An exact solution for transversely isotropic, simply supported and layered rectangular plates

1991 ◽  
Vol 25 (2) ◽  
pp. 101-116 ◽  
Author(s):  
Ernian Pan
Keyword(s):  
Exact Solution ◽  
Transversely Isotropic ◽  
Rectangular Plates ◽  
Simply Supported

An Analytical Solution for Transversely Isotropic Simply Supported Thick Rectangular Plates Using Displacement Potential Functions

2011 ◽  
Vol 46 (2) ◽  
pp. 121-142 ◽  
Author(s):  
M Nematzadeh ◽  
M Eskandari-Ghadi ◽  
B Navayi Neya
Keyword(s):  
Isotropic Material ◽  
Transversely Isotropic ◽  
Numerical Results ◽  
Potential Functions ◽  
Constant Thickness ◽  
Rectangular Plates ◽  
Displacement Potential ◽  
Simply Supported ◽  
Axial Forces ◽  
Internal Forces

Using a complete set of displacement potential functions, the exact solution of three-dimensional elasticity equations of a simply supported rectangular plates with constant thickness consisting of a transversely isotropic linearly elastic material subjected to an arbitrary static load is presented. The governing partial differential equations for the potential functions are solved through the use of the Fourier method, which results in exponential and trigonometric expression along the plate thickness and the other two lengths respectively. The displacements, stresses, and internal forces are determined through the potential functions at any point of the body. To prove the validity of this approach, the analytical solutions developed in this paper are degenerated for the simpler case of plates containing isotropic material and compared with the existing solution. In addition, the numerical results obtained from this study are compared with those reported in other researches for the isotropic material, where excellent agreement is achieved for both thin and thick plates. The results show that increasing the thickness ratios of the plate causes compressive axial forces and central shear forces inside the plate. Finally, the internal forces and displacement components are calculated numerically for several kinds of transversely isotropic materials with different anisotropies and are compared with a finite element (FE) solution obtained from the ANSYS software, where the high accuracy of the present method is demonstrated. The effects of the material anisotropy are clearly revealed in the numerical results presented.

Buckling of Rectangular Plates With Built-In Edges

1942 ◽  
Vol 9 (4) ◽  
pp. A171-A174
Author(s):  
Samuel Levy
Keyword(s):  
Exact Solution ◽  
Rectangular Plate ◽  
Infinite Series ◽  
Numerical Results ◽  
Buckling Load ◽  
Rectangular Plates

Abstract This paper presents an exact solution in terms of infinite series of the problem of buckling by compressive forces in one direction of a rectangular plate with built-in edges (zero slope, zero displacement in the direction normal to the plane of the plate). The buckling load is calculated for 14 ratios of length to width, ranging in steps of 0.25 from 0.75 to 4. On the basis of convergence, as the number of terms used in the infinite series is increased, it is estimated that the possible error in the numerical results presented is of the order of 0.1 per cent. A comparison is given with the work of other authors.

Deformation of Rectangular Slender Webplates with Boundary Members Flexible in the Webplate Plane

1966 ◽  
Vol 17 (4) ◽  
pp. 371-394 ◽  
Author(s):  
J. Djubek
Keyword(s):  
Linear Problem ◽  
Numerical Results ◽  
Rectangular Plates ◽  
Simply Supported ◽  
Non Linear

SummaryThe paper presents a solution of the non-linear problem of the deformation of slender rectangular plates which are stiffened along their edges by elastically compressible stiffeners flexible in the plane of the plate. The webplate is assumed to be simply-supported along its contour. Numerical results showing the effect of flexural and normal rigidity of stiffeners are given for a square webplate loaded by shear and compression.

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.

Sign in / Sign up

Export Citation Format

Share Document