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.

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.

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.

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 ELEMENT DKT_CST FOR ANALYSIS OF LAMINATED ANISOTROPIC PLATES/ELEMENTAS DKT_CST SLUOKSNIUOTŲ ANIZOTROPINIŲ PLOKŠTELIŲ ANALIZEI

2000 ◽  
Vol 6 (5) ◽  
pp. 351-356
Author(s):  
Edvard Michnevič ◽  
Rimantas Belevičius
Keyword(s):  
Finite Element ◽  
Numerical Solutions ◽  
Triangular Element ◽  
Plate Bending ◽  
Anisotropic Plates ◽  
Numerical Examples ◽  
Out Of Plane ◽  
Bending Problems ◽  
Slab Bending ◽  
Plate Bending Problem

The new finite element of multilayered built up with an arbitrary series of layers plate for plate bending problem is formulated on the ground of widely used, effective finite element Discrete Kirchhof Theory (DKT). The material of each layer is supposed to be different and orthotopic. Triangular element has 6 d.o.f.'s at each of 3 nodal points: 3 displacements and 2 rotations about co-ordinate axes. The 6th fictitious rotation about axis perpendicular to the element is also introduced due to numerical requirements. The element takes into account all the in-plane/out-of-plane effects except the shear. The element could find an application in the slab bending problems or in the plate, where the shear influence could be neglected, bending problems. The numerical examples are presented. Present solutions are compared with available analytical and numerical solutions.

scholarly journals THE LAYERED ELEMENT DKT_CST FOR ANALYSIS OF ANISOTROPIC PLATES

2007 ◽  
Vol 13 (1) ◽  
pp. 41-46
Author(s):  
Edvard Michnevič
Keyword(s):  
Finite Element ◽  
Numerical Solutions ◽  
Triangular Element ◽  
Plate Bending ◽  
Anisotropic Plates ◽  
Numerical Examples ◽  
Out Of Plane ◽  
Bending Problems ◽  
Slab Bending ◽  
Plate Bending Problem

The new finite element of multilayered built up with an arbitrary series of layers plate for plate bending problem is formulated on the ground of widely used, effective finite element Discrete Kirchhof Theory (DKT). The material of each layer is supposed to be different and orthotropic. Triangular element has 6 d.o.f.’s at each of 3 nodal points: 3 displacements and 3 rotations about co‐ordinate axes. The element takes into account all the in‐plane/out‐of‐plane effects except for shear. The element could find an application in the slab bending problems or in the plate, where the shear influence could be neglected, bending problems. Numerical examples are presented. Present solutions are compared with available analytical and numerical solutions.

Sign in / Sign up

Export Citation Format

Share Document