An Elegant and Rigorous Analytical Solution for Anti-symmetric Angle-ply Rectangular Plates with any Combination of Simply Supported and Clamped Edges

2006 ◽  
Vol 25 (16) ◽  
pp. 1679-1689 ◽  
Author(s):  
K. Bhaskar
Keyword(s):  
Analytical Solution ◽  
Rectangular Plates ◽  
Simply Supported ◽  
Clamped Edges

Application of large-deflection theory to normally loaded rectangular plates with clamped edges

1970 ◽  
Vol 5 (2) ◽  
pp. 140-144 ◽  
Author(s):  
A Scholes
Keyword(s):  
Large Deflection ◽  
Rectangular Plates ◽  
Simply Supported ◽  
Aspect Ratios ◽  
Non Linear ◽  
Deflection Theory ◽  
Large Deflection Theory ◽  
Clamped Edges ◽  
Clamped Edge ◽  
Good Agreement

A previous paper (1)∗described an analysis for plates that made use of non-linear large-deflection theory. The results of the analysis were compared with measurements of deflections and stresses in simply supported rectangular plates. In this paper the analysis has been used to calculate the stresses and deflections for clamped-edge plates and these have been compared with measurements made on plates of various aspect ratios. Good agreement has been obtained for the maximum values of these stresses and deflections. These maximum values have been plotted in such a form as to be easily usable by the designer of pressure-loaded clamped-edge rectangular plates.

scholarly journals Series-Based Solution for Analysis of Simply Supported Rectangular Thin Plate with Internal Rigid Supports

2017 ◽  
Vol 2017 ◽  
pp. 1-7 ◽  
Author(s):  
Abubakr E. S. Musa ◽  
Husain J. Al-Gahtani
Keyword(s):  
Analytical Solution ◽  
Bending Moment ◽  
Accurate Solution ◽  
Rectangular Plates ◽  
Compatibility Conditions ◽  
Element Analysis ◽  
Simply Supported ◽  
The Finite Element Analysis ◽  
Rigid Supports ◽  
The Given

In this study, Navier’s solution for the analysis of simply supported rectangular plates is extended to consider rigid internal supports. The proposed method offers a more accurate solution for the bending moment at the critical section and therefore serves as a better analytical solution for design purposes. To model the plate-support interaction, the patched areas representing the contact between the plate and supports are divided into groups of cells. The unknown internal reactions at the centers of the divided cells are obtained by satisfying the compatibility conditions at the centers of the cells. Three numerical examples are presented to demonstrate the accuracy of the proposed analytical solution. The given examples reveal good agreements with those obtained by the finite element analysis. In addition, they show the advantage of the new solution as compared to the existing analytical solution which inaccurately estimates the location and magnitude of the maximum bending moment.

Bending of Elastically Restrained Rectangular Plates Under Uniform Pressure

1958 ◽  
Vol 62 (575) ◽  
pp. 834-836 ◽  
Author(s):  
C. Lakshmi Kantham
Keyword(s):  
Natural Frequencies ◽  
Unit Length ◽  
Rectangular Plates ◽  
Uniform Pressure ◽  
Simply Supported ◽  
Edge Conditions ◽  
Definition Of ◽  
Elastically Restrained ◽  
Clamped Edges ◽  
Clamped Edge

In the bending and vibration of plates it is found that the values of maximum deflection and natural frequencies, respectively, vary considerably from the simply-supported to clamped edge conditions. For an estimation of these characteristics in the intermediate range a generalised boundary condition may be assumed, of which the simply-supported and clamped edges become limiting cases. While Bassali considers the ratio of edge moment to the cross-wise moment as a constant, Newmark, Lurie and Klein and other investigators, in their analyses of various structures, consider that moment and slope at an end are proportional.Here the definition of elastic restraint as given by Timoshenko, α=βM, is followed, where α is the slope at any edge, M the corresponding edge moment per unit length while β is the elastic restraint factor. β→0 and β→∞ represent the two limiting cases of simply-supported and clamped edge conditions.

scholarly journals Analytical solution to bending of stiffened and continuous antisymmetric laminates

2015 ◽  
Vol 2 (1) ◽  
Author(s):  
Liecheng Sun ◽  
Issam E. Harik
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Analytical Solution ◽  
Displacement Function ◽  
The Other ◽  
Order Partial Differential Equation ◽  
Eighth Order ◽  
Coupling Problem ◽  
Simply Supported ◽  
General Response

AbstractAnalytical Strip Method is presented for the analysis of the bending-extension coupling problem of stiffened and continuous antisymmetric thin laminates. A system of three equations of equilibrium, governing the general response of antisymmetric laminates, is reduced to a single eighth-order partial differential equation (PDE) in terms of a displacement function. The PDE is then solved in a single series form to determine the displacement response of antisymmetric cross-ply and angle-ply laminates. The solution is applicable to rectangular laminates with two opposite edges simply supported and the other edges being free, clamped, simply supported, isotropic beam supports, or point supports.

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.

Sign in / Sign up

Export Citation Format

Share Document