Three dimensional solid-shell transition finite elements for heat conduction

Surana, Karan S.; Phillips, Robert K.

doi:10.1016/0045-7949(87)90111-8

Cited by 24 publications

(3 citation statements)

References 14 publications

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“…Applications of the elements of this type to axi-symmetric [28] and three-dimensional [29] problems are presented. Extension onto thermo-mechanical analysis was done in Reference [30]. Note that the independent research of Bathe and Bolourchi [31], based on the mentioned work of Ahmad, led to the analogous transition elements.…”

Section: Non-adaptive Transition Elements For Elasticitymentioning

confidence: 99%

3D-Based Transition hpq/hp-Adaptive Finite Elements for Analysis of Piezoelectrics

Zboiński

Zielińska

2021

Applied Sciences

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This paper concerns the algorithm of transition piezoelectric elements for adaptive analysis of electro-mechanical systems. In addition, effectivity of the proposed elements in such an analysis is presented. The elements under consideration are assigned for joining basic elements which correspond to the mechanical models of either the first or higher order, while the electric model is of arbitrary order. In this work, three variants of the transition models are applied. The first one assures continuity of displacements between the basic models and continuity of electric potential between these models, as well. The second transition piezoelectric model guarantees additional continuity of the stress field between the basic models. The third transition model additionally enables continuous change of the strain state between the basic models. Based on the mentioned models, three types of the corresponding transition finite elements are introduced. The applied finite element approximations are hpq/hp-adaptive ones, which allows element-wise changes of the element size parameter h, and the element longitudinal and transverse orders of approximation, respectively, p and q, depending on the error level. Numerical effectiveness of the models and their approximations is investigated in the contexts of: ability to remove high stress gradients between the basic and transition models, and convergence of the numerical solutions for the model problems of piezoelectrics with and without the proposed transition elements.

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Section: Non-adaptive Transition Elements For Elasticitymentioning

confidence: 99%

3D-Based Transition hpq/hp-Adaptive Finite Elements for Analysis of Piezoelectrics

Zboiński

Zielińska

2021

Applied Sciences

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“…[72,73]. Finally, it should be noted that similar elements are available for (Fourier) heat conduction problems where the nodal temperature and temperature gradients are included as primary variables [74,75].…”

Section: Introductionmentioning

confidence: 99%

“…However, for cases involving inertia terms, non-linearities, or arbitrary body loads, additional degrees of freedom have to be introduced to achieve high order convergence [60,67,68]. Extensive research in the area of transition elements, especially with respect to coupling solid (continuum) and shell elements has been conducted by Surana [69][70][71][72][73][74][75]. In Ref, [69] Surana provides shape functions for transition elements which can be used to couple quadrilateral with beam-like or other quadrilateral elements for different polynomial orders (p = 1, 2, 3).…”

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confidence: 99%

High order transition elements: The xy-element concept—Part I: Statics

Duczek

Saputra

Gravenkamp

2020

Computer Methods in Applied Mechanics and Engineering

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Advanced transition elements are of utmost importance in many applications of the finite element method (FEM) where a local mesh refinement is required. Considering problems that exhibit singularities in the solution, an adaptive hp-refinement procedure must be applied. Even today, this is a very demanding task especially if only quadrilateral/hexahedral elements are deployed and consequently the hanging nodes problem is encountered. These element types, are, however, favored in computational mechanics due to the improved accuracy compared to triangular/tetrahedral elements. Therefore, we propose a compatible transition element -xNy-element -which provides the capability of coupling different element types. The adjacent elements can exhibit different element sizes, shape function types, and polynomial orders. Thus, it is possible to combine independently refined h-and p-meshes. The approach is based on the transfinite mapping concept and constitutes an extension/generalization of the pNh-element concept. By means of several numerical examples, the convergence behavior is investigated in detail, and the asymptotic rates of convergence are determined numerically. Overall, it is found that the proposed approach provides very promising results for local mesh refinement procedures.

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Curved shell elements based on hierarchical p‐approximation in the thickness direction for linear static analysis of laminated composites

Surana

Sorem

1990

Numerical Meth Engineering

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This paper presents a new curved shell finite element formulation for linear static analysis of laminated composite plates and shells, where the displacement approximation in the direction of the shell thickness can be of an arbitrary polynomial order p , thereby permitting strains of at least ( p -1) order. This is accomplished by introducing additional nodal variables in the element displacement approximation corresponding to the Lagrange interpolating polynomials in the element thickness .direction. The resulting element displacement approximation has an important hierarchical property i.e. the approximation functions and the generalized nodal variables corresponding to an approximation order p are a subset of those corresponding to an approximation order ( p + 1). The element formulation ensures Co continuity or smoothness of displacements across the interelement boundaries.The element properties (stiffness matrix and equivalent load vectors) are derived using the principle of virtual work and the hierarchical element approximation. The formulation is extended for generally orthotropic material behaviour where the material directions are not necessarily parallel to the global axes. Further extension of this formulation for laminated composites is accomplished by incorporating the material properties of each lamina by numerically integrating the element stiffness matrix for each lamina. The formulation has no restriction on either the number of laminas or the layup pattern of the laminas. Each lamina can be generally orthotropic, and the material directions and the lamina thicknesses may vary from point to point within each lamina. The geometry of the laminated shell element is described by the co-ordinates of the nodes lying on the middle surface of the element and the lamina thicknesses at each node. The formulation permits any desired order displacement or strain approximation in the shell thickness direction without remodelling.Numerical examples are presented to demonstrate the accuracy, efficiency, and overall superiority of the present formulation. The results obtained from the present formulation are compared with those available in the literature as well as the analytical solutions.

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Three dimensional solid-shell transition finite elements for heat conduction

Cited by 24 publications

References 14 publications

3D-Based Transition hpq/hp-Adaptive Finite Elements for Analysis of Piezoelectrics

3D-Based Transition hpq/hp-Adaptive Finite Elements for Analysis of Piezoelectrics

High order transition elements: The xy-element concept—Part I: Statics

Curved shell elements based on hierarchical p‐approximation in the thickness direction for linear static analysis of laminated composites

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