A BEM-BASED MESHLESS METHOD FOR ELASTIC BUCKLING ANALYSIS OF PLATES

2007 ◽  
Vol 07 (01) ◽  
pp. 81-99 ◽  
Author(s):  
BOONME CHINNABOON ◽  
SOMCHAI CHUCHEEPSAKUL ◽  
JOHN T. KATSIKADELIS
Keyword(s):  
Boundary Conditions ◽  
Meshless Method ◽  
Boundary Integral Equations ◽  
Boundary Integral ◽  
Buckling Analysis ◽  
Plate Bending ◽  
Elastic Plates ◽  
Actual Problem ◽  
Fictitious Load ◽  
Plate Bending Problem

In this paper, a BEM-based meshless method is developed for buckling analysis of elastic plates with various boundary conditions that include elastic supports and restraints. The proposed method is based on the concept of the Analog Equation Method (AEM) of Katsikadelis. According to this method, the original eigenvalue problem for a governing differential equation of buckling is replaced by an equivalent plate bending problem subjected to an appropriate fictitious load under the same boundary conditions. The fictitious load is established using a technique based on BEM and approximated by using the radial basis functions. The eigenmodes of the actual problem are obtained from the known integral representation of the solution for the classical plate bending problem, which is derived using the fundamental solution of the biharmonic equation. Thus, the kernels of the boundary integral equations are conveniently established and evaluated. The method has all the advantages of the pure BEM. To validate its effectiveness, accuracy as well as applicability of the proposed method, numerical results of various problems are presented.

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.

Vibration of a Simply Supported L-Shaped Plate

1997 ◽  
Vol 119 (3) ◽  
pp. 464-467 ◽  
Author(s):  
R. Solecki
Keyword(s):  
Boundary Conditions ◽  
Integral Equations ◽  
Natural Vibration ◽  
Boundary Integral Equations ◽  
Rectangular Domain ◽  
Boundary Integral ◽  
Theoretical Development ◽  
Natural Vibrations ◽  
Simply Supported ◽  
Discontinuous Functions

Recently Solecki (1996) has shown that a differential equation for vibration of a rectangular plate with a cutout can be reduced to boundary integral equations. This was accomplished by filling the cutout with a “patch” made of the same material as the rest of the plate and separated from it by an infinitesimal gap. Thanks to this procedure it was possible to apply finite Fourier transformation of discontinuous functions in a rectangular domain. Subsequent application of the available boundary conditions led to a system of boundary integral equations. A plate simply supported along the perimeter, and fixed along the cutout (an L-shaped plate), was analyzed as an example. The general solution obtained by Solecki (1996) serves here to determine the frequencies of natural vibration of a L-shaped plate simply supported all around its perimeter. This problem is, however, more complicated than the previous example: to satisfy the boundary conditions an infinite series depending on discontinuous functions must be differentiated. The theoretical development is illustrated by numerical values of the frequencies of the natural vibrations of a square plate with a square cutout. The results are compared with the results obtained using finite elements method.

Effects of thermal and electric boundary conditions on fracture of three-dimensional thermopiezoelectric media

2017 ◽  
Vol 29 (6) ◽  
pp. 1255-1271 ◽  
Author(s):  
MingHao Zhao ◽  
Yuan Li ◽  
CuiYing Fan
Keyword(s):  
Stress Intensity ◽  
Boundary Conditions ◽  
Stress Intensity Factors ◽  
Boundary Integral Equations ◽  
Three Dimensional ◽  
Transversely Isotropic ◽  
Boundary Integral ◽  
Displacement Discontinuity ◽  
Green Functions ◽  
Intensity Factors

An arbitrarily shaped planar crack under different thermal and electric boundary conditions on the crack surfaces is studied in three-dimensional transversely isotropic thermopiezoelectric media subjected to thermal–mechanical–electric coupling fields. Using Hankel transformations, Green functions are derived for unit point extended displacement discontinuities in three-dimensional transversely isotropic thermopiezoelectric media, where the extended displacement discontinuities include the conventional displacement discontinuities, electric potential discontinuity, as well as the temperature discontinuity. On the basis of these Green functions, the extended displacement discontinuity boundary integral equations for arbitrarily shaped planar cracks in the isotropic plane of three-dimensional transversely isotropic thermopiezoelectric media are established under different thermal and electric boundary conditions on the crack surfaces, namely, the thermally and electrically impermeable, permeable, and semi-permeable boundary conditions. The singularities of near-crack border fields are analyzed and the extended stress intensity factors are expressed in terms of the extended displacement discontinuities. The effect of different thermal and electric boundary conditions on the extended stress intensity factors is studied via the extended displacement discontinuity boundary element method. Subsequent numerical results of elliptical cracks subjected to combined thermal–mechanical–electric loadings are obtained.

The Study of Meshless Method Simulation of Plate Bending Problem

2012 ◽  
Vol 446-449 ◽  
pp. 3633-3638
Author(s):  
Yu Ling Jiao ◽  
Guang Wei Meng ◽  
Xu Xi Qin
Keyword(s):  
Weight Function ◽  
Elastic Plate ◽  
Basis Function ◽  
Meshless Method ◽  
Least Square ◽  
Mindlin Plate ◽  
Plate Bending ◽  
Field Function ◽  
Moving Least Square ◽  
Plate Bending Problem

moving least square meshless method is a numerical approximation based on points that do not generate the grid of cells, as long as the node information. Basis function and weight function meshless method for the calculation of accuracy have a significant impact. In order to compare the order of the base functions and powers of the radius of influence domain function meshless method for computational accuracy and efficiency , this paper selected first, second and third basis function and spline-type weight function in a different influence domain radius, respectively construct the field function. Mindlin plate element is derived based on the format of the plate bending problem meshless discrete equations. Programming examples are calculated with elastic plate bending problems non-grid solutions, and analysis and comparison of their accuracy and efficiency, results show that the meshless method using elastic plate bending problem is feasible and effective.

Sign in / Sign up

Export Citation Format

Share Document