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.

Bending of a circular plate with an eccentric circular patch symmetrically loaded with respect to its centre

1956 ◽  
Vol 52 (3) ◽  
pp. 584-598 ◽  
Author(s):  
W. A. Bassali ◽  
R. H. Dawoud
Keyword(s):  
Boundary Condition ◽  
Circular Plate ◽  
Complex Variable ◽  
Poisson’S Ratio ◽  
Complex Variable Method ◽  
Variable Method ◽  
Poisson's Ratio ◽  
General Boundary ◽  
General Boundary Condition ◽  
Circular Patch

ABSTRACTThe complex variable method is applied to obtain solutions for the deflexion of a supported circular plate with uniform line loading along an eccentric circle under a general boundary condition including the clamped boundary , a boundary with zero peripheral couple , a boundary with equal boundary cross-couples , a hinged boundary and a boundary for which , η being Poisson's ratio. These solutions are used to obtain the deflexion at any point of a circular plate having an eccentric circular patch symmetrically loaded with respect to its centre. Expressions for the slope and cross-couples over the boundary and the deflexions at the centres of the plate and the loaded patch are obtained.

Bending of an elastically restrained circular plate under a linearly varying load over an eccentric circle

1956 ◽  
Vol 52 (4) ◽  
pp. 734-741 ◽  
Author(s):  
W. A. Bassali
Keyword(s):  
Boundary Condition ◽  
Circular Plate ◽  
Complex Potentials ◽  
General Boundary ◽  
General Boundary Condition ◽  
Thin Circular Plate ◽  
Elastically Restrained

ABSTRACTThe complex potentials and deflexion at any point of a thin circular plate with a normal linearly varying load over an eccentric circle are determined under a general boundary condition including the usual clamped and hinged boundaries.

Transverse bending of a thin circular plate loaded normally over an eccentric circle

1956 ◽  
Vol 52 (4) ◽  
pp. 742-749 ◽  
Author(s):  
W. A. Bassali
Keyword(s):  
Boundary Condition ◽  
Circular Plate ◽  
Complex Variable ◽  
Concentric Circle ◽  
Complex Potentials ◽  
Variable Method ◽  
General Boundary ◽  
Simply Supported ◽  
Circular Patch ◽  
The Common

ABSTRACTComplex variable methods have been applied to isotropic and aelotropic plate problems by several authors. The notation used here is that of Stevenson(14). Dawoud(5) has expressed the continuity conditions between two differently loaded regions in terms of the complex potentials and the particular integrals for the two regions.The problem of a transverse load at any point of a clamped circular plate was solved by Clebsch(4), Michell(11), Melan(10) and Flügge(6). A series solution for the simply supported circular plate under the same load was given by Foeppel(8). Using Stevenson's tentative method Dawoud(5) applied complex potentials to solve the problem of an eccentric isolated load under certain boundary conditions. Applying Muskhelishvili's method, Washizu(15) obtained the same results for clamped and simply supported boundaries.It is easy to get solutions for a circular plate concentrically and uniformly loaded. For non-uniform loadings there are the solutions found by Sen (13) for certain distributions of normal thrust over the complete plate or over a concentric circle and the solution of Flügge (7) for a linearly varying load over the simply supported circular plate. The present author and Dawoud(3) obtained the solutions for a circular plate with the load over the complete plate or over a concentric circle, under a general boundary constraint including as special cases the usual clamped and hinged boundaries. Ghose (9) worked out the problem of a clamped circular plate when the load is uniformly distributed between two concentric circles and two radii. Schmidt (12) found the solution for a clamped circular plate uniformly loaded over an eccentric circle. The complex variable method was applied by the author and Dawoud(2) to obtain the solutions for a circular plate having an eccentric circular patch symmetrically loaded with respect to its centre under the general boundary condition mentioned before. The author (1) also found the solution for a linearly varying load over an eccentric circle under the same boundary condition. In this paper the power of the complex variable method is exhibited by rinding the appropriate complex potentials corresponding to the loadover an eccentric circular patch, where R, θ are measured from the centre of the patch and the common diameter of the plate and the patch. Since the two cases n = 0, 1 require special consideration and were dealt with separately (in (2) and (1) respectively), we see that this paper completes the solution of the problem of a circular plate with an eccentric circular patch symmetrically loaded with respect to the common diameter of the plate and patch, the load being in this case expressible in the form .For a clamped boundary the solution is obtained in finite terms.

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.

Flexure of a Circular Plate With a Ring of Holes

1962 ◽  
Vol 29 (3) ◽  
pp. 489-496 ◽  
Author(s):  
H. Kraus
Keyword(s):  
Circular Plate ◽  
Shear Force ◽  
General Boundary Condition ◽  
Uniform Pressure ◽  
Simply Supported ◽  
Moment Distribution ◽  
Theory Of Plates ◽  
Circular Holes ◽  
The Moment ◽  
Kirchhoff Theory

The problem of the moment distribution resulting from a uniform pressure load acting over the surface of a circular plate containing a ring of equally spaced circular holes with, and without, a central circular hole is solved within the framework of the Poisson-Kirchhoff theory of plates. A general boundary condition is applied at the outer rim of the plate to make the solution valid for a range of conditions from the simply supported case to the clamped case. The edges of the perforations are allowed to be either free or to have a net shear force acting. Numerical results in the form of curves are given for typical cases, and the results of a photoelastic test are also presented.

scholarly journals Analysis of sectorial plates normally loaded over circular domains. II

1984 ◽  
Vol 7 (4) ◽  
pp. 739-754
Author(s):  
Wadie A. Bassali
Keyword(s):  
Circular Domain ◽  
Method Of Images ◽  
Normal Loading ◽  
Simply Supported ◽  
Circular Domains ◽  
Elastically Restrained

The method of images is applied to derive exact expressions for the deflections of unlimited wedge-shaped plates the central parts of which are cut, when the plate is simply supported on the radial edges, elastically restrained or free along the circular edge and is acted upon by one of three types of normal loading distributed over the surface of a circular domain. Formulae for the bending and twisting moments along the circular edge are given. Limiting forms of the obtained solutions are considered.

The NAVMI Factor and Natural Frequency of a Circular Plate Exposed to Water in Flexural Vibration

2011 ◽  
Vol 199-200 ◽  
pp. 1445-1450
Author(s):  
Hui Juan Ren ◽  
Mei Ping Sheng
Keyword(s):  
Boundary Condition ◽  
Natural Frequency ◽  
Circular Plate ◽  
Natural Frequencies ◽  
Integration Method ◽  
Flexural Vibration ◽  
The Other ◽  
Additional Mass ◽  
Simply Supported ◽  
Higher Order Modes

The expression of NAVMI factor and the natural frequency of a circular plate, which is placed in a hole of an infinite grid wall with one side exposed to water, are derived from the viewpoint of the additional mass. 10 Nodes Gauss-Legender integration method and the iteration method are employed to obtain the numerical results of the NAVMI factors, AVMI factors and the natural frequencies. It can be found from the results that NAVMI factors of the first two order modes are far bigger than those of the other modes when the boundary condition of a circular plate is certain. The first two order modal NAVMI factors of the circular plate with clamped and simply supported boundary conditions are far bigger than those of the circular plate with free-edged boundary condition, and the NAVMI factors are almost the same for the three order or much higher order modes regardless of the boundary condition. It is also observed that the natural frequencies of the circular plate exposed to water are smaller than those exposed to air, and the natural frequencies of the circular plate exposed to water with both sides are smaller than those of the circular plate exposed to water with one side.

The deflection of a thin circular plate with an eccentric circular hole

1976 ◽  
Vol 11 (2) ◽  
pp. 107-124 ◽  
Author(s):  
E Ollerton
Keyword(s):  
Circular Plate ◽  
Circular Hole ◽  
Theoretical Investigation ◽  
Outer Edge ◽  
Plate Surface ◽  
Concentrated Load ◽  
Simply Supported ◽  
Thin Circular Plate ◽  
Clamped Edge

A theoretical investigation of the small deflections of a thin circular plate is reported. The plate has a flat circular clamp at the outer edge and a similar clamp at the inner edge, which is placed eccentrically. These supports can be arranged to prescribe either a clamped edge or a simply supported edge, and all combinations of the two types are investigated. The plate can be subjected to a concentrated load at the centre of the inner clamp, moments about two perpendicular axes of the inner clamp, or pressure on the plate surface between the clamps. Deflections and slopes of the inner clamp have been determined, and in all cases the new values tend towards established values for the case of a central inner clamp, as the eccentricity of the inner clamp is reduced.

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