On analytical-computerized method to solve nonlinear bending problem of circular plate under a concentrated load

1987 ◽  
Vol 8 (8) ◽  
pp. 759-766 ◽  
Author(s):  
Zheng Xiao-jing ◽  
Zhou You-he
Keyword(s):  
Circular Plate ◽  
Nonlinear Bending ◽  
Concentrated Load ◽  
Computerized Method

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.

Bending of Circular and Ring-Shaped Plates on an Elastic Foundation

1954 ◽  
Vol 21 (1) ◽  
pp. 45-51
Author(s):  
Herbert Reismann
Keyword(s):  
Circular Plate ◽  
Elastic Foundation ◽  
Series Solution ◽  
Circular Disk ◽  
Symmetric Problem ◽  
Concentrated Load ◽  
Transverse Loads ◽  
Infinite Extent ◽  
Theory Of Plates ◽  
Pure Moment

Abstract This paper develops a method for the evaluation of deflections, moments, shears, and stresses of a circular or ring-shaped plate on an elastic foundation under transverse loads. A series solution is derived for plates subjected to edge and/or concentrated loads and is given in terms of tabulated functions. It is exact within the assumptions underlying the classical theory of plates and includes, as a particular case, the known solution of the corresponding radially symmetric problem. Two examples displaying radial asymmetry are worked. A solution is given for (a) a circular plate resting on an elastic foundation, clamped at the boundary and subjected to an arbitrarily placed concentrated load, and (b) a plate of infinite extent, resting on an elastic foundation and clamped to the boundary of a rigid circular disk to which a pure moment is applied.

The Bending Mechanics of Aged Paper

2018 ◽  
Vol 85 (7) ◽  
Author(s):  
Andrea K. I. Hall ◽  
Thomas C. O'Connor ◽  
Molly K. McGath ◽  
Patricia McGuiggan
Keyword(s):  
Elastic Moduli ◽  
Large Deflection ◽  
Single Point ◽  
Massachusetts Institute Of Technology ◽  
Endurance Test ◽  
Nonlinear Bending ◽  
Concentrated Load ◽  
Bending Modulus ◽  
Institute Of Technology ◽  
Bending Length

Brittleness in paper is one of the primary reasons library books are removed from circulation, digitized, or have their access limited. Yet, paper brittleness is difficult to characterize as it has multiple definitions and no single measurable physical or chemical property associated with it. This study reevaluates the cantilever test as applied to aged papers. In this nondestructive test, the deflection of a strip of paper held horizontally is measured across its length. The deflection data are then fit to nonlinear bending theories assuming large deflection of a cantilever beam under a combined uniform and concentrated load. Fitting the shape of the deflection profiles provides bending and elastic moduli, the bending length, and confirms that the paper sheets respond linearly. The results are compared to those calculated from a simplified single point measurement of the maximum deflection of the cantilevered sample. Young's modulus measured by the cantilever test is lower for paper-based materials than that measured by tensile testing, and the bending modulus was found to correlate with the destructive Massachusetts Institute of Technology (MIT) fold endurance test.

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

Isotropic Clamped-Free Thin Annular Circular Plate Subjected to a Concentrated Load

2005 ◽  
Vol 73 (4) ◽  
pp. 658-663 ◽  
Author(s):  
Ajayi O. Adewale
Keyword(s):  
Circular Plate ◽  
Annular Plate ◽  
The Other ◽  
Load Application ◽  
Concentrated Load ◽  
Deflection Coefficient ◽  
Series Approximation ◽  
Radial Moments ◽  
Radial Moment

The problem of an isotropic annular plate clamped along one edge and free at the other and subjected to a concentrated load is solved by a series approximation. The continuity conditions of deflection, slope, shear and radial moments at the radius of load application are satisfied. Variations of deflection coefficient, radial moment coefficients and shear coefficients with radius and angle are presented.

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.

Sign in / Sign up

Export Citation Format

Share Document