity and polyconvexity cannot be invoked in small strains.…”

Section: A Consistent Incrementally Linearised Solid Mechanics Approachmentioning

confidence: 99%

“…C 0 and the geometric stiffness term is absent from the formulation. The technique developed by [56] falls into this category. 3.…”

Section: A Consistent Incrementally Linearised Solid Mechanics Approachmentioning

confidence: 99%

“…It is worth noting that the approach pursued in [56,77] corresponds to a linear elastic approach with only the geometry being updated at each increment x = x n .…”

Section: The Classical Linear Elastic Casementioning

confidence: 99%

“…In order to alleviate this problem, it is possible to split the desired (potentially large) displacement of boundary nodes into smaller load increments. Other approaches to increase the robustness of the linear elastic analogy have been recently introduced, see for instance [56], where pseudo thermal effects are introduced. It is worth noting that mesh moving strategies based on an elastic analogy have also been proposed and successfully used with a proven track record of robustness in the low-order context [39,68,69].…”

Section: Introductionmentioning

confidence: 99%

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A unified approach for a posteriori high-order curved mesh generation using solid mechanics

2016

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The paper presents a unified approach for the a posteriori generation of arbitrary high-order curvilinear meshes via a solid mechanics analogy. The approach encompasses a variety of methodologies, ranging from the popular incremental linear elastic approach to very sophisticated non-linear elasticity. In addition, an intermediate consistent incrementally linearised approach is also presented and applied for the first time in this context. Utilising a consistent derivation from energy principles, a theoretical comparison of the various approaches is presented which enables a detailed discussion regarding the material characterisation (calibration) employed for the different solid mechanics formulations. Five independent quality measures are proposed and their relations with existing quality indicators, used in the context of a posteriori mesh generation, are discussed. Finally, a comprehensive range of numerical examples, both in two and three dimensions, including challenging geometries of interest to the solids, fluids and electromagnetics communities, are shown in order to illustrate and thoroughly compare the performance of the different methodologies. This comparison considers the influence of material parameters and number of load increments on the quality of the generated high-order mesh, overall computational cost and, crucially, the approximation properties of the resulting mesh

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Section: A Consistent Incrementally Linearised Solid Mechanics Approachmentioning

confidence: 99%

“…C 0 and the geometric stiffness term is absent from the formulation. The technique developed by [56] falls into this category. 3.…”

Section: A Consistent Incrementally Linearised Solid Mechanics Approachmentioning

confidence: 99%

“…It is worth noting that the approach pursued in [56,77] corresponds to a linear elastic approach with only the geometry being updated at each increment x = x n .…”

Section: The Classical Linear Elastic Casementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A unified approach for a posteriori high-order curved mesh generation using solid mechanics

2016

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“…We note that this work is an extension of the initial implementation introduced in [14]. The goal of this work is to give a detailed derivation of the thermal stress terms, which differs from [14] in the choice of the isoparametric mapping that is used to determine the thermal stress.…”

Section: Introductionmentioning

confidence: 99%

High-order curvilinear meshing using a thermo-elastic analogy

Moxey

Ekelschot

Keskin

et al. 2016

Computer-Aided Design

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A study of properties of adaptive quadratic grids for three‐dimensional near‐surface field computations

Kallinderis

Lymperopoulou

Spyridonos

et al. 2019

Numerical Methods in Fluids

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Summary Curved geometries and the corresponding near‐surface fields typically require a large number of linear computational elements. High‐order numerical solvers have been primarily used with low‐order meshes. There is a need for curved, high‐order computational elements. Typical near‐surface meshes consist of hexahedral and/or prismatic elements. The present work studies the employment of quadratic meshes that are relatively coarse for field simulations. Directionally quadratic high‐order elements are proposed for the near‐surface field regions. The quadratic meshes are compared with the conventional low‐order ones in terms of accuracy and efficiency. The cases considered include closed surface volume calculations, as well as computation of gradients of several analytic fields. A special method of adaptive local quadratic meshes is proposed and evaluated. Truncation error analysis for quadratic grids yields comparison with the conventional linear hexahedral/prismatic meshes, which are subject to typical distortions such as stretching, skewness, and torsion.

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A Thermo-elastic Analogy for High-order Curvilinear Meshing with Control of Mesh Validity and Quality

Cited by 25 publications

References 10 publications

A unified approach for a posteriori high-order curved mesh generation using solid mechanics

A unified approach for a posteriori high-order curved mesh generation using solid mechanics

High-order curvilinear meshing using a thermo-elastic analogy

A study of properties of adaptive quadratic grids for three‐dimensional near‐surface field computations

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