Generalized Bending of a Large, Shear Deformable Isotropic Plate Containing a Circular Hole or Rigid Inclusion

2000 ◽  
Vol 68 (2) ◽  
pp. 230-233 ◽  
Author(s):  
C. W. Bert ◽  
H. Zeng
Keyword(s):  
Circular Hole ◽  
Isotropic Plate ◽  
Plate Theory ◽  
Three Dimensional ◽  
Bending Moment ◽  
Circular Inclusion ◽  
Experimental Result ◽  
Classical Plate Theory ◽  
Geometric Ratio ◽  
Three Dimensional Elasticity

The problem of a large isotropic plate with a circular hole or rigid circular inclusion is considered here. The plate experiences transverse shear deformation and is subjected to an arbitrary bending field. By using Reissner’s plate theory, a general solution, in terms of Poisson’s ratio ν, a geometric ratio, and bending moment ratio B, is obtained to satisfy both the boundary conditions along the edge and at great distances from the edge. The stress couple concentration factors are calculated and compared with classical plate theory, three-dimensional elasticity theory, higher-order plate theory, and an experimental result.

Accurate analytical solutions for shear-deformable web-core sandwich plates

2016 ◽  
Vol 19 (5) ◽  
pp. 616-643 ◽  
Author(s):  
Anup Pydah ◽  
K Bhaskar
Keyword(s):  
Analytical Solutions ◽  
Plate Theory ◽  
Three Dimensional ◽  
Sandwich Plates ◽  
Lateral Bending ◽  
Classical Plate Theory ◽  
Transverse Bending ◽  
The Face ◽  
Three Dimensional Elasticity ◽  
Shear Deformable

An accurate discrete model and analytical solutions thereof are presented for shear-deformable web-core sandwich plates. The face-plates are analyzed using the equations of three-dimensional elasticity, while the webs are accurately modelled using the classical plate theory with a plane stress solution for transverse bending and a Levy-type methodology for lateral bending. It is shown that this obviates the need for a complete three-dimensional analysis of the sandwich plate. Results obtained by this approach are used to highlight the effect of shear deformation of the face-plates.

The Effect of a Rigid Circular Inclusion on the Bending of a Thick Elastic Plate

1952 ◽  
Vol 19 (1) ◽  
pp. 28-32
Author(s):  
R. A. Hirsch
Keyword(s):  
Plane Strain ◽  
Elastic Plate ◽  
Plate Theory ◽  
Plate Thickness ◽  
Three Dimensional ◽  
Inclusion Size ◽  
Circular Inclusion ◽  
Stress Concentrations ◽  
Classical Plate Theory ◽  
Rigid Circular Inclusion

Abstract The three-dimensional problem of the effect of a rigid circular inclusion on the bending of a thick elastic plate is solved approximately by the method of E. Reissner (1, 2). Comparison is made for the limiting cases of vanishing inclusion size, (plane strain), and vanishing thickness (Poisson-Kirchoff plate theory), with the work of J. N. Goodier (3) and M. Goland (4). Graphs showing the transition from the plane-strain solution to the Poisson-Kirchoff solution are given. Stress concentrations are calculated and plotted versus the inclusion diameter-plate thickness ratio. The stress concentrations are found to be less than predicted by the classical plate theory when the inclusion diameter approaches the same order of magnitude as the plate thickness.

Three-Dimensional Plate Theory for Flexible Multibody Dynamics

2015 ◽  
Author(s):  
Shilei Han ◽  
Olivier A. Bauchau
Keyword(s):  
Plate Theory ◽  
Three Dimensional ◽  
Laminated Composite ◽  
Flexible Multibody Dynamics ◽  
Composite Plates ◽  
Complex Stress ◽  
Mindlin Plate ◽  
Stress States ◽  
Three Dimensional Elasticity ◽  
Material Line

In structural analysis, many components are approximated as plates. More often that not, classical plate theories, such as Kirchhoff or Reissner-Mindlin plate theories, form the basis of the analytical developments. The advantage of these approaches is that they leads to simple kinematic descriptions of the problem: the plate’s normal material line is assumed to remain straight and its displacement field is fully defined by three displacement and two rotation components. While such approach is capable of capturing the kinetic energy of the system accurately, it cannot represent the strain energy adequately. For instance, it is well known from three-dimensional elasticity theory that the normal material line will warp under load for laminated composite plates, leading to three-dimensional deformations that generate complex stress states. To overcome this problem, several high-order, refined plate theories have been proposed. While these approaches work well for some cases, they often lead to inefficient formulations because they introduce numerous additional variables. This paper presents a different approach to the problem: based on a finite element semi-discretization of the normal material line, plate equations are derived from three-dimensional elasticity using a rigorous dimensional reduction procedure.

scholarly journals Buckling and Vibration of Non-Homogeneous Rectangular Plates Subjected to Linearly Varying In-Plane Force

2013 ◽  
Vol 20 (5) ◽  
pp. 879-894 ◽  
Author(s):  
Roshan Lal ◽  
Renu Saini
Keyword(s):  
Differential Equation ◽  
Plate Theory ◽  
Differential Quadrature Method ◽  
Three Dimensional ◽  
Axial Direction ◽  
Mode Shapes ◽  
Rectangular Plates ◽  
Plate Material ◽  
Classical Plate Theory ◽  
Simply Supported

The present work analyses the buckling and vibration behaviour of non-homogeneous rectangular plates of uniform thickness on the basis of classical plate theory when the two opposite edges are simply supported and are subjected to linearly varying in-plane force. For non-homogeneity of the plate material it is assumed that young's modulus and density of the plate material vary exponentially along axial direction. The governing partial differential equation of motion of such plates has been reduced to an ordinary differential equation using the sine function for mode shapes between the simply supported edges. This resulting equation has been solved numerically employing differential quadrature method for three different combinations of clamped, simply supported and free boundary conditions at the other two edges. The effect of various parameters has been studied on the natural frequencies for the first three modes of vibration. Critical buckling loads have been computed. Three dimensional mode shapes have been presented. Comparison has been made with the known results.

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.

Thickness Effects Are Minor in the Energy-Release Rate Integral for Bent Plates Containing Elliptic Holes or Cracks

1981 ◽  
Vol 48 (2) ◽  
pp. 320-326 ◽  
Author(s):  
J. G. Simmonds ◽  
J. Duva
Keyword(s):  
Energy Release Rate ◽  
Energy Release ◽  
Relative Error ◽  
Release Rate ◽  
Plate Theory ◽  
Semimajor Axis ◽  
Elliptic Hole ◽  
Three Dimensional ◽  
Radius Of Curvature ◽  
Classical Plate Theory

The exact value of Sanders’ path-independent, energy-release rate integral I for an infinite, bent elastic slab containing an elliptic hole is shown to be approximated by its value from classical plate theory to within a relative error of O(h/c)F(e), where h is the thickness, c is the semimajor axis of the ellipse, and F is a function of the eccentricity e. This result is based on Golden’veiser’s analysis of three-dimensional edge effects in plates, as developed by van der Heijden. As the elliptic hole approaches a crack, F(e)~In (1−e). However, this limit is physically meaningless, because Golden’veiser’s analysis assumes that h is small compared to the minimum radius of curvature of the ellipse. Using Knowles and Wang’s analysis of the stresses in a cracked plate predicted by Reissner’s theory, we show that the relative error in computing I from classical plate theory is only O(h/c)In(h/c), where c is the semicrack length. Our results suggest that classical plate and shell theories are entirely adequate for predicting crack growth, within the limitations of applying any elastic theory to an inherently inelastic phenomenon.

Thermostatics of an elastic Cosserat plate containing a circular hole

1971 ◽  
Vol 70 (1) ◽  
pp. 169-174 ◽  
Author(s):  
İ. T. Gürgöze
Keyword(s):  
Temperature Gradient ◽  
General Theory ◽  
Circular Hole ◽  
Thermal Stresses ◽  
Plate Theory ◽  
The Other ◽  
Uniform Temperature ◽  
Classical Plate Theory ◽  
Cosserat Surface ◽  
Limiting Case

AbstractIn this paper, the general theory of a Cosserat surface given by Green, Naghdi and Wainwright(1), has been applied to the problem of a thermo-elastic Cosserat plate containing a circular hole of radius a. We assume that the major surfaces of the plate and the boundary of the hole are thermally insulated and that a uniform temperature gradient τ exists at infinity. In the limiting case, when h/a → 0, where h is the thickness of the plate, the thermal stresses at the circular hole reduce to those obtained by Florence and Goodier (4), by means of the classical plate theory. Results for the other limiting case h/a → ∞ are also given.

Transverse bending of infinite and semi-infinite thin elastic plates. III

1958 ◽  
Vol 54 (2) ◽  
pp. 288-299 ◽  
Author(s):  
W. A. Bassali ◽  
M. Nassif ◽  
H. P. F. Swinnerton-Dyer
Keyword(s):  
Isotropic Plate ◽  
Plate Theory ◽  
Outer Boundary ◽  
Exact Expression ◽  
Transverse Displacement ◽  
Elastic Plates ◽  
Classical Plate Theory ◽  
Transverse Bending ◽  
Elastically Restrained ◽  
Limiting Case

ABSTRACTWithin the restrictions of the classical plate theory, complex variable methods are used in this paper to develop an exact expression for the transverse displacement of an infinitely large isotropic plate having a free outer boundary and elastically restrained at an inner circular boundary, the plate being subjected to a general type of loading distributed over the area of a circle. The limiting case of a half-plane clamped along the straight edge and acted upon normally by the same loading is also considered.

Prediction of Energy Release Rate for Mixed-Mode Delamination Using Classical Plate Theory

1990 ◽  
Vol 43 (5S) ◽  
pp. S281-S287 ◽  
Author(s):  
R. A. Schapery ◽  
B. D. Davidson
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Energy Release Rate ◽  
Energy Release ◽  
Release Rate ◽  
Mixed Mode ◽  
Plate Theory ◽  
Three Dimensional ◽  
The Finite Element Method ◽  
Classical Plate Theory

Prediction of the energy release rate (ERR) and its components for mixed-mode delamination of composite laminates is discussed. A classical plate theory (CPT) version of Irwin’s virtual crack closure method is developed and used for the ERR, first for plane strain and then for three-dimensional deformations. It is shown that CPT does not provide quite enough information to obtain a decomposition of ERR into its opening and shearing mode components. Results from a continuum analysis are needed to complete the decomposition; but analysis of only one loading case is required for two-dimensional and certain three-dimensional problems. In two example problems the finite element method is used with CPT to complete the mode decomposition. Results from CPT and the finite element method are then compared for several cases.

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