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.

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.

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.

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.

Large-Amplitude Oscillations of Unsymmetrically Laminated Anisotropic Rectangular Plates Including Shear, Rotatory Inertia, and Transverse Normal Stress

1985 ◽  
Vol 52 (3) ◽  
pp. 536-542 ◽  
Author(s):  
K. S. Sivakumaran ◽  
C. Y. Chia
Keyword(s):  
Boundary Conditions ◽  
Normal Stress ◽  
Transverse Shear ◽  
Plate Theory ◽  
Orientation Angle ◽  
Nonlinear Frequency ◽  
Rectangular Plates ◽  
Elastic Plates ◽  
Rotatory Inertia ◽  
Transverse Normal Stress

This paper is concerned with nonlinear free vibrations of generally laminated anisotropic elastic plates. Based on Reissner’s variational principle a nonlinear plate theory is developed. The effects of transverse shear, rotatory inertia, transverse normal stress, and transverse normal contraction or extension are included in this theory. Using the Galerkin procedure and principle of harmonic balance, approximate solutions to governing equations of unsymmetrically laminated rectangular plates including transverse shear, rotatory inertia, and transverse normal stress are formulated for various boundary conditions. Numerical results for the ratio of nonlinear frequency to linear frequency of unsymmetric angle-ply and cross-ply laminates are presented graphically for various values of elastic properties, fiber orientation angle, number of layers, and aspect ratio and for different boundary conditions. Present results are also compared with available data.

On the Vibration of Layered Sandwich Elastic Plates

2008 ◽  
Author(s):  
Vincent O. S. Olunloyo ◽  
Charles A. Osheku
Keyword(s):  
Plate Theory ◽  
Impact Damage ◽  
Local Buckling ◽  
Recent Analysis ◽  
Sandwich Plates ◽  
Elastic Plates ◽  
Interface Pressure ◽  
Engineering Structures ◽  
Thin Plate Theory ◽  
Operational Methods

Sandwich elastic plates have found increasing applications in civil, aerospace, military and offshore industries to enhance superior resistance to fatigue crack propagation, impact damage, local buckling and are very effective for vibration damping and noise reduction. Such structural application has significantly led to reduction in vulnerability of warships to blasts, ballistics, bomb and fire attacks. In engineering structures, one of the effective ways of damping vibration and noise attenuation, is to exploit the occurrence of slip at the interface of structural laminates where such members are held together in a pressurised environment. Recent analysis and experimental investigation of vibration characteristics and damping properties of layered sandwich structures, are mostly limited to elastic beams. This paper is an attempt to extend such analytical investigations to layered sandwich plates. By employing contact mechanics and laminated thin plate theory, the generalised equation governing the vibration of two layered sandwich plates that are held together in pressurised environment is presented. In particular, by invoking operational methods for the case of linear interface pressure distribution, closed form analytical results for the system natural frequency and dynamic response under external excitation are reported for design analysis and applications.

Effects of In-plane Load on Flutter of Homogeneous Laminated Beam Plates with Delamination

2000 ◽  
Vol 123 (1) ◽  
pp. 61-66 ◽  
Author(s):  
Le-Chung Shiau ◽  
Yuan-Shih Chen
Keyword(s):  
Mach Number ◽  
Natural Frequencies ◽  
Plate Theory ◽  
Compressive Load ◽  
Two Dimensional ◽  
Plate Model ◽  
Laminated Beam ◽  
Simply Supported ◽  
Flutter Boundary ◽  
Homogeneous Beam

The effects of in-plane load on flutter characteristics of delaminated two-dimensional homogeneous beam plates at high supersonic Mach number are investigated theoretically. Linear plate theory and quasi-steady supersonic aerodynamic theory are employed. A simple beam-plate model is developed to predict the effects of in-plane load on flutter boundaries for the delaminated beam plates with simply supported ends. Results reveal that the presence of an in-plane compressive load degrades the stiffness and natural frequencies of the plate and thereby decreases the flutter boundary for the plate. However, for certain geometry, the flutter boundaries were raised due to flutter coalescence modes of the plate altered by the presence of the in-plane load on the plate.

Comparison of First-Order Shear and Plane Strain Assumptions in Warpage Prediction of Simply Supported Printed Wiring Boards

2000 ◽  
Vol 123 (1) ◽  
pp. 1-5 ◽  
Author(s):  
Yarom Polsky ◽  
I. Charles Ume
Keyword(s):  
Plane Strain ◽  
Plate Theory ◽  
Shear Deformation Theory ◽  
Transverse Load ◽  
Transverse Shear Strain ◽  
Printed Wiring Board ◽  
Simply Supported ◽  
First Order ◽  
Support Conditions ◽  
Wiring Board

The influence of transverse shear strain in the lamination theory modeling of Printed Wiring Board (PWB) deflection due to support conditions was examined. The in-plane mechanical properties of the core materials of a commercial PWB were measured as a function of temperature. Classical laminated plate theory and first-order shear deformation theory solutions for the out-of-plane deflection of a bare board configuration with two opposite edges simply supported and the remaining edges free were obtained. The weight of the board was approximated as a distributed transverse load. The effect of material property decrease with temperature and FR-4 layer thickness were examined to compare first-order shear and plane strain assumptions for the predicted warpage.

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