Boundary integral equations for bending of thermoelastic plates with transmission boundary conditions

2009 ◽  
Vol 33 (1) ◽  
pp. 117-124
Author(s):  
I. Chudinovich ◽  
C. Constanda
Keyword(s):  
Boundary Conditions ◽  
Integral Equations ◽  
Boundary Integral Equations ◽  
Boundary Integral ◽  
Thermoelastic Plates

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.

A New Boundary Equation Solution to the Plate Problem

1989 ◽  
Vol 56 (2) ◽  
pp. 364-374 ◽  
Author(s):  
J. T. Katsikadelis ◽  
A. E. Armena`kas
Keyword(s):  
Boundary Element Method ◽  
Boundary Conditions ◽  
Integral Equations ◽  
Boundary Integral Equations ◽  
Boundary Integral ◽  
Boundary Equation ◽  
Arbitrary Geometry ◽  
Equation Solution ◽  
The Finite Difference Method ◽  
Boundary Equations

A new boundary equation method is presented for analyzing plates of arbitrary geometry. The plates may have holes and may be subjected to any type of boundary conditions. The boundary value problem for the plate is formulated in terms of two differential and two integral coupled boundary equations which are solved numerically by discretizing the boundary. The differential equations are solved using the finite difference method while the integral equations are solved using the boundary element method. The main advantages of this new method are that the kernels of the boundary integral equations are simple and do not have hyper-singularities. Moreover, the same set of equations is employed for all types of boundary conditions. Furthermore, the use of intrinsic coordinates facilitates the modeling of plates with curvilinear boundaries. The numerical results demonstrate the accuracy and the efficiency of the method.

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