Stresses and Deflections in an Elastically Restrained Circular Plate Under Uniform Normal Loading Over a Segment

1959 ◽  
Vol 26 (1) ◽  
pp. 44-54
Author(s):  
W. A. Bassali ◽  
M. Nassif
Keyword(s):  
Circular Plate ◽  
Plate Theory ◽  
Exact Expression ◽  
Normal Loading ◽  
Complex Variable Methods ◽  
Deflection Plate ◽  
Small Deflection ◽  
In Series ◽  
Elastically Restrained ◽  
Elastic Constraint

Abstract Within the limits of the small-deflection plate theory and using complex variable methods, an exact expression is developed in series form for the solution of the problem of a thin circular plate elastically restrained along the boundary and subjected to uniform normal loading over a segment of the plate. The elastic constraint considered includes as particular cases the rigidly clamped and simply supported boundaries. For a rigidly clamped boundary the results are expressed in finite terms. Some details of calculations of deflections, moments, and shears based on the theory are provided in tables and curves. Timoshenko’s notation [1] is used in the paper. Other symbols will be defined as they appear in the text.

Problems concerning the bending of isotropic thin elastic plates subject to various distributions of normal pressures

1958 ◽  
Vol 54 (2) ◽  
pp. 265-287 ◽  
Author(s):  
W. A. Bassali ◽  
H. P. F. Swinnerton-Dyer
Keyword(s):  
Circular Plate ◽  
Plate Theory ◽  
Normal System ◽  
Free Boundaries ◽  
Elastic Plates ◽  
Normal Loading ◽  
Complex Variable Methods ◽  
Concentrated Forces ◽  
Special Case ◽  
Thin Elastic Plates

ABSTRACTWithin the limitations of the small-deflexion plate theory, complex variable methods are used in this paper to obtain an exact solution for the problem of a thin circular plate supported at several interior or boundary points, and subjected to a certain normal loading spread over the area of an eccentric circle, the boundary of the plate being free. The load considered includes as a special case a linearly varying load over the circle and, as the radius of the loaded circle tends to zero, this load can be made to tend to a couple nucleus at its centre. As limiting cases the procedure adopted provides us with solutions appropriate to a circular plate, an infinitely large plate and a half-plane having free boundaries and acted upon by any normal system of concentrated forces and concentrated couples in equilibrium. Formulae for the moments, shears and deflexions relating to special examples are worked out in detail.

Bending of an Elastically Restrained Circular Plate Under Normal Loading Over a Sector

1958 ◽  
Vol 25 (1) ◽  
pp. 37-46
Author(s):  
W. A. Bassali ◽  
R. H. Dawoud
Keyword(s):  
Boundary Condition ◽  
Circular Plate ◽  
Complex Variable ◽  
Variable Method ◽  
General Boundary Condition ◽  
Single Treatment ◽  
Normal Loading ◽  
Simply Supported ◽  
Thin Circular Plate ◽  
Elastically Restrained

Abstract The complex variable method is used to find the deflection, bending and twisting moments, and shearing forces at any point of a thin circular plate normally loaded over a sector and supported at its edge under a general boundary condition including the usual clamped and simply supported boundaries. In this way separate treatments for these two cases are avoided and a single treatment is available.

Transverse bending of infinite and semi-infinite thin elastic plates. III

1958 ◽  
Vol 54 (2) ◽  
pp. 288-299 ◽  
Author(s):  
W. A. Bassali ◽  
M. Nassif ◽  
H. P. F. Swinnerton-Dyer
Keyword(s):  
Isotropic Plate ◽  
Plate Theory ◽  
Outer Boundary ◽  
Exact Expression ◽  
Transverse Displacement ◽  
Elastic Plates ◽  
Classical Plate Theory ◽  
Transverse Bending ◽  
Elastically Restrained ◽  
Limiting Case

ABSTRACTWithin the restrictions of the classical plate theory, complex variable methods are used in this paper to develop an exact expression for the transverse displacement of an infinitely large isotropic plate having a free outer boundary and elastically restrained at an inner circular boundary, the plate being subjected to a general type of loading distributed over the area of a circle. The limiting case of a half-plane clamped along the straight edge and acted upon normally by the same loading is also considered.

Bending of an eccentrically loaded and concentrically supported thin circular plate. I

1966 ◽  
Vol 62 (1) ◽  
pp. 99-111 ◽  
Author(s):  
W. A. Bassali ◽  
F. R. Barsoum
Keyword(s):  
Circular Plate ◽  
Complex Variable ◽  
Concentric Circle ◽  
Thin Plates ◽  
Simply Supported ◽  
Series Form ◽  
Thin Circular Plate ◽  
Circular Patch ◽  
Complex Variable Methods ◽  
In Series

AbstractWithin the limitations of the classical small deflexion theory of thin plates and using complex variable methods, exact expressions are obtained in series form for the deflexion at any point of a thin isotropic circular plate simply supported along a concentric circle and subject to loading symmetrically distributed over an eccentric circular patch which lies inside the circle of support. In special and limiting cases the solutions reduce to those obtained before.

Hydroelastic Instability of Infinite Strips Under Shearing Load on an Elastic Foundation

1984 ◽  
Vol 51 (2) ◽  
pp. 263-268 ◽  
Author(s):  
J. Tani
Keyword(s):  
Elastic Foundation ◽  
Fourier Transforms ◽  
Plate Theory ◽  
Inviscid Flow ◽  
The Other ◽  
Simply Supported ◽  
Deflection Plate ◽  
Small Deflection ◽  
Divergence Velocity ◽  
The Galerkin Method

The paper examines the hydroelastic instability of an infinitely long plate subjected to shearing load with two different boundary conditions, one side of which is exposed to an incompressible inviscid flow, and the other side supported on an elastic foundation. The analysis is based on the small deflection plate theory and the classical linearized potential flow theory. The Galerkin method and Fourier transforms are used. It is found that the effects of the shearing load and the elastic foundation on the divergence velocity can be illustrated by a single curve for both clamped and simply supported cases.

Normal Loading on a Wedge-Shaped Plate

1955 ◽  
Vol 6 (3) ◽  
pp. 196-204 ◽  
Author(s):  
D. E. R. Godfrey
Keyword(s):  
Thin Plate ◽  
Mellin Transform ◽  
Plate Theory ◽  
Normal Loading ◽  
Thin Plate Theory

SummaryThe equations of thin plate theory are expressed in polar co-ordinates and transformed using the Mellin transform. Problems involving discontinuous and isolated normal loadings may then be solved in the case of the built-in or freely supported wedge-shaped boundary.

Bending of a Cylindrically Aeolotropic Circular Plate With Eccentric Load

1952 ◽  
Vol 19 (1) ◽  
pp. 9-12
Author(s):  
A. M. Sen Gupta
Keyword(s):  
Boundary Conditions ◽  
Circular Plate ◽  
Uniform Thickness ◽  
Eccentric Load ◽  
Concentrated Load ◽  
Different Boundary Conditions ◽  
Small Deflection ◽  
Deflection Theory ◽  
Clamped Edge

Abstract The problem of small-deflection theory applicable to plates of cylindrically aeolotropic material has been developed, and expressions for moments and deflections produced have been found by Carrier in some symmetrical cases under uniform lateral loadings and with different boundary conditions. The author has also found the moments and deflection in the case of an unsymmetrical bending of a plate loaded by a distribution of pressure of the form p = p0r cos θ, with clamped edge. The object of the present paper is to investigate the problem of the bending of a cylindrically aeolotropic circular plate of uniform thickness under a concentrated load P applied at a point A at a distance b from the center, the edge being clamped.

scholarly journals An Exact Series Solution for the Vibration of Mindlin Rectangular Plates with Elastically Restrained Edges

2014 ◽  
Vol 2014 ◽  
pp. 1-11
Author(s):  
Xue Kai ◽  
Wang Jiufa ◽  
Li Qiuhong ◽  
Wang Weiyuan ◽  
Wang Ping
Keyword(s):  
Boundary Conditions ◽  
Plate Theory ◽  
Mindlin Plate ◽  
Rectangular Plates ◽  
Cross Sectional ◽  
Fourier Cosine ◽  
Cosine Series ◽  
The Matrix ◽  
Elastically Restrained Edges ◽  
Elastically Restrained

An analysis method is proposed for the vibration analysis of the Mindlin rectangular plates with general elastically restrained edges, in which the vibration displacements and the cross-sectional rotations of the mid-plane are expressed as the linear combination of a double Fourier cosine series and four one-dimensional Fourier series. The use of these supplementary functions is to solve the possible discontinuities with first derivatives at each edge. So this method can be applied to get the exact solution for vibration of plates with general elastic boundary conditions. The matrix eigenvalue equation which is equivalent to governing differential equations of the plate can be derived through using the boundary conditions and the governing equations based on Mindlin plate theory. The natural frequencies can be got through solving the matrix equation. Finally the numerical results are presented to validate the accuracy of the method.

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