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.

A Variational Boundary Element Formulation for Shear-Deformable Plate Bending Problems

2013 ◽  
Vol 80 (5) ◽  
Author(s):  
Taha H. A. Naga ◽  
Youssef F. Rashed
Keyword(s):  
Integral Equation ◽  
Boundary Element ◽  
Energy Functional ◽  
Boundary Integral ◽  
Element Formulation ◽  
Plate Bending ◽  
Bending Problems ◽  
The One ◽  
Shear Deformable ◽  
Element Method

This paper presents the derivation of a new boundary element formulation for plate bending problems. The Reissner's plate bending theory is employed. Unlike the conventional direct or indirect formulations, the proposed integral equation is based on minimizing the relevant energy functional. In doing so, variational methods are used. A collocation based series, similar to the one used in the indirect discrete boundary element method (BEM), is used to remove domain integrals. Hence, a fully boundary integral equation is formulated. The main advantage of the proposed formulation is production of a symmetric stiffness matrix similar to that obtained in the finite element method. Numerical examples are presented to demonstrate the accuracy and the validity of the proposed formulation.

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.

scholarly journals LIMIT WAVES ON HORIZONTAL SEA FLOOR

1986 ◽  
Vol 1 (20) ◽  
pp. 41
Author(s):  
Chia-Chi Lu ◽  
John D. Wang ◽  
Bernard Le Mehaute
Keyword(s):  
Integral Equation ◽  
Numerical Solution ◽  
Boundary Integral Equation ◽  
Gravity Waves ◽  
Integral Equation Method ◽  
Boundary Integral ◽  
Wave Crest ◽  
Solution Technique ◽  
Sea Floor ◽  
Surface Gravity Waves

A numerical solution to periodic nonlinear irrotational surface gravity waves on a horizontal sea floor is developed using an iterative Boundary Integral Equation Method (BIEM). This solution technique is subsequently applied to determine the characteristics of limit waves for which the wave crest theoretically ceases to be rounded and become angled with an included angle of 120 degrees.

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