Uniformly Loaded Circular Plates With a Central Hole and Both Edges Supported

1957 ◽  
Vol 24 (2) ◽  
pp. 306-310
Author(s):  
J. C. Georgian
Keyword(s):  
Outer Edge ◽  
Central Hole ◽  
Circular Plates ◽  
Simply Supported ◽  
Edge Conditions

Abstract Several catalogs giving results of circular plates with a central hole with various loading and edge conditions have been published. However, these do not cover the case where each edge is supported, either simply or clamped. The usual recommendation is to solve these cases by superposition from the known elementary cases. This is not easily done. The results of the following two cases are given in this paper: (a) Inner and outer edge clamped; (b) inner and outer edge simply supported.

Splines in vibration analysis of non-homogeneous circular plates of quadratic thickness

2022 ◽  
Vol 0 (0) ◽  
Author(s):  
Robin Singh ◽  
Neeraj Dhiman ◽  
Mohammad Tamsir
Keyword(s):  
Radial Direction ◽  
Outer Edge ◽  
Thickness Variation ◽  
Circular Plates ◽  
Plate Material ◽  
Quintic Spline ◽  
Simply Supported ◽  
Edge Conditions ◽  
Modes Of Vibration ◽  
First Time

Abstract Mathematical model to account for non-homogeneity of plate material is designed, keeping in mind all the physical aspects, and analyzed by applying quintic spline technique for the first time. This method has been applied earlier for other geometry of plates which shows its utility. Accuracy and versatility of the technique are established by comparing with the well-known existing results. Effect of quadratic thickness variation, an exponential variation of non-homogeneity in the radial direction, and variation in density; for the three different outer edge conditions namely clamped, simply supported and free have been computed using MATLAB for the first three modes of vibration. For all the three edge conditions, normalized transverse displacements for a specific plate have been presented which shows the shiftness of nodal radii with the effect of taperness.

Bending of Circular Plates Under a Uniform Load on a Concentric Circle—Part II

1968 ◽  
Vol 90 (2) ◽  
pp. 279-293
Author(s):  
J. C. Heap
Keyword(s):  
Boundary Conditions ◽  
Circular Plate ◽  
Concentric Circle ◽  
Outer Edge ◽  
Circular Plates ◽  
Uniform Load ◽  
Simply Supported ◽  
Basic Equations

The basic equations of deflection, slope, and moments for a thin, flat, circular plate subjected to a uniform load on a concentric circle were derived for four generalized cases. From these generalized cases, six simplified cases were deduced. The four generalized cases have the uniform load acting on a concentric circle of the plate between the inner and outer edges, with the following boundary conditions: (a) Outer edge supported and fixed, inner edge fixed; (b) outer edge simply supported, inner edge free; (c) outer edge simply supported, inner edge fixed; and (d) outer edge supported and fixed, inner edge free.

Bending of Circular Plates Under a Variable Symmetrical Load—Part I

1968 ◽  
Vol 90 (2) ◽  
pp. 268-278 ◽  
Author(s):  
J. C. Heap
Keyword(s):  
Radial Distance ◽  
Outer Edge ◽  
Variable Load ◽  
Constant Force ◽  
Circular Plates ◽  
Simply Supported ◽  
Inner Radius ◽  
Solid Plate ◽  
Basic Equations ◽  
Symmetrical Load

The basic equations of deflection, slope, and moment for a thin, flat, circular plate, under a symmetrical variable load, for a constant force divided by the square of the radial distance, have been developed. Six cases have been derived. The first four cases cover the variable load acting over the entire plate, viz., (a) fixed, supported, outer edge and fixed, inner edge, (b) simply supported, outer edge and free, inner edge, (c) simply supported, outer edge and fixed, inner edge, (d) fixed, supported, outer edge and free, inner edge; and the final two cases are for a solid plate having the acting variable load bounded by circles of an inner radius and the outer support-load-radius; i.e., (e) fixed, supported, outer edge and (f) simply supported, outer edge.

The Bending of the Cylindrically Aeolotropic Plate

1944 ◽  
Vol 11 (3) ◽  
pp. A129-A133
Author(s):  
G. F. Carrier
Keyword(s):  
Radial Symmetry ◽  
Outer Edge ◽  
Circular Plates ◽  
Concentrated Force ◽  
Design Problems ◽  
Simply Supported ◽  
Uniform Shear ◽  
Small Deflection ◽  
Degree Of Anisotropy ◽  
Deflection Theory

Abstract In this paper, the small-deflection theory, applicable to plates of cylindrically aeolotropic material, is presented, and expressions are obtained for the moments and deflections produced by the following combinations of loading and boundary conditions: The disk clamped along its circumference and loaded by a uniform lateral pressure; the clamped disk loaded by a central concentrated force; the simply supported disk loaded by uniform edge moment; the disk with a rigid core clamped along its circumference and loaded by a central concentrated force; the ring clamped along its outer edge and loaded by a uniform shear distribution along the inner edge; the simply supported disk with an elastic isotropic core loaded by a uniform edge moment; and the disk under the loading given by p = p0r cos θ. The six symmetrical problems of this group were chosen for evaluation since they and their linear combinations comprise a large part of the total set of such problems. Curves are included showing, for three of the foregoing problems, the effect of the degree of anisotropy on the stresses. The practical application of solutions obtained by the following theory might lie, for example, in design problems involving circular plates which are built up of laminas of radial symmetry with different tangential and radial stiffnesses. The theory could also be applied to the design of circular concrete slabs with different amounts of reinforcing steel in the radial and tangential directions.

Bending of Thin Ring-Sector Plates

1951 ◽  
Vol 18 (4) ◽  
pp. 359-363
Author(s):  
L. I. Deverall ◽  
C. J. Thorne
Keyword(s):  
Continuous Function ◽  
Bending Moment ◽  
Circular Ring ◽  
Circular Plates ◽  
Thin Ring ◽  
Special Cases ◽  
Edge Conditions

Abstract General expressions for the deflection of plates whose planform is a sector of a circular ring are given for cases in which the straight edges have arbitrary but given deflection and bending moment. The solutions are given for all combinations of physically important edge conditions on the two circular edges. Sectors of circular plates are included as special cases. Solutions are given for a general load which is a continuous function of r, and a sectionally continuous function of θ, where r and θ are the usual polar co-ordinates with the pole at the center of the ring. Several specific examples are given.

A Suction Device Using Air Under Pressure

1956 ◽  
Vol 23 (2) ◽  
pp. 269-272
Author(s):  
L. F. Welanetz
Keyword(s):  
Fluid Flow ◽  
Flow Rate ◽  
Fluid Flows ◽  
Central Hole ◽  
Fluid Flow Rate ◽  
Circular Plates ◽  
Suction Device ◽  
Holding Power ◽  
Plate Separation

Abstract An analysis is made of the suction holding power of a device in which a fluid flows radially outward from a central hole between two parallel circular plates. The holding power and the fluid flow rate are determined as functions of the plate separation. The effect of changing the proportions of the device is investigated. Experiments were made to check the analysis.

scholarly journals Polya Counting Theory Applied to Combination of Edge Conditions for Generally Shaped Isotropic Plates

2019 ◽  
Vol 2 (2) ◽  
pp. 194-202
Author(s):  
Yoshihiro Narita
Keyword(s):  
Material Properties ◽  
Structural Design ◽  
Plate Boundary ◽  
Trial And Error ◽  
Simply Supported ◽  
Isotropic Plates ◽  
Edge Conditions ◽  
Structural Responses ◽  
Structural Behaviors ◽  
Clamped Edges

Structural behaviors of plate components, such as internal stress, deflection, buckling and dynamic response, are important in the structural design of aerospace, mechanical, civil and other industries. These behaviors are known to be affected not only by plate shapes and material properties but also by edge conditions. Any one of the three classical edge conditions in bending, namely free, simply supported and clamped edges, may be used to model the constraint along an edge of plates. Along the entre boundary with plural edges, there exist a wide variety of combinations in the entire plate boundary, each giving different values of structural responses. For counting the total number of possible combinations, the present paper considers Polya counting theory in combinatorial mathematics. For various plate shapes, formulas are derived for counting exact numbers in combination. In some examples, such combinations are confirmed in the figures by a trial and error approach.

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