A necessary and sufficient set of boundary integral equations with indirect unknowns for plate bending problem

1992 ◽  
Vol 8 (2) ◽  
pp. 127-135 ◽  
Author(s):  
Hu Haichang
Keyword(s):  
Integral Equations ◽  
Boundary Integral Equations ◽  
Boundary Integral ◽  
Plate Bending ◽  
Sufficient Set ◽  
Necessary And Sufficient ◽  
Plate Bending Problem

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.

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