Closure to “Discussions of ‘Bending of Circular Plates Under a Uniform Load on a Concentric Circle—Parts I and II’” (1968, ASME J. Eng. Ind., 90, p. 293)

1968 ◽  
Vol 90 (2) ◽  
pp. 294-294
Author(s):  
J. C. Heap
Keyword(s):  
Concentric Circle ◽  
Circular Plates ◽  
Uniform Load

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.

Large Deflections of Circular Plates of Variable Thickness

1982 ◽  
Vol 49 (1) ◽  
pp. 243-245 ◽  
Author(s):  
B. Banerjee
Keyword(s):  
Circular Plate ◽  
Variable Thickness ◽  
Large Deflection ◽  
Numerical Results ◽  
Large Deflections ◽  
Circular Plates ◽  
Uniform Load ◽  
Plate Of Variable Thickness ◽  
Plates Of Variable Thickness

The large deflection of a clamped circular plate of variable thickness under uniform load has been investigated using von Karman’s equations. Numerical results obtained for the deflections and stresses at the center of the plate have been given in tabular forms.

About the Bending Calculus for Circular Tapping Plates, Embedded at the Interior Circumference, with Uniform Load at all the Crown by Transfer-Matrix Method

2013 ◽  
Vol 325-326 ◽  
pp. 218-222
Author(s):  
Mihaela Suciu
Keyword(s):  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
State Vector ◽  
Matrix Method ◽  
The State ◽  
Vertical Load ◽  
Circular Plates ◽  
Uniform Load ◽  
Ring Elements

This article presents the bending calculus of the circular tapping plates, embedded at the interior circumference, free at the exterior circumference, charged with an uniform vertical load at the all the crown, using the Transfer-Matrix Method. This method had the mathematical bases in the theory of Diracs and Heavisides functions and operators. The circular plates calculus is very important for its applications in the mechanical, robotic, medical, military and aerospace industries. First, we can obtain the state vector for the first ring, the exterior circumferential element and the state vector for the latest ring, the interior circumferential element. After, we can calculate for the values r0<r<R, all the state vectors for all the ring elements of the circular tapping plate by Transfer-Matrix Method. With this method is very easy to program this algorithm for the bending calculus of the circular tapping plates.

Deflection of uniformly loaded circular plates upon equispaced point supports

1970 ◽  
Vol 5 (2) ◽  
pp. 115-120 ◽  
Author(s):  
Henry Vaughan
Keyword(s):  
Single Point ◽  
Central Area ◽  
Sine Wave ◽  
Point Load ◽  
Optical Methods ◽  
Maximum Deviation ◽  
Circular Plates ◽  
Uniform Load ◽  
Plate Edge ◽  
Superposition Of Solutions

A simple formula is derived for predicting the flexure of uniformly loaded point-supported circular plates. The classical solution of Michell for a clamped plate under a single point load is extended for any number of point loads regularly spaced around a circle concentric with the plate edge. The resulting series for the edge moments and shears are summed and are shown to be very similar to a simple sine wave. Replacing the exact expressions by single sine waves enables the clamped edges to be set free by a simple superposition of solutions. The point reactions are equilibrated by a uniform load and the resulting deflection surface for a free uniformly loaded point-supported plate is obtained immediately. Deflection curves for the particular case of a plate supported at three points are given in the form of contours of equal deflection. This particular case is compared with some experimental results which were obtained by optical methods. For three supports, maximum deviation from the flat is least when the supports are equispaced around a circle of radius approximately two-thirds that of the plate. The contours for this case show that the central area is remarkably flat and that there are three diameters along which the deflections are almost constant.

scholarly journals An analysis of annular plate in curvilinear non-orthogonal coordinates with the help of equations of a shell theory

2020 ◽  
Vol 16 (6) ◽  
pp. 472-480
Author(s):  
Sergey N. Krivoshapko
Keyword(s):  
Small Parameter ◽  
Shell Theory ◽  
Annular Plate ◽  
Complete System ◽  
Parameter Method ◽  
Circular Plates ◽  
Uniform Load ◽  
Small Parameter Method ◽  
Orthogonal Coordinates

The complete system of equations of a linear theory of thin shells in curvilinear non-orthogonal coordinates proposed in the paper was taken as the basis of the investigation. Earlier, this system was used for static analysis of a long developable helicoid. In the article, this system is applied for the determination of stress-strain state of annular and circular plates under action of the external axisymmetric uniform load acting both in the plane of the plate and out-of-their plane. Presented results for annular plate given in the non-orthogonal coordinates ex-pand a number of problems that can be solved analytically. They can be used as the first terms of series of expansion of displacements of degrees of the small parameter if a small parameter method is applied for examining a long tangential developable helicoid.

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