scholarly journals Dual-series equations formulation for static deformation of plates with a partial internal line support

2007 ◽  
Vol 34 (3) ◽  
pp. 221-248 ◽  
Author(s):  
Yos Sompornjaroensuk ◽  
Kraiwood Kiattikomol
Keyword(s):  
Integral Equation ◽  
Fredholm Integral Equation ◽  
Hankel Transform ◽  
Internal Line ◽  
Rectangular Plates ◽  
Simply Supported ◽  
Distributed Load ◽  
Dual Series Equations ◽  
Finite Hankel Transform ◽  
Standard Techniques

The paper deals with the application of dual-series equations to the problem of rectangular plates having at least two parallel simply supported edges and a partial internal line support located at the centre where the length of internal line support can be varied symmetrically, loaded with a uniformly distributed load. By choosing the proper finite Hankel transform, the dual-series equations can be reduced to the form of a Fredholm integral equation which can be solved conveniently by using standard techniques. The solutions of integral equation and the deformations for each case of the plates are given and discussed in details.

INVERSE SQUARE ROOT MOMENT SINGULARITIES IN RECTANGULAR PLATES CONTAINING AN INTERNAL LINE SUPPORT

2009 ◽  
Vol 06 (01) ◽  
pp. 1-21 ◽  
Author(s):  
YOS SOMPORNJAROENSUK ◽  
KRAIWOOD KIATTIKOMOL
Keyword(s):  
Strain Energy ◽  
Integral Transform ◽  
Internal Line ◽  
Square Root ◽  
Rectangular Plates ◽  
Bending Moments ◽  
Partial Support ◽  
Uniform Loading ◽  
Dual Series Equations ◽  
Standard Techniques

Two cases of a rectangular plate having moment singularities at the ends of a partial internal line support are analytically investigated. The bending of the plate by uniform loading is formulated in terms of dual-series equations. Application of the finite Hankel integral transform reduces the dual-series equations to a Fredholm integral equation of the second kind that can be solved by standard techniques. Numerical results are given for the deflections and bending moments along the line outside of an internal line support and the change in strain energy due to the presence of a partial support.

scholarly journals The solution of certain loss of contact between a plate and unilateral supports

2007 ◽  
Vol 34 (4) ◽  
pp. 289-308
Author(s):  
Yos Sompornjaroensuk ◽  
Kiattikomol Kraiwood
Keyword(s):  
Mixed Boundary ◽  
Mixed Boundary Conditions ◽  
Free Edge ◽  
Hankel Transform ◽  
Middle Line ◽  
Distributed Load ◽  
Dual Series Equations ◽  
Loss Of Contact ◽  
Finite Hankel Transform ◽  
Square Plate

This paper examines the loss of contact between a square plate and the unilateral supports under uniformly distributed load. Since the plate is rested on the unilateral supports, it will have the regions of lost contact between a plate and the supports due to the absence of restraining corner force at the plate corners. This leads to the mixed boundary conditions and these conditions are then written in the form of dual-series equations which can further be reduced to a Fredholm integral equation by taking advantage of finite Hankel transform technique. Numerical results are given for the deflections of free edge and deflections along the middle line of the plate with deferent values of the Poisson?s ratio. In addition, the deflection surface is also presented. From the investigation, it can be indicated that the loss of contact is decreased upon the increasing Poisson?s ratio.

Eigenvalue Problems of Rectangular Plates With Mixed Edge Conditions

1972 ◽  
Vol 39 (2) ◽  
pp. 513-520 ◽  
Author(s):  
L. M. Keer ◽  
B. Stahl
Keyword(s):  
Integral Equations ◽  
Eigenvalue Problems ◽  
Coupled System ◽  
Mode Shapes ◽  
Fredholm Integral Equations ◽  
Rectangular Plates ◽  
Buckling Mode ◽  
Simply Supported ◽  
Edge Conditions ◽  
Dual Series Equations

The vibration and stability of plates with mixed edge conditions are considered in this paper. A simply supported rectangular plate which is clamped along the central portion on two opposite edges and a plate with partial clamping along one edge are analyzed. The problems are formulated as dual series equations and reduced to homogeneous Fredholm integral equations of the second kind. Comparisons with numerical results obtained by other investigators are made. Vibration and buckling mode shapes are illustrated. A vibration analysis of a plate simply supported adjacent to the corners is also made. This case is formulated as a coupled system of dual series equations which is reduced to a system of homogeneous integral equations. In all of the solutions given, the singularity is isolated and treated analytically.

Under Uniformly Distributed Load are Fixed on one Side (Simple) on the Edge Simply Supported and Fixed Half Bending of Rectangular Plates

2012 ◽  
Vol 152-154 ◽  
pp. 840-845
Author(s):  
Ying Jie Chen ◽  
Bao Lian Fu ◽  
Liang Wang ◽  
Jie Wu
Keyword(s):  
Rectangular Plate ◽  
Variable Method ◽  
Engineering Practice ◽  
Rectangular Plates ◽  
Simply Supported ◽  
Distributed Load ◽  
Uniformly Distributed Load ◽  
Surface Deflection ◽  
Mixed Variable

In this paper mixed variable method is generalized to solve the problem of bending of the rectangular plate with one side is fixed (simple) on the edge simply supported and fixed half under the action of a uniformly distributed load. Gives the surface deflection equation and a chart, the chart can be directly applied to engineering practice.

BUCKLING AND VIBRATION OF ORTHOTROPIC PLATES WITH AN INTERNAL LINE HINGE

2002 ◽  
Vol 02 (04) ◽  
pp. 457-486 ◽  
Author(s):  
P. R. GUPTA ◽  
J. N. REDDY
Keyword(s):  
Solution Method ◽  
Natural Frequencies ◽  
The Other ◽  
Internal Line ◽  
Rectangular Plates ◽  
Vibration Frequencies ◽  
Decomposition Technique ◽  
Orthotropic Plates ◽  
Buckling Loads ◽  
Simply Supported

This paper presents the exact buckling loads and vibration frequencies of orthotropic rectangular plates with internal line hinge and having two opposite edges simply supported while the other two edges may have any combination of free, simply supported, and clamped conditions. An analytical method that uses the Lévy solution method and the domain decomposition technique is employed to determine the buckling loads and natural frequencies of rectangular plates with internal line hinge.

On Improved Approximate Solution of the Fredholm Integral Equation

2006 ◽  
Vol 6 (3) ◽  
pp. 264-268
Author(s):  
G. Berikelashvili ◽  
G. Karkarashvili
Keyword(s):  
Integral Equation ◽  
Approximate Solution ◽  
Fredholm Integral Equation ◽  
Algebraic Equations ◽  
Order Convergence ◽  
One Dimensional ◽  
Averaging Operator ◽  
Linear Algebraic Equations ◽  
Convergence Solution

AbstractA method of approximate solution of the linear one-dimensional Fredholm integral equation of the second kind is constructed. With the help of the Steklov averaging operator the integral equation is approximated by a system of linear algebraic equations. On the basis of the approximation used an increased order convergence solution has been obtained.

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