Axisymmetrical Bending of Circular Plates Under Simultaneous Action of Lateral Load, Force in the Middle Plane, and Elastic Foundation

1957 ◽  
Vol 24 (1) ◽  
pp. 141-143
Author(s):  
Yi-Yuan Yu
Keyword(s):  
Heat Exchangers ◽  
Tensile Force ◽  
Bending Moment ◽  
Load Force ◽  
Simultaneous Action ◽  
Middle Plane ◽  
Circular Plates ◽  
Simply Supported ◽  
Small Deflection ◽  
Deflection Theory

Abstract In this note the problem indicated in the title is solved in closed form on the basis of the classical small-deflection theory. As the problem is directly related to the stress analysis of tube sheets in heat exchangers, the present investigation also constitutes the preliminary step of a more exact analysis of the latter problem. Results of numerical examples are presented showing the influence of a tensile force in the middle plane and the rotation-resisting capability of the foundation on the deflection and bending moment of a uniformly loaded circular plate, either simply supported or clamped.

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.

Effects of Boundary Conditions and Initial Out-of-Roundness on the Strength of Thin-Walled Cylinders Subject to External Hydrostatic Pressure

1956 ◽  
Vol 23 (3) ◽  
pp. 351-358
Author(s):  
G. D. Galletly ◽  
R. Bart
Keyword(s):  
Hydrostatic Pressure ◽  
Boundary Conditions ◽  
Semiempirical Methods ◽  
Test Results ◽  
External Hydrostatic Pressure ◽  
Simply Supported ◽  
Small Deflection ◽  
The Difference ◽  
Deflection Theory ◽  
Theoretical Results

Abstract Using classical small-deflection theory, an investigation was made of the effects of boundary conditions and initial out-of-roundness on the strength of cylinders subject to external hydrostatic pressure. The equations developed in this paper for initially out-of-round cylinders with clamped ends, and a slightly modified form of the equations previously derived by Bodner and Berks for simply supported ends, were applied to some actual test results obtained from nine steel cylinders which had been subjected to external hydrostatic pressure. Three semiempirical methods for determining the initial out-of-roundness of the cylinders also were investigated and these are described in the paper. The investigation indicates that if the initial out-of-roundness is determined in a manner similar to that suggested by Holt then the correlation between the experimental and theoretical results is quite good. The investigation also indicates that while the difference in collapse pressures for clamped-end and simply supported perfect cylinders may be quite considerable, this does not appear to be the case when initial out-of-roundnesses of a practical magnitude are considered.

Buckling of Circular Plate on Elastic Foundation

1965 ◽  
Vol 87 (3) ◽  
pp. 323-324 ◽  
Author(s):  
L. V. Kline ◽  
J. O. Hancock
Keyword(s):  
Circular Plate ◽  
Middle Surface ◽  
Elastic Plates ◽  
Buckling Loads ◽  
Simply Supported ◽  
Small Deflection ◽  
Edge Conditions ◽  
Deflection Theory ◽  
Plate On Elastic Foundation ◽  
Clamped Edge

The buckling loads are found for the simply supported and clamped-edge conditions for a circular plate on a springy foundation under the action of edge loading in the middle surface of the plate. The small deflection theory of bending of thin elastic plates has been used.

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.

Unified Iso-Response Curves for Orthotropic Plates Under Lateral Pressure Pulse

1989 ◽  
Vol 111 (4) ◽  
pp. 246-249 ◽  
Author(s):  
J. Ari-Gur ◽  
M. J. Kenig
Keyword(s):  
Pressure Pulse ◽  
Lateral Pressure ◽  
Bending Moment ◽  
Elastic Response ◽  
Rectangular Plates ◽  
Orthotropic Plates ◽  
Response Curves ◽  
Small Deflection ◽  
Theory Of Plates ◽  
Deflection Theory

General nondimensional iso-deflection and iso-bending moment curves for the elastic response of orthotropic rectangular plates under lateral pressure pulse are presented. Similarities of loads and plate properties are employed to develop the curves, which represent the peak response for various combinations of orthotropy, density, geometry and loading. The presented curves are valid within the elastic small deflection theory of plates, and their usefulness and limitations are discussed in the paper.

scholarly journals Stability of cylindrical panel with variable thickness

2006 ◽  
Vol 28 (1) ◽  
pp. 56-65 ◽  
Author(s):  
Nguyen Thi Hien Luong ◽  
Thach Som So Hoach
Keyword(s):  
Variable Thickness ◽  
Shell Thickness ◽  
Cylindrical Panel ◽  
Thickness Variation ◽  
Simply Supported ◽  
Small Deflection ◽  
Linear Buckling ◽  
Variation Parameter ◽  
Deflection Theory ◽  
Linear Buckling Analysis

A linear buckling analysis based on the small deflection theory is presented for the cylindrical panel with sinusoidal changes in the shell thickness. The buckling load for simply supported cylindrical panel around the periphery is defined by using the hybrid perturbation - Galerkin method. The influence of the thickness variation parameter on the critical loads is investigated.

Bending and Twisting of Pipes With Strain Hardening

1984 ◽  
Vol 106 (2) ◽  
pp. 188-195 ◽  
Author(s):  
J. H. Lau ◽  
T. T. Lau
Keyword(s):  
Effective Strain ◽  
Closed Form Solution ◽  
Bending Moment ◽  
Small Deformation ◽  
Form Solution ◽  
Simultaneous Action ◽  
Deformation Analysis ◽  
Engineering Practice ◽  
Strain Diagram ◽  
Interaction Curves

A closed-form solution is presented for the small deformation analysis of a straight thin-walled circular cylinder subjected to the simultaneous action of bending and twisting moments. Dimensionless interaction curves and charts which relate the variables, bending moment, curvature, maximum effective strain, twisting moment, and shear strain are also provided for engineering practice convenience. The average stress-strain diagram of the cylinder is described by two straight lines. The result presented herein is not only a good approximation of a wide class of piping materials, but also provides a standard tool for estimating the accuracy of different direct schemes such as numerical integration, finite-difference, and finite-element methods.

The Mixed-Body Model: A Method for Predicting Large Deflections in Stepped Cantilever Beams

2021 ◽  
pp. 1-18
Author(s):  
Brandon Sargent ◽  
Collin Ynchausti ◽  
Todd G Nelson ◽  
Larry L Howell
Keyword(s):  
Large Deflections ◽  
Cantilever Beams ◽  
Element Analysis ◽  
Body Model ◽  
Minimal Error ◽  
Small Deflection ◽  
Rigid Body Model ◽  
Expected Values ◽  
Deflection Theory ◽  
Sample Set

Abstract This paper presents a method for predicting endpoint coordinates, stress, and force to deflect stepped cantilever beams under large deflections. This method, the Mixed-Body Model or MBM, combines small deflection theory and the Pseudo-Rigid-Body Model for large deflections. To analyze the efficacy of the model, the MBM is compared to a model that assumes the first step in the beam to be rigid, to finite element analysis, and to the numerical boundary value solution over a large sample set of loading conditions, geometries, and material properties. The model was also compared to physical prototypes. In all cases, the MBM agrees well with expected values. Optimization of the MBM parameters yielded increased agreement, leading to average errors of <0.01 to 3%. The model provides a simple, quick solution with minimal error that can be particularly helpful in design.

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.

scholarly journals State space approach with FEM for the determination of structural behaviour of composite plates

2017 ◽  
Vol 8 (4) ◽  
pp. 468-483
Author(s):  
Asad Shukri Albostami ◽  
Zhangjian Wu ◽  
Zhenmin Zou
Keyword(s):  
Plate Thickness ◽  
Composite Plates ◽  
Thickness Direction ◽  
Middle Plane ◽  
Structural Behaviour ◽  
State Space Approach ◽  
Content Type ◽  
Simply Supported ◽  
Space Approach

Purpose An analytical investigation has been carried out for a simply supported rectangular plate with two different loading conditions by using 3D state space approach (SSA). Also, the accurate location of the neutral plane (N.P.) through the thickness of the plate can be identified: the N.P. is shifted away from the middle plane according to the loading condition. The paper aims to discuss these issues. Design/methodology/approach SSA and finite element method are used for the determination of structural behaviour of simply supported orthotropic composite plates under different types of loading. The numerical results from a finite element model developed in ABAQUS. Findings The effect of the plate thickness on displacements and stresses is described quantitatively. It is found that the N.P. of the plate, identified according to the values of the in-plane stresses through the thickness direction, is shifted away from the middle plane. Further investigation shows that the position of the N.P. is loading dependant. Originality/value This paper describe the effect of the plate thickness on displacements and stresses quantitatively by using an exact solution called SSA. Also, it is found that the N.P. of the plate, identified according to the values of the in-plane stresses through the thickness direction, is shifted away from the middle plane. Further investigation shows that the position of the N.P. is loading dependant.

Sign in / Sign up

Export Citation Format

Share Document