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.

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.

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.

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.

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.

Basis of the Tubesheet Heat Exchanger Design Rules Used in the French Pressure Vessel Code

1992 ◽  
Vol 114 (1) ◽  
pp. 124-131 ◽  
Author(s):  
F. Osweiller
Keyword(s):  
Heat Exchanger ◽  
Pressure Vessel ◽  
Heat Exchangers ◽  
Tube Bundle ◽  
Outer Edge ◽  
Design Rules ◽  
Effective Elastic Constants ◽  
Heat Exchanger Design ◽  
Solid Plate ◽  
Main Basis

For about 40 years most tubesheet exchangers have been designed according to the standards of TEMA. Partly due to their simplicity, these rules do not assure a safe heat-exchanger design in all cases. This is the main reason why new tubesheet design rules were developed in 1981 in France for the French pressure vessel code CODAP. For fixed tubesheet heat exchangers, the new rules account for the “elastic rotational restraint” of the shell and channel at the outer edge of the tubesheet, as proposed in 1959 by Galletly. For floating-head and U-tube heat exchangers, the approach developed by Gardner in 1969 was selected with some modifications. In both cases, the tubesheet is replaced by an equivalent solid plate with adequate effective elastic constants, and the tube bundle is simulated by an elastic foundation. The elastic restraint at the edge of the tubesheet due the shell and channel is accounted for in different ways in the two types of heat exchangers. The purpose of the paper is to present the main basis of these rules and to compare them to TEMA rules.

Impulsive Loading of a Simply Supported Circular Rigid Plastic Plate

1968 ◽  
Vol 35 (1) ◽  
pp. 59-65 ◽  
Author(s):  
Norman Jones
Keyword(s):  
Yield Condition ◽  
Impulsive Loading ◽  
Bending Moments ◽  
Circular Plates ◽  
Governing Equations ◽  
Rigid Plastic ◽  
Static Loads ◽  
Simply Supported ◽  
Experimental Values ◽  
Theoretical Procedure

It is clear from a survey of literature on the dynamic deformation of rigid-plastic plates that most work has been focused on plates in which either membrane forces or bending moments alone are considered important, while the combined effect of membrane forces and bending moments on the behavior of plates under static loads and beams under dynamic loads is fairly well established. This paper, therefore, is concerned with the behavior of circular plates loaded dynamically and with deflections in the range where both bending moments and membrane forces are important. A general theoretical procedure is developed from the equations for large deflections of plates and a simplified yield condition due to Hodge. The results obtained when solving the governing equations for the particular case of a simply supported circular plate loaded with a uniform impulsive velocity are found to compare favorably with the corresponding experimental values recorded by Florence.

On limiting cases in the flexure of simply supported regular polygonal plates

1969 ◽  
Vol 65 (3) ◽  
pp. 831-834 ◽  
Author(s):  
K. Rajaiah ◽  
Akella Kameswara Rao
Keyword(s):  
Circular Plate ◽  
Regular Polygons ◽  
Circular Plates ◽  
Axisymmetric Loading ◽  
Simply Supported ◽  
Significant Factors

AbstractLimiting solutions are derived for the flexure of simply supported many-sided regular polygons, as the number of sides is increased indefinitely. It is shown that these solutions are different from those for simply supported circular plates. For axisymmetric loading, circular plate solutions overestimate the deflexions and the moments by significant factors.

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