Plate Element (plate + element)

Distribution by Scientific Domains


Selected Abstracts


Cretaceous,Tertiary geodynamics: a North Atlantic exercise

GEOPHYSICAL JOURNAL INTERNATIONAL, Issue 3 2001
Trond H. Torsvik
Summary New reconstructions are presented for the Cretaceous,Early Tertiary North Atlantic using a combination of palaeomagnetic, hotspot and magnetic anomaly data. We utilize these reconstructions in an analysis of previously described misfits between the North Atlantic Plate elements at successive intervals during this time period. We are able to achieve reasonable overlap between the hotspot and palaeomagnetic reconstructions between 40 and 95 Ma and thus are able to support the idea that the Indo,Atlantic hotspots are relatively stationary. Small, but systematic discrepancies for this time interval can readily be modelled with a long-term, octopole non-dipole field contribution (G3 = g30/g10 = 0.08). However, hotspot and palaeomagnetic reconstructions for the Early Cretaceous North Atlantic show substantial differences that cannot be explained by constant, non-dipole fields and we favour an explanation for these discrepancies in terms of true polar wander (TPW) triggered by mantle instabilities between 125 and 95 Ma; this constitutes the only identifiable event of significant TPW since the Early Cretaceous. Taken in the context of available geochronological and geological data and seismic tomography from the region, the 95,40 Ma reconstructions and their time-consequent geological products are interpreted in terms of specific conditions of mantle-crust coupling and global plate motions/tectonic activity. Highlights from these reconstructions show uniform NE movement of the coupled North American, Greenland and Eurasian plates from 95 to 80 Ma; a marked cusp in the paths for all three elements at 80 Ma where the three plates simultaneously change direction and follow a uniform NW-directed motion until c. 20 Ma when Eurasia diverges NE, away from the still-NW-moving Greenland and North American elements. Positioning of the Iceland plume beneath the spreading-ridge at 20 Ma may have increased upwelling below the ridge, increased the ridge-push, and caused a NE shift in the absolute direction of Eurasia. [source]


Finite element modelling of thick plates on two-parameter elastic foundation

INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 14 2001
Ryszard Buczkowski
Abstract This paper is intended to give some information about how to build a model necessary for bending analysis of rectangular and circular plates resting on a two-parameter elastic foundation, subjected to combined loading and permitting various types of boundary conditions. The formulation of the problem takes into account the shear deformation of the plate and the surrounding interaction effect outside the plate. The numerical model based on an 18-node zero-thickness isoparametric interface element interacting with a thick Reissner,Mindlin plate element with three degrees of freedom at each of the nine nodes, which enforce C0 continuity requirements for the displacements and rotations of the midsurface, is proposed. Stiffness matrices of a special interface element are superimposed on the global stiffness matrix to represent the stiffening elastic foundation under and beyond the plate. Some numerical examples are given to illustrate the advantages of the method presented. Copyright © 2001 John Wiley & Sons, Ltd. [source]


A new triangular layered plate element for the non-linear analysis of reinforced concrete slabs

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 7 2006
Y. X. Zhang
Abstract A new 3-node, 18-DOF triangular layered plate element is developed in this paper for the geometric and material non-linear analysis of isotropic plates and reinforced concrete slabs under service loads. The proposed model is a combination of Allman's 3-node, 9-DOF triangular membrane element with drilling degrees of freedom and the refined non-conforming 3-node, 9-DOF triangular plate-bending element RT9 in order to account for the coupling effects between membrane and bending actions. The element is modelled as a layered system of concrete and equivalent smeared steel reinforcement layers, and perfect bond is assumed between the concrete layers and the smeared steel layers. The maximum normal stress criterion is employed to detect cracking of the concrete, and a smeared fixed crack model is assumed. Both geometric non-linearity with large displacements but moderate rotations and material non-linearity, which incorporates tension, compression, concrete cracking and tension stiffening, are included in the model. An updated Lagrangian approach is employed as a solution strategy for the non-linear finite element analysis and a numerical example of reinforced concrete slab is given to demonstrate the efficacy of this robust element. Copyright © 2005 John Wiley & Sons, Ltd. [source]


A triangular plate element for thermo-elastic analysis of sandwich panels with a functionally graded core

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 9 2006
M. Das
Abstract A sandwich construction is commonly composed of a single soft isotropic core with relatively stiff orthotropic face sheets. The stiffness of the core may be functionally graded through the thickness in order to reduce the interfacial shear stresses. In analysing sandwich panels with a functionally gradient core, the three-dimensional conventional finite elements or elements based on the layerwise (zig-zag) theory can be used. Although these elements accurately model a sandwich panel, they are computationally costly when the core is modelled as composed of several layers due to its grading material properties. An alternative to these elements is an element based on a single-layer plate theory in which the weighted-average field variablescapture the panel deformation in the thickness direction. This study presents a new triangular finite element based on {3,2}-order single-layer theory for modelling thick sandwich panels with or without a functionally graded core subjected to thermo-mechanical loading. A hybrid energy functional is employed in the derivation of the element because of a C1 interelement continuity requirement. The variations of temperature and distributed loading acting on the top and bottom surfaces are non-uniform. The temperature also varies arbitrarily through the thickness. Copyright © 2006 John Wiley & Sons, Ltd. [source]


A triangular hybrid equilibrium plate element of general degree

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 3 2005
E. A. W. Maunder
Abstract Hybrid stress-based finite elements with side displacement fields have been used to generate equilibrium models having the property of equilibrium in a strong form. This paper establishes the static and kinematic characteristics of a flat triangular hybrid equilibrium element with both membrane and plate bending actions of general polynomial degree p. The principal characteristics concern the existence of hyperstatic stress fields and spurious kinematic modes. The former are shown to exist for p>3, and their significance to finite element analysis is reviewed. Knowledge of the latter is crucial to the determination of the stability of a mesh of triangular elements, and to the choice of procedure adopted for the solution of the system of equations. Both types of characteristic are dependent on p, and are established as regards their numbers and general algebraic forms. Graphical illustrations of these forms are included in the paper. Copyright © 2005 John Wiley & Sons, Ltd. [source]


A new shear flexible cubic spline plate element for vibration analysis

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 11 2002
B. P. Patel
Abstract Here, a new cubic B-spline plate element is developed using field consistency principle, for vibration analysis. The formulation includes anisotropy, transverse shear deformation, in-plane and rotary inertia effects. The element is based on a laminated refined plate theory, which satisfies the interface transverse shear stress and displacement continuity, and has a vanishing shear stress on the top and bottom surfaces of the plates. The lack of consistency in the shear strain field interpolations in its constrained physical limits produces poor convergence and results in unacceptable solutions due to locking phenomenon. Hence, numerical experimentation for the evaluation of natural frequencies of plates is carried out to check this deficiency with a series of assumed shear strain functions, redistributed in a field consistent manner. Copyright © 2002 John Wiley & Sons, Ltd. [source]


Mixed piezoelectric plate elements with direct evaluation of transverse electric displacement

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 4 2009
E. Carrera
Abstract A mixed variational statement for the analysis of layered structures under the effect of mechanical and electrical fields is proposed in this paper to develop finite plate elements that permit the direct evaluation of transverse electrical displacement Dz. The original Reissner mixed variational theorem, RMVT, has been modified to account for ,only' interlaminar continuous Dz. Continuity of mechanical variables, such as transverse shear and normal stress components, has been discarded to provide a simple ,electrical' modified RMVT, here called RMVT- Dz. Finite element implementations are made via the Carrera unified formulation. The advantages of the proposed approach have been demonstrated through numerical comparisons with classical formulations based on the principle of virtual displacements as well as with available 3D solutions. Copyright © 2009 John Wiley & Sons, Ltd. [source]


The stability of stars of triangular equilibrium plate elements

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 7 2009
E. A. W. Maunder
Abstract Equilibrium models for finite element analyses are becoming increasingly important in complementary roles to those from conventional conforming models, but when formulating equilibrium models questions of stability, or admissibility of loads, are of major concern. This paper addresses these questions in the context of flat plates modelled with triangular hybrid elements involving membrane and/or flexural actions. Patches of elements that share a common vertex are considered, and such patches are termed stars. Stars may be used in global analyses as assemblies of elements forming macro-elements, or in local analyses. The conditions for stability, or the existence and number of spurious kinematic modes, are determined in a general algebraic procedure for any degree of the interpolation polynomials and for any geometric configuration. The procedure involves the determination of the rank of a compatibility matrix by its transformation to row echelon form. Examples are presented to illustrate some of the characteristics of spurious kinematic modes when they exist in stars with open or closed links. Copyright © 2008 John Wiley & Sons, Ltd. [source]


Classical and advanced multilayered plate elements based upon PVD and RMVT.

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 3 2002
Part 2: Numerical implementations
Abstract This paper presents numerical evaluations related to the multilayered plate elements which were proposed in the companion paper (Part 1). Two-dimensional modellings with linear and higher-order (up to fourth order) expansion in the z -plate/layer thickness direction have been implemented for both displacements and transverse stresses. Layer-wise as well as equivalent single-layer modellings are considered on both frameworks of the principle of virtual displacements and Reissner mixed variational theorem. Such a variety has led to the implementation of 22 plate theories. As far as finite element approximation is concerned, three quadrilaters have been considered (four-, eight- and nine-noded plate elements). As a result, 22×3 different finite plate elements have been compared in the present analysis. The automatic procedure described in Part 1, which made extensive use of indicial notations, has herein been referred to in the considered computer implementations. An assessment has been made as far as convergence rates, numerical integrations and comparison to correspondent closed-form solutions are concerned. Extensive comparison to early and recently available results has been made for sample problems related to laminated and sandwich structures. Classical formulations, full mixed, hybrid, as well as three-dimensional solutions have been considered in such a comparison. Numerical substantiation of the importance of the fulfilment of zig-zag effects and interlaminar equilibria is given. The superiority of RMVT formulated finite elements over those related to PVD has been concluded. Two test cases are proposed as ,desk-beds' to establish the accuracy of the several theories. Results related to all the developed theories are presented for the first test case. The second test case, which is related to sandwich plates, restricts the comparison to the most significant implemented finite elements. It is proposed to refer to these test cases to establish the accuracy of existing or new higher-order, refined or improved finite elements for multilayered plate analyses. Copyright © 2002 John Wiley & Sons, Ltd. [source]