Forced Axisymmetric Motions of Circular Elastic Plates

1965 ◽  
Vol 32 (4) ◽  
pp. 893-898 ◽  
Author(s):  
R. S. Weiner
Keyword(s):  
Elastic Plate ◽  
Integral Transform ◽  
Plate Theory ◽  
Uniform Pressure ◽  
Elastic Plates ◽  
Pressure Loading ◽  
Concentric Ring ◽  
Simply Supported ◽  
Arbitrary Time Dependence ◽  
Central Load

Axisymmetric motions of a circular elastic plate are considered here according to the Poisson-Kirchhoff plate theory. A concentric ring loading of arbitrary time dependence is examined and used to construct solutions for a concentrated central load and for a uniform pressure loading. The boundary of the plate is considered to be elastically built-in in a manner that prevents transverse edge motion and provides a restoring edge moment linearly related to edge rotation. Thus, limiting cases are a clamped plate and a simply supported plate. Finally, a discussion relating this work to the integral-transform approach of Sneddon is presented to enable physical interpretation and generalization of his approach.

General Solutions for the Statics of Anisotropic, Transversely Inhomogeneous Elastic Plates in Terms of Complex Functions

2006 ◽  
Vol 11 (6) ◽  
pp. 596-628 ◽  
Author(s):  
Kostas P. Soldatos
Keyword(s):  
General Solution ◽  
Elastic Plate ◽  
Plate Theory ◽  
High Order ◽  
Transverse Strain ◽  
Elastic Plates ◽  
General Solutions ◽  
Material Inhomogeneity ◽  
Complex Functions ◽  
Anisotropic Elastic

This paper develops the general solution of high-order partial differential equations (PDEs) that govern the static behavior of transversely inhomogeneous, anisotropic, elastic plates, in terms of complex functions. The basic development deals with the derivation of such a form of general solution for the PDEs associated with the most general, two-dimensional (“equivalent single-layered”), elastic plate theory available in the literature. The theory takes into consideration the effects of bending–stretching coupling due to possible un-symmetric forms of through-thickness material inhomogeneity. Most importantly, it also takes into consideration the effects of both transverse shear and transverse normal deformation in a manner that allows for a posteriori, multiple choices of transverse strain distributions. As a result of this basic and most general development, some interesting specializations yield, as particular cases, relevant general solutions of high-order PDEs associated with all of the conventional, elastic plate theories available in the literature.

On the Singularities in Reissner’s Theory for the Bending of Elastic Plates

1986 ◽  
Vol 53 (1) ◽  
pp. 220-222 ◽  
Author(s):  
W. S. Burton ◽  
G. B. Sinclair
Keyword(s):  
Plate Theory ◽  
Elastic Plates ◽  
Singular Behavior ◽  
Simply Supported ◽  
Reissner’S Theory

Wedge-shaped elastic plates under bending, with the edges forming the wedge vertex being either stress-free, clamped or simply supported, are characterized as to possible singular behavior within the context of Reissner’s plate theory.

EXACT SOLUTION FOR BENDING OF AN ELASTIC PLATE CONTAINING A CRACK AND SUBJECTED TO A CONCENTRATED MOMENT

2007 ◽  
Vol 04 (02) ◽  
pp. 265-281
Author(s):  
LALITHA CHATTOPADHYAY ◽  
S. SRIDHARA MURTHY ◽  
S. VISWANATH
Keyword(s):  
Stress Intensity Factor ◽  
Elastic Plate ◽  
Integral Transform ◽  
Plate Theory ◽  
Infinite Plate ◽  
Bending Moment ◽  
Single Line ◽  
Bending Stress ◽  
Single Crack ◽  
Classical Plate Theory

The problem of estimating the bending stress distribution in the vicinity of cracks located on a single line in an elastic plate subjected to concentrated moment is examined. Using classical plate theory and integral transform techniques, the general formulae for the bending moment and twisting moment in an elastic plate containing cracks located on a single line are derived. The solution is obtained in detail for the case in which there is a single crack in an infinite plate, and the bending stress intensity factor is determined in a closed form. Two examples are considered to illustrate the present approach.

The Nonlinear Behaviour of Thin, Orthotropic, Curved Panels under Lateral Loading

1977 ◽  
Vol 19 (1) ◽  
pp. 30-37 ◽  
Author(s):  
I. H. Marshall ◽  
J. Rhodes ◽  
W. M. Banks
Keyword(s):  
Theoretical Analysis ◽  
Experimental Studies ◽  
Central Point ◽  
Lateral Loading ◽  
Nonlinear Behaviour ◽  
Uniform Pressure ◽  
Pressure Loading ◽  
Simply Supported ◽  
Aspect Ratios ◽  
Curved Panels

A theoretical analysis is presented for the snap-buckling behaviour of thin, orthotropic, spherically curved panels subject to central point and uniform pressure loading on the convex face. Clamped and simply supported edges are considered. The results are presented graphically for a range of panel aspect ratios and comparison is made with experimental studies.

Loss of Contact in the Vicinity of a Right-Angle Corner for a Simply Supported, Laterally Loaded Plate

1981 ◽  
Vol 48 (3) ◽  
pp. 597-600 ◽  
Author(s):  
L. M. Keer ◽  
A. F. Mak
Keyword(s):  
Integral Transform ◽  
Space Region ◽  
Rectangular Plates ◽  
Elastic Plates ◽  
Concentrated Force ◽  
Simply Supported ◽  
Quarter Space ◽  
Loss Of Contact ◽  
Restraining Force ◽  
Laterally Loaded

The solutions to problems of laterally loaded, simply supported rectangular plates are classical ones that can be found in standard textbooks. It is found that forces directed downward must be present to prevent the corners of the plate from rising up during bending. The objective of the present analysis is to determine the extent to which such a plate will rise if the corner force is not present and the plate is unilaterally constrained. Rather than determine the solution for a rectangular plate, we consider a laterally loaded, simply supported plate which occupies a quarter space region. The plate is unilaterally constrained and may rise at the corner due to an absence of restraining force there. Using integral transform techniques appropriate to the quarter space for elastic plates, the region of lost contact is determined for a general loading. The special loading due to a concentrated force is given as an example.

Limit Design of Condenser Hotwell Floors

1975 ◽  
Vol 97 (4) ◽  
pp. 628-632
Author(s):  
A. I. Soler
Keyword(s):  
Flat Plate ◽  
Elastic Plate ◽  
Pressure Vessel ◽  
Plate Theory ◽  
Limit Load ◽  
Uniform Pressure ◽  
Plastic Plate ◽  
Rigid Plastic ◽  
Division 1 ◽  
Section Viii

Rigid plastic plate theory is used to determine the limit load for a pipe-supported flat plate loaded by uniform pressure. The solution is applied to design of condenser hotwell floors under hydrotest loading. A comparison is made with a formula for design of similar configurations suggested in Section VIII, Division 1 of the ASME Pressure Vessel Code, and in texts on elastic plate theory.

Characterization of the vibration, stability and static responses of graphene-reinforced sandwich plates under mechanical and thermal loadings using the refined shear deformation plate theory

2021 ◽  
pp. 109963622199386
Author(s):  
Hessameddin Yaghoobi ◽  
Farid Taheri
Keyword(s):  
Shear Deformation ◽  
Volume Fraction ◽  
Plate Theory ◽  
Micromechanical Model ◽  
Sheet Thickness ◽  
Analytical Investigation ◽  
Sandwich Plates ◽  
Simply Supported ◽  
Vibration Stability ◽  
Shear Deformation Plate Theory

An analytical investigation was carried out to assess the free vibration, buckling and deformation responses of simply-supported sandwich plates. The plates constructed with graphene-reinforced polymer composite (GRPC) face sheets and are subjected to mechanical and thermal loadings while being simply-supported or resting on different types of elastic foundation. The temperature-dependent material properties of the face sheets are estimated by employing the modified Halpin-Tsai micromechanical model. The governing differential equations of the system are established based on the refined shear deformation plate theory and solved analytically using the Navier method. The validation of the formulation is carried out through comparisons of the calculated natural frequencies, thermal buckling capacities and maximum deflections of the sandwich plates with those evaluated by the available solutions in the literature. Numerical case studies are considered to examine the influences of the core to face sheet thickness ratio, temperature variation, Winkler- and Pasternak-types foundation, as well as the volume fraction of graphene on the response of the plates. It will be explicitly demonstrated that the vibration, stability and deflection responses of the sandwich plates become significantly affected by the aforementioned parameters.

Bifurcation and Chaos of a 4-Side Simply Supported Rectangular Thin Electro-Magneto-Elastic Plate in Many Fields

2010 ◽  
Vol 97-101 ◽  
pp. 442-448
Author(s):  
Wei Guo Zhu ◽  
Xiang Zhong Bai
Keyword(s):  
Elastic Plate ◽  
Transverse Magnetic ◽  
Temperature Fields ◽  
Bifurcation And Chaos ◽  
Simply Supported ◽  
Runge Kutta Method ◽  
Displacement Wave ◽  
Nonlinear Temperature ◽  
Electro Magnetic ◽  
Chaos Motion

The problem of bifurcation and chaos in a 4-side simply supported rectangular thin electro-magneto-elastic plate in electro-magnetic, mechanical and temperature fields is studied. Based on the basic nonlinear electro-magneto-elastic motion equations for a rectangular thin plate and expressions of electromagnetic forces, vibration equations are derived for the mechanical loading in a nonlinear temperature field and a steady transverse magnetic field. By using Melnikov function method, the criteria are obtained for chaos motion to exist as demonstrated by the Smale horseshoe mapping. The vibration equations are solved numerically by using a fourth-order Runge-Kutta method. Its bifurcation diagram, Lyapunov exponents diagram, displacement wave diagram, phase diagram and Poincare section diagram are obtained for some examples. The characteristics of the vibration system are analyzed, and the roles of parameters on the systems are discussed separately as well, such as electromagnetic field intensity, temperature and mechanical force.

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