Conditions at the Root of a Crack in a Bent Plate

1966 ◽  
Vol 33 (2) ◽  
pp. 441-443 ◽  
Author(s):  
R. G. Redwood ◽  
W. M. Shepherd
Keyword(s):  
Boundary Conditions ◽  
Circular Plate ◽  
Radial Crack ◽  
Small Deflection ◽  
Deflection Theory ◽  
Bent Plate

Transverse displacements of a circular plate containing a radial crack are considered using classical small-deflection theory. Particular sets of boundary conditions on the circumferential edge are derived which require either infinite or zero radial slopes at the root of the crack, and these results are discussed in relation to previous work in this field.

Bending of a Cylindrically Aeolotropic Circular Plate With Eccentric Load

1952 ◽  
Vol 19 (1) ◽  
pp. 9-12
Author(s):  
A. M. Sen Gupta
Keyword(s):  
Boundary Conditions ◽  
Circular Plate ◽  
Uniform Thickness ◽  
Eccentric Load ◽  
Concentrated Load ◽  
Different Boundary Conditions ◽  
Small Deflection ◽  
Deflection Theory ◽  
Clamped Edge

Abstract The problem of small-deflection theory applicable to plates of cylindrically aeolotropic material has been developed, and expressions for moments and deflections produced have been found by Carrier in some symmetrical cases under uniform lateral loadings and with different boundary conditions. The author has also found the moments and deflection in the case of an unsymmetrical bending of a plate loaded by a distribution of pressure of the form p = p0r cos θ, with clamped edge. The object of the present paper is to investigate the problem of the bending of a cylindrically aeolotropic circular plate of uniform thickness under a concentrated load P applied at a point A at a distance b from the center, the edge being clamped.

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.

Displacements and Stresses of a Laterally Loaded Semicircular Plate With Clamped Edges

1959 ◽  
Vol 26 (2) ◽  
pp. 224-226
Author(s):  
W. H. Jurney
Keyword(s):  
Circular Plate ◽  
Normal Load ◽  
Constant Thickness ◽  
Small Deflection ◽  
Deflection Theory ◽  
Laterally Loaded ◽  
Superposition Of Solutions ◽  
Clamped Edges

Abstract A solution is obtained for the case of the clamped semicircular plate of constant thickness, subjected to a uniformly distributed normal load. The method employed is superposition of solutions for a circular plate with fixed edges. The technique involved could be extended to study more general types of loading of the clamped semicircular plate. Results are based on the assumption that the Kirchhoff, or small deflection, theory applies.

The Large Elastic-Plastic Deflection With Springback of a Circular Plate Subjected to Circumferential Moments

1982 ◽  
Vol 49 (3) ◽  
pp. 507-515 ◽  
Author(s):  
T. X. Yu ◽  
W. Johnson
Keyword(s):  
Circular Plate ◽  
Large Deflection ◽  
Computer Programs ◽  
Bending Moments ◽  
Plastic Bending ◽  
Elastic Plastic ◽  
Small Deflection ◽  
Deflection Theory

The large deflection elastic-plastic bending of a circular plate subjected to radially outward acting bending moments uniformly distributed around its circumference is analyzed, and computer programs are given to facilitate the determination of the distributions of bending moments, in-plane forces, and displacements during the bending and after unloading or springback. Computed examples are given, and the errors developed by small deflection theory are discussed.

Transient Interaction of a Circular Plate and a Fluid Medium

1979 ◽  
Vol 46 (1) ◽  
pp. 26-30 ◽  
Author(s):  
J. W. Berglund
Keyword(s):  
Boundary Conditions ◽  
Circular Plate ◽  
Applied Pressure ◽  
Plate Boundary ◽  
Fluid Medium ◽  
Fluid Field ◽  
Elastic Circular Plate ◽  
Unstrained State ◽  
State Of Rest ◽  
Acoustic Fluid

The transient dynamic response of an elastic circular plate subjected to a suddenly applied pressure is determined for several edge boundary conditions. The plate boundary is attached to a semi-infinite, radially rigid tube which is filled with an acoustic fluid, and pressure is applied to the in-vacuo side of the plate. The transient solution is determined by using a technique in which the plate is subjected to a periodic pressure function constructed of appropriately signed and time-shifted Heaviside step functions, and by relying on a physical mechanism which returns the plate and fluid near the plate to an unstrained state of rest between pulses. The plate response is presented for a number of radius-to-thickness ratios and edge boundary conditions when interacting with water. Comparisons are also made with solutions obtained using a plane wave approximation to the fluid field.

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.

Study on Deformation and Stress of CRCP under Concentrated Vertical Load with Hollow Foundation

2011 ◽  
Vol 250-253 ◽  
pp. 3415-3420
Author(s):  
Xiao Bing Chen ◽  
Xiao Ming Huang ◽  
Jin Hu Tong
Keyword(s):  
Equivalence Principle ◽  
Transverse Crack ◽  
Torsion Theory ◽  
Slab Thickness ◽  
Vertical Load ◽  
Effective Measure ◽  
Small Deflection ◽  
Half Wave ◽  
Elastic Thin Plate ◽  
Deflection Theory

Based on the equivalence principle, the concentrated vertical load which acts on the Continuously Reinforced Concrete Pavement(CRCP) transverse crack is translated into the equivalent half-wave sine load by Fourier transform. According to the translation principle of the force, the half-wave sine vertical load acting on the CRCP transverse crack is decomposed to the half-wave sine vertical load and the torsion force acting on the center of CRCP. Lastly, the deflection, torsional displacement and stress formulas of CRCP under the concentrated vertical load with hollow foundation are put forward, which is on the basis of the small deflection theory of elastic thin plate and torsion theory. The results show that increasing the slab thickness is the most effective measure to reduce maximal deflection, distortion displacement and stress of CRCP concentrated vertical load with hollow foundation.

scholarly journals Thermoelastic coupling vibration and stability analysis of rotating circular plate in friction clutch

2018 ◽  
Vol 38 (2) ◽  
pp. 558-573 ◽  
Author(s):  
Yongqiang Yang ◽  
Zhongmin Wang ◽  
Yongqin Wang
Keyword(s):  
Differential Equation ◽  
Boundary Conditions ◽  
Circular Plate ◽  
Coupling Coefficient ◽  
Inertial Force ◽  
Angular Speed ◽  
Circular Plates ◽  
Thermoelastic Coupling ◽  
Coupling Vibration ◽  
Friction Clutch

Rotating friction circular plates are the main components of a friction clutch. The vibration and temperature field of these friction circular plates in high speed affect the clutch operation. This study investigates the thermoelastic coupling vibration and stability of rotating friction circular plates. Firstly, based on the middle internal forces resulting from the action of normal inertial force, the differential equation of transverse vibration with variable coefficients for an axisymmetric rotating circular plate is established by thin plate theory and thermal conduction equation considering deformation effect. Secondly, the differential equation of vibration and corresponding boundary conditions are discretized by the differential quadrature method. Meanwhile, the thermoelastic coupling transverse vibrations with three different boundary conditions are calculated. In this case, the change curve of the first two-order dimensionless complex frequencies of the rotating circular plate with the dimensionless angular speed and thermoelastic coupling coefficient are analyzed. The effects of the critical dimensionless thermoelastic coupling coefficient and the critical angular speed on the stability of the rotating circular plate with simply supported and clamped edges are discussed. Finally, the relation between the critical divergence speed and the dimensionless thermoelastic coupling coefficient is obtained. The results provide the theoretical basis for optimizing the structure and improving the dynamic stability of friction clutches.

Parameter Estimation for an Imperfectly Clamped Plate: Numerical Examples

1995 ◽  
Author(s):  
H. T. Banks ◽  
R. C. Smith ◽  
Yun Wang
Keyword(s):  
Parameter Estimation ◽  
Boundary Conditions ◽  
Circular Plate ◽  
Simple Zero ◽  
Numerical Examples ◽  
Vibrating Structures ◽  
Physical Experiments ◽  
Slight Rotation ◽  
Physical Manifestation ◽  
Clamped Edges

Abstract The problems associated with maintaining truly fixed (zero displacement and slope) or simple (zero displacement and moment) boundary conditions in applications involving vibrating structures have led to the development of models which admit slight rotation and displacement at the boundaries. In this paper, numerical examples demonstrating the dynamics of a model for a circular plate with imperfectly clamped boundary conditions are presented. The latitude gained when using the model for estimating parameters through fit-to-data techniques is also demonstrated. Through these examples, the manner in which the model accounts for the physical manifestation of imperfectly clamped edges is illustrated, and issues regarding the use of the model in physical experiments are defined.

Sign in / Sign up

Export Citation Format

Share Document