scholarly journals 3-D elasticity buckling solution for simply supported thick rectangular plates using displacement potential functions

2016 ◽  
Vol 40 (11-12) ◽  
pp. 5717-5730 ◽  
Author(s):  
Abdollah Moslemi ◽  
Bahram Navayi Neya ◽  
Javad Vaseghi Amiri
Keyword(s):  
Potential Functions ◽  
Rectangular Plates ◽  
Displacement Potential ◽  
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.

Free Vibration Analysis of a Simply Supported Rectangular Tank Partially Filled With a Liquid

2010 ◽  
Author(s):  
Kyeong-Hoon Jeong ◽  
Jin-Seok Park ◽  
Won-Jae Lee
Keyword(s):  
Boundary Conditions ◽  
Ritz Method ◽  
Free Vibration Analysis ◽  
Ideal Liquid ◽  
Rectangular Plates ◽  
Element Analysis ◽  
Displacement Potential ◽  
Simply Supported ◽  
Rectangular Tank ◽  
Liquid Displacement

This paper presents a theoretical analysis for the hydroelastic vibration of a rectangular tank partially filled with an ideal liquid. The wet dynamic displacement of the tank is approximated by combining the orthogonal polynomials satisfying the simply supported boundary conditions, since the rectangular tank is composed of four rectangular plates. As the facing rectangular plates are geometrically identical, the vibration modes of the facing plates can be divided into two categories: symmetric modes and asymmetric modes with respect to the vertical centerlines of the plates. The liquid displacement potential satisfying the boundary conditions is derived and the wet dynamic modal functions of the four plates are expanded by the finite Fourier transformation for a compatibility requirement along the contacting surface between the tank and the liquid. The natural frequencies of the rectangular tank in the wet condition are calculated by using the Rayleigh-Ritz method. The proposed analytical method is verified by observing an excellent agreement with three-dimensional finite element analysis results.

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.

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