A class of high order adaptive mixed element methods for Kirchhoff plate bending problems

2012 ◽  
Vol 42 (5) ◽  
pp. 473-489 ◽  
Author(s):  
JianGuo HUANG ◽  
YiFeng XU
Keyword(s):  
High Order ◽  
Kirchhoff Plate ◽  
Plate Bending ◽  
Bending Problems ◽  
Mixed Element

scholarly journals A Hybrid High-Order method for Kirchhoff–Love plate bending problems

2018 ◽  
Vol 52 (2) ◽  
pp. 393-421 ◽  
Author(s):  
Francesco Bonaldi ◽  
Daniele A. Di Pietro ◽  
Giuseppe Geymonat ◽  
Françoise Krasucki
Keyword(s):  
Sharp Estimate ◽  
High Order ◽  
Plate Bending ◽  
Mechanical Modeling ◽  
High Order Method ◽  
Local Polynomial ◽  
Bending Behavior ◽  
Bending Problems ◽  
Norm Of The Error ◽  
Theoretical Results

We present a novel Hybrid High-Order (HHO) discretization of fourth-order elliptic problems arising from the mechanical modeling of the bending behavior of Kirchhoff–Love plates, including the biharmonic equation as a particular case. The proposed HHO method supports arbitrary approximation orders on general polygonal meshes, and reproduces the key mechanical equilibrium relations locally inside each element. When polynomials of degree k ≥ 1 are used as unknowns, we prove convergence in hk+1 (with h denoting, as usual, the meshsize) in an energy-like norm. A key ingredient in the proof are novel approximation results for the energy projector on local polynomial spaces. Under biharmonic regularity assumptions, a sharp estimate in hk+3 is also derived for the L2-norm of the error on the deflection. The theoretical results are supported by numerical experiments, which additionally show the robustness of the method with respect to the choice of the stabilization.

scholarly journals Numerical Solution of the Kirchhoff Plate Bending Problem with BEM

2011 ◽  
Vol 2011 ◽  
pp. 1-14
Author(s):  
V. V. Zozulya
Keyword(s):  
Integral Equation ◽  
Numerical Solution ◽  
Boundary Integral ◽  
Kirchhoff Plate ◽  
Reciprocal Theorem ◽  
Plate Bending ◽  
Linear Boundary ◽  
Analytical Formulas ◽  
Bending Problems ◽  
Plate Bending Problem

Direct approach based on Betty's reciprocal theorem is employed to obtain a general formulation of Kirchhoff plate bending problems in terms of the boundary integral equation (BIE) method. For spatial discretization a collocation method with linear boundary elements (BEs) is adopted. Analytical formulas for regular and divergent integrals calculation are presented. Numerical calculations that illustrate effectiveness of the proposed approach have been done.

Trefftz method for Kirchhoff plate bending problems

1993 ◽  
Vol 36 (5) ◽  
pp. 765-781 ◽  
Author(s):  
W. G. Jin ◽  
Y. K. Cheung ◽  
O. C. Zienkiewicz
Keyword(s):  
Kirchhoff Plate ◽  
Plate Bending ◽  
Trefftz Method ◽  
Bending Problems

scholarly journals Development of High-Order Infinite Element Method for Bending Analysis of Mindlin–Reissner Plates

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
D. S. Liu ◽  
Y. W. Chen ◽  
C. J. Lu
Keyword(s):  
Plate Theory ◽  
Reduction Process ◽  
High Order ◽  
Plate Bending ◽  
Computational Domain ◽  
Infinite Element ◽  
Infinite Element Method ◽  
Bending Problems ◽  
Complicated Geometries ◽  
Element Method

An approach is presented for solving plate bending problems using a high-order infinite element method (IEM) based on Mindlin–Reissner plate theory. In the proposed approach, the computational domain is partitioned into multiple layers of geometrically similar virtual elements which use only the data of the boundary nodes. Based on the similarity, a reduction process is developed to eliminate virtual elements and overcome the problem that the conventional reduction process cannot be directly applied. Several examples of plate bending problems with complicated geometries are reported to illustrate the applicability of the proposed approach and the results are compared with those obtained using ABAQUS software. Finally, the bending behavior of a rectangular plate with a central crack is analyzed to demonstrate that the stress intensity factor (SIF) obtained using the high-order PIEM converges faster and closer than low-order PIEM to the analytical solution.

An Analytical Singular Element for Kirchhoff Plate Bending With V-Shaped Notches

2012 ◽  
Vol 79 (5) ◽  
Author(s):  
Weian Yao ◽  
Shan Wang
Keyword(s):  
Numerical Technique ◽  
Local Stress ◽  
Kirchhoff Plate ◽  
Plate Bending ◽  
Stress Singularities ◽  
Singular Element ◽  
Global Method ◽  
Annular Sector ◽  
Bending Problems ◽  
Plate Bending Problem

An analytical singular element with arbitrary high-order precision is constructed using the analytical symplectic eigenfunctions of an annular sector thin plate with both straight sides free. These values can be used to describe the local stress singularities near an arbitrary V-notch or a crack tip. Numerical examples of Kirchhoff’s plate bending problem with V-shaped notches are given by applying the Local-Global method. This method combines the present analytical singular element and the conventional finite element method. The numerical results show that the present method is an effective numerical technique for analysis of Kirchhoff plate bending problems with boundary stress singularities.

scholarly journals A Pseudospectral Approach for Kirchhoff Plate Bending Problems with Uncertainties

2012 ◽  
Vol 2012 ◽  
pp. 1-14
Author(s):  
Ling Guo ◽  
Jianguo Huang
Keyword(s):  
Original Problem ◽  
Grid Method ◽  
High Accuracy ◽  
Kirchhoff Plate ◽  
Plate Bending ◽  
Sparse Grid Method ◽  
Bending Problems ◽  
And Performance ◽  
Fourth Order Pde ◽  
Plate Bending Problem

This paper proposes a pseudospectral approach for the Kirchhoff plate bending problem with uncertainties. The Karhunen-Loève expansion is used to transform the original problem to a stochastic fourth-order PDE depending only on a finite number of random variables. For the latter problem, its exact solution is approximated by a gPC expansion, with the coefficients obtained by the sparse grid method. The main novelty of the method is that it can be carried out in parallel directly while keeping the high accuracy and fast convergence of the gPC expansion. Several numerical results are performed to show the accuracy and performance of the method.

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