Large Deflections of Circular Plates

1952 ◽  
Vol 19 (3) ◽  
pp. 287-292
Author(s):  
M. Stippes ◽  
A. H. Hausrath
Keyword(s):  
Circular Plate ◽  
Critical Values ◽  
Graphical Form ◽  
Series Expansions ◽  
Large Deflections ◽  
Circular Plates ◽  
Simply Supported ◽  
Perturbation Procedure

Abstract This paper contains a solution of von Kármán’s equations for a uniformly loaded, simply supported circular plate. The method used to obtain the solution is the perturbation procedure. Series expansions for the deflection and stresses in the plate are obtained. The legitimacy of these expansions is demonstrated in the Appendix. Critical values of stress and deflection are presented in graphical form. Furthermore, tables of coefficients for the afore-mentioned series are presented if anyone desires to extend the results which are presented here.

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.

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.

Nonlinear Bending of Composite Circular Plates with Embedded Shape Memory Alloy Fibers

2008 ◽  
Vol 33-37 ◽  
pp. 501-506
Author(s):  
Shi Rong Li ◽  
Wen Shan Yu
Keyword(s):  
Shape Memory ◽  
Circular Plate ◽  
Mechanical Load ◽  
Constitutive Relations ◽  
Thin Plates ◽  
Circular Plates ◽  
Nonlinear Bending ◽  
One Dimensional ◽  
Bending Deformation ◽  
Simply Supported

Based on Brinson’s one-dimensional thermo-mechanical constitutive relations of shape memory alloys and the theory of thin plates in the von Kármán sense, the response of bending of a uniform heated circular plate embedded with SMA fibers in the radial directions and subjected to a uniform distributed mechanical load is studied. The characteristic curves of the central deflection versus temperature rise of the circular plate with both clamped and simply supported boundary conditions are obtained. The numerical results show that, the recovery forces of the pre-strained SMA caused by the phase transformation from martensite to austenite can modify the bending deformation significantly. So, it can be concluded that the bending deformation can be adjusted effectively and actively by embedment of the SMA fibers into the circular plates

Deflection of Uniformly Loaded Circular Plates

1943 ◽  
Vol 10 (4) ◽  
pp. A181-A182
Author(s):  
F. C. W. Olson
Keyword(s):  
General Theory ◽  
Circular Plate ◽  
Elastic Constants ◽  
Energy Method ◽  
Plate Thickness ◽  
Large Deflections ◽  
Bending Moments ◽  
Circular Plates ◽  
Boundary Parameter ◽  
Center Deflection

Abstract The equation for small deflections of a uniformly loaded and supported circular plate is rewritten so that the two constants of integration are interpreted as the center deflection ω0 and a boundary parameter α. Stresses and bending moments are given in terms of ω0 and α. A particular advantage of this treatment is that the nature of the support may be found experimentally even if the elastic constants, plate thickness, and load are unknown. The energy method is used to develop a more general theory of large deflections, valid for any condition of uniform support at the 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.

Axi-Symmetric Buckling of Orthotopic Circular Plates with Variable Thickness

1967 ◽  
Vol 71 (675) ◽  
pp. 218-223 ◽  
Author(s):  
Sharad A. Patel ◽  
Franklin J. Broth
Keyword(s):  
Circular Plate ◽  
Variable Thickness ◽  
Material Properties ◽  
Radial Direction ◽  
Constant Thickness ◽  
Thickness Variation ◽  
Circular Plates ◽  
Plate Edge ◽  
Simply Supported

Axi-symmetric buckling of a circular plate having different material properties in the radial and circumferential directions was analysed in ref. 1. A plate with constant thickness and subjected to a uniform edge compression was considered. The plate edge was assumed clamped or simply-supported. The analysis of ref. 1 is extended to include plates with thickness variation in the radial direction.

Large Axisymmetric Deformations of Elastic/Plastic Perforated Circular Plates

2003 ◽  
Vol 125 (4) ◽  
pp. 357-364 ◽  
Author(s):  
D. Wu ◽  
J. Peddieson ◽  
G. R. Buchanan ◽  
S. G. Rochelle
Keyword(s):  
Mathematical Model ◽  
Differential Equations ◽  
Circular Plate ◽  
Numerical Solutions ◽  
Outer Edge ◽  
Plate Bending ◽  
Large Deflections ◽  
Circular Plates ◽  
Elastic Plastic ◽  
Thickness Variations

A mathematical model of axisymmetric elastic/plastic perforated circular plate bending and stretching is developed which accounts for through thickness yielding, through thickness variations in perforation geometry, elastic outer edge restraint, and moderately large deflections. Selected numerical solutions of the resulting differential equations are presented graphically and used to illustrate interesting trends.

Symmetrically Loaded Circular Plates under the Combined Action of Lateral and End Loading

1959 ◽  
Vol 10 (3) ◽  
pp. 266-282 ◽  
Author(s):  
Raymond Hicks
Keyword(s):  
Circular Plate ◽  
Infinite Plate ◽  
Lateral Load ◽  
Simultaneous Action ◽  
Bending Moments ◽  
Circular Plates ◽  
Simply Supported ◽  
Combined Action

Expressions are obtained for the radial and tangential bending moments in a circular plate under the combined action of (a) a lateral load concentrated on the circumference of a circle and an end tension or compression, and (b) a uniformly distributed lateral load, having a diameter less than the diameter of the plate, and an end tension or compression. For both types of loading, solutions are obtained for plates which are simply-supported and for plates with an arbitrary end rotation.In addition, the following limiting cases are considered: (i) concentrated lateral load with end tension or compression, and (ii) an infinite plate under the simultaneous action of an end tension and a lateral load concentrated on the circumference of a circle of finite diameter.

NONLINEAR ANALYSIS OF FUNCTIONALLY GRADED CIRCULAR PLATES UNDER DIFFERENT LOADS AND BOUNDARY CONDITIONS

2008 ◽  
Vol 08 (01) ◽  
pp. 131-159 ◽  
Author(s):  
RECEP GUNES ◽  
J. N. REDDY
Keyword(s):  
Nonlinear Analysis ◽  
Strain Tensor ◽  
Homogenization Method ◽  
Functionally Graded ◽  
Gradient Material ◽  
Graphical Form ◽  
Circular Plates ◽  
Geometrically Nonlinear Analysis ◽  
Steady State Heat Transfer ◽  
Lagrange Strain

Geometrically nonlinear analysis of functionally graded circular plates subjected to mechanical and thermal loads is carried out in this paper. The Green–Lagrange strain tensor in its entirety is used in the analysis. The locally effective material properties are evaluated using homogenization method which is based on the Mori–Tanaka scheme. In the case of thermally loaded plates, the temperature variation through the thickness is determined by solving a steady-state heat transfer (i.e. energy) equation. As an example, a functionally gradient material circular plate composed of zirconium and aluminum is used and results are presented in graphical form.

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