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.

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.

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.

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.

Bending of Orthogonally Stiffened Plates

1955 ◽  
Vol 22 (2) ◽  
pp. 267-271
Author(s):  
W. H. Hoppmann
Keyword(s):  
Boundary Conditions ◽  
Experimental Method ◽  
Circular Plate ◽  
Elastic Constants ◽  
Orthotropic Material ◽  
Elastic Moduli ◽  
Unit Area ◽  
Stiffened Plates ◽  
Stiffened Plate ◽  
Clamped Edge

Abstract In this paper the flexure theory for plates of orthotropic material is applied in the case of orthogonally stiffened plates using an experimental method to determine plate stiffnesses in bending and in twisting. Once these stiffnesses, or elastic moduli, have been determined by test they may be used in calculating bending deflections for plates of identical stiffened construction but any given boundary conditions. As an example, calculated deflections of a stiffened circular plate with clamped edge are compared with those which were determined experimentally. It is also demonstrated that the theory can be applied to the case of vibration of a stiffened plate if in addition to the orthotropic elastic constants the weight per unit area of the plate is determined. The various experimental results show considerable promise for use of the proposed combination of theory and experimental method in the analysis of both statically and dynamically loaded plates with attached stiffeners.

The deflection of a thin circular plate with an eccentric circular hole

1976 ◽  
Vol 11 (2) ◽  
pp. 107-124 ◽  
Author(s):  
E Ollerton
Keyword(s):  
Circular Plate ◽  
Circular Hole ◽  
Theoretical Investigation ◽  
Outer Edge ◽  
Plate Surface ◽  
Concentrated Load ◽  
Simply Supported ◽  
Thin Circular Plate ◽  
Clamped Edge

A theoretical investigation of the small deflections of a thin circular plate is reported. The plate has a flat circular clamp at the outer edge and a similar clamp at the inner edge, which is placed eccentrically. These supports can be arranged to prescribe either a clamped edge or a simply supported edge, and all combinations of the two types are investigated. The plate can be subjected to a concentrated load at the centre of the inner clamp, moments about two perpendicular axes of the inner clamp, or pressure on the plate surface between the clamps. Deflections and slopes of the inner clamp have been determined, and in all cases the new values tend towards established values for the case of a central inner clamp, as the eccentricity of the inner clamp is reduced.

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.

Cantilever Plate With Concentrated Edge Load

1937 ◽  
Vol 4 (1) ◽  
pp. A8-A10 ◽  
Author(s):  
D. L. Holl
Keyword(s):  
Approximate Solution ◽  
Boundary Conditions ◽  
Finite Length ◽  
Finite Differences ◽  
Free Edge ◽  
Cantilever Plate ◽  
Transverse Stress ◽  
Longitudinal Stress ◽  
Concentrated Load ◽  
Clamped Edge

Abstract The author gives, by the method of finite differences, an approximate solution of the problem of a finite length of a cantilever plate which bears a concentrated load at the longitudinal free edge. All the boundary conditions are taken into account, and the plate action is determined approximately at all points of the plate. The author points out that a secondary maximum transverse stress occurs at the clamped edge nearest the loading point, and that the longitudinal stress is greatest directly under the loading point.

scholarly journals Mechanics of tubular helical assemblies: ensemble response to axial compression and extension

2021 ◽  
Author(s):  
Jacopo Quaglierini ◽  
Alessandro Lucantonio ◽  
Antonio DeSimone
Keyword(s):  
Boundary Conditions ◽  
Elastic Properties ◽  
Central Region ◽  
Mechanical Response ◽  
Different Boundary Conditions ◽  
Kirchhoff Rods ◽  
Model Versus ◽  
The Individual ◽  
Opposite Chirality

Abstract Nature and technology often adopt structures that can be described as tubular helical assemblies. However, the role and mechanisms of these structures remain elusive. In this paper, we study the mechanical response under compression and extension of a tubular assembly composed of 8 helical Kirchhoff rods, arranged in pairs with opposite chirality and connected by pin joints, both analytically and numerically. We first focus on compression and find that, whereas a single helical rod would buckle, the rods of the assembly deform coherently as stable helical shapes wound around a common axis. Moreover, we investigate the response of the assembly under different boundary conditions, highlighting the emergence of a central region where rods remain circular helices. Secondly, we study the effects of different hypotheses on the elastic properties of rods, i.e., stress-free rods when straight versus when circular helices, Kirchhoff’s rod model versus Sadowsky’s ribbon model. Summing up, our findings highlight the key role of mutual interactions in generating a stable ensemble response that preserves the helical shape of the individual rods, as well as some interesting features, and they shed some light on the reasons why helical shapes in tubular assemblies are so common and persistent in nature and technology. Graphic Abstract We study the mechanical response under compression/extension of an assembly composed of 8 helical rods, pin-jointed and arranged in pairs with opposite chirality. In compression we find that, whereas a single rod buckles (a), the rods of the assembly deform as stable helical shapes (b). We investigate the effect of different boundary conditions and elastic properties on the mechanical response, and find that the deformed geometries exhibit a common central region where rods remain circular helices. Our findings highlight the key role of mutual interactions in the ensemble response and shed some light on the reasons why tubular helical assemblies are so common and persistent.

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