Accuracy and optimal meshes in finite element computation for nearly incompressible materials

Ladevèze, Pierre; Marin, Philippe; Pelle, Jean-Pierre; Gastine, J. L.

doi:10.1016/0045-7825(92)90057-q

Cited by 60 publications

(31 citation statements)

References 9 publications

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“…The criterion used to define the size of the elements in new meshes is based on the criterion of minimization of the number of elements in the new mesh described by Ladeveze et al [26,27] and Coorevits et al [28]. Figure 10 shows two sequences of h-adapted meshes, obtained with quadratic triangles and quadrilaterals, used to analyse the problem represented in Figure 9.…”

Section: Domain With Straight Boundariesmentioning

confidence: 99%

A hierarchical h adaptivity methodology based on element subdivision

Ródenas

Albelda

Tur

et al. 2017

revuin

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Este artículo puede compartirse bajo la licencia CC BY-ND 4.0 y se referencia usando el siguiente formato: J.J. Ródenas, J.Albelda, M. Tur, F.J. Fuenmayor, "A hierarchical h adaptivity methodology based on element subdivision", UIS Ingenierías, vol. 16, no. ABSTRACTThis paper presents a hierarchical h adaptive methodology for Finite Element Analysis based on the hierarchical relations between parent and child elements that come out if these elements are geometrically similar. Under this similarity condition the terms involved in the evaluation of element stiffness matrices of parent and child elements are related by a constant which is a function of the element sizes ratio (scaling factor). These relations have been the basis for the development of a hierarchical h adaptivity methodology based on element subdivision and the use of multipoint-constraints to ensure C 0 continuity. The use of a hierarchical data structure significantly reduces the amount of calculations required for the mesh refinement, the evaluation of the global stiffness matrix, element stresses and element error estimation. The data structure also produces a natural reordering of the global stiffness matrix that improves the behaviour of the Cholesky factorization. KEYWORDS:Adaptive Modelling, Hierarchical properties, Mesh Enrichment, Mesh Generation. RESUMENEn este artículo se presenta una metodología h adaptativa para el Análisis por Elementos Finitos basada en las relaciones jerárquicas entre elementos padre e hijo que surgen si estos elementos son geométricamente similares. Bajo esta condición de similitud, los términos resultantes de la evaluación de las matrices de rigidez de elementos padre e hijo están relacionados por una constante que es una función de la relación de tamaños de elemento (factor de escala). Estas relaciones han sido la base para el desarrollo de una metodología jerárquica h adaptativa basada en la subdivisión de elementos y el uso de restricciones multipunto para asegurar la continuidad C 0 . El uso de una estructura de datos jerárquica reduce significativamente la cantidad de cálculos requeridos para el refinamiento de la malla, la evaluación de la matriz de rigidez global, las tensiones de los elementos y la estimación del error del elemento. La estructura de datos también produce un reordenamiento natural de la matriz de rigidez global que mejora el comportamiento de la factorización de Cholesky. PALABRAS CLAVE:Modelado Adaptativo, Propiedades jerárquicas, Enriquecimiento de malla, Mallado.

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Section: Domain With Straight Boundariesmentioning

confidence: 99%

A hierarchical h adaptivity methodology based on element subdivision

Ródenas

Albelda

Tur

et al. 2017

revuin

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“…in the definition of (31). These are: (i) w 1 = 1 (see for example [25], [32]) (equilibration of Type A);…”

Section: B Element Residual Estimators With Various Types Of Equilibmentioning

confidence: 99%

“…Specific choices of solutions are suggested in [8], [25], [32], [60] and [61]; in the numerical implementations we employed these choices. Below we give the definition of the edgewise-linear correction 0, (q-degree (q _> 1) polynomial representation of the correction 0, over each edge is also possible) which results by using the equilibration procedures in [8], [25], [32], [60] and [61]. Let us consider the interior-vertex X and let us also denote 4, i = 1...,Nx the edges connected to X.…”

Section: Ladeveze's Flux-splitting Techniquementioning

confidence: 99%

“…Here the index ,(e, X) identifies the local enumeration of node X, as used in (26) for the unknowns associated with the edge; see is minimized for I = 1 and I = 2 separately, where w, is the weight associated with each edge ei. In [25] and [32] the weights wi have been taken as 1. For this choice of weights, the solution of (24) is given explicitly as, If we take the weights w, := Ic,1-1, as suggested in [60] and [61], we can obtain a different 0, satisfying (29).…”

Section: Ladeveze's Flux-splitting Techniquementioning

confidence: 99%

“…Implicit element residual based on complementary energy principle (Est. 3) (defined below) [25], [26], [27], [28], [32], [60], [61].…”

Section: S Numerical Optimizationmentioning

confidence: 99%

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Error Estimation and Adaptivity in Elastoplasticity

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SUMMARYIn this paper, a method is developed to control the parameters of a finite element computation for time-dependent material models. This method allows the user to obtain a prescribed accuracy with a computational cost as low as possible. To evaluate discretization errors, we use a global error measure in constitutive relation based on Drucker's inequality. This error includes, over the studied time interval, the error of the finite element model and the error of the algorithm being used. In order to master the size of the elements of the mesh and the length of the time increments, an error estimator, which permits estimating the errors due to the time discretization, is proposed. These tools are used to elaborate two procedures of adaptivity. Various examples for monotonous or non-monotonous loadings, for 2-D or axisymmetric problems, show the reliability of these procedures.

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Accuracy and optimal meshes in finite element computation for nearly incompressible materials

Cited by 60 publications

References 9 publications

A hierarchical h adaptivity methodology based on element subdivision

A hierarchical h adaptivity methodology based on element subdivision

Validation of A-Posteriori Error Estimators by Numerical Approach

Error Estimation and Adaptivity in Elastoplasticity

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