Showing papers on "Plate theory published in 1975"

Bridge deck analysis

Abstract: The book presents the theory and applications of the analytical techniques used in finding stresses in highway and other bridge decks. Current trends in bridge design and construction are discussed and are followed by the various analytical methods. The plate method is dealt with, initially by the basic derivation and solution of the plate equation. A chapter is devoted to the determination of the equivalent plate rigidities of various representative types of bridge deck. An approximate method of determination of bending moments for initial design is described. Various special applications of orthotropic plate theory are covered and the finite difference method for plates is described, including a summary of the dynamic relaxation method. The last four chapters deal with the stiffness method and its application: grillage and space frame analysis, the folded plate method, the finite element method, and the finite strip method. The book is intended for use by bridge designers and students with a particular interest in bridge engineering. /TRRL/

Side-Cracked Plates Subject to Combined Direct and Bending Forces

Abstract: The opening mode stress intensity factor and the associated crack mouth displacement are comprehensively treated using planar boundary collocation results supplemented by end point values from the literature. Data are expressed in terms of dimensionless coefficients of convenient form which are each functions of two dimensionless parameters, the relative crack length, and a load combination parameter which uniquely characterizes all possible combinations of tension or compression with bending or counterbending. Accurate interpolation expressions are provided which cover the entire ranges of both parameters. Application is limited to specimens with ratios of effective half-height to width not less than unity.

The influence of crack closure and elasto-plastic flow on the bending of a cracked plate

Abstract: The influence of crack closure and elasto-plastic flow on the bending behavior of thin cracked plates is investigated through use of an incremental elasto-plastic plate bending finite element computer program The finite element program was developed using assumptions consistent with Kirchhoff fourth order plate theory while the material property treatment permits general isotropic work hardening with local elastic unloading

Theory of unsymmetric laminated plates

Abstract: Timoshenko’s shear correction factor for an unsymmetric laminated plate is derived rigorously from a formulation involving the theory of elasticity. This approach includes the effect of nonlinear in−plane displacements and emphasizes the effect of shear deformation. As a consequence of the derivation, physically meaningful quantities including the neutral axis, mean elastic constant, and bending rigidity of a composite plate are obtained. After substituting these quantities into the homogeneous plate equation, which includes the transverse shear developed by Reissner and Mindlin, it is applied directly to unsymmetric laminates.

Bending and vibration of transversely isotropic two-layer plates

Abstract: T use of composite materials in various aerospace and industrial applications has prompted a considerable amount of research on the static and dynamic response of multilayer plates. During the past decade, several authors' have formulated plate theories by a direct extension of Mindlin's theory for homogeneous plates. Sun and Whitney have shown that laminated plate theories which are based on Kirchhoff's hypothesis, or a simple extension of Mindlin's theory, yield grossly inaccurate natural-frequency predictions for twoand three-layer plates whose layers have widely differing shear rigidities. In a recent paper, the principle of virtual work was used to derive the equations of motion in an invariant form for an arbitrary three-layered plate. No restrictions were placed on the relative thicknesses, densities, elastic moduli, or symmetries of the layers. The formulation accounts for the shear deformation of each layer as well as the translational and rotational inertia of the composite. Continuity of displacements and stresses was imposed in accordance with a perfect interface bond assumption. In the current analysis, the previously derived equations will be used to analyze a transversely isotropic two-layer plate by deleting the terms associated with the third layer and neglecting the transverse contraction of the composite. The theory then becomes the two-dimensional analog of Theory II as presented by Sun and Whitney. If we assume that each layer is transversely isotropic, the equations of motion are written in vector notation and can be uncoupled to yield a sixth-order equation in the transverse displacement. By neglecting certain in-plane and rotatory inertia terms, we can obtain a somewhat simpler fourth-order equation, which is very similar to Mindlin's dynamic plate equation with modified stiffness, mass, and inertia coefficients. This equation reduces to Mindlin's formulation if either of the layers is assumed to vanish or the properties of both layers are identical. From virtual work, the natural boundary conditions

Part 3. Present plate boundary and its evolution in the New Zealand region: New Zealand 60 m.y. ago

Abstract: Rigid plate theory has been highly successful in explaining the origin of the oceans, but far less so in explaining the twisted rock belts of the continents. The New Zealand region is the smallest of the continents, and its rocks have a fairly simple twist, which is well mapped and has been termed a recurved arc. Can New Zealand be straightened out while keeping the ocean floor rigid? The following is a preliminary attempt.

Analysis of Impact Stresses in Composite Plates

Abstract: In this paper an analytical study is presented of the two-dimensional response of an elastic laminated composite plate to an impact load applied to its surface. The surface load is arbitrarily distributed along the extentof the plate surface and varies sharply in time to model the impact loading. Each layer of the laminated plate is of arbitrary (constant) thickness with specified density and orthotropic material properties, with the material axes coincident with the plate axes. The physical behavior of the plate is exactly represented along the extent of plate in the form of a Fourier series, and its behavior in the thickness direction is modeled by a sufficiently large number of generalized coordinates to capture quantitatively the propagation and dispersion of stress waves due to the surface impact, with emphasis directed to calculating stresses on laminate interfaces. This method of analysis results in a sequence of algebraic eigenvalue problems, the solutions of which are used to decouple the equations of motion into a large number of simple differential equations in time. This procedure is quite straightforward and computationally effective and may be used to study the impact problem for an arbitrarily laminated plate. An isotropic plate with a specified surface impact loading is presented to indicate both the accuracy of the results obtained and the time domain for which they are valid. A two-layer boron-epoxy plate is examined in detail to indicate the quantity and quality of information which may be generated by this method for composite material structures in impact environments. The results for this problem also reveal potentially harmful effects which develop during impact. Sufficient information is presented to permit an experimental verification of the results obtained, for regions of time where the magnitudes of the impact stresses are most critical to material integrity.

Floating sea ice plates and the significance of the dependence of the Poisson ratio on brine content

Abstract: This article investigates the influence of the temperature profile in ice plates on the plate characteristic coefficients for a dynamical theory of flexible plates that accounts for such effects as the variation of the Poisson ratio across the thickness of the plate. The mathematical solution of two simple problems is constructed, dealing with the response of an infinite plate on a Winkler foundation to static line loads and with the propagation of plane waves in a system consisting of a liquid layer and floating ice plate. The static problem is solved by means of the Green function technique, while the wave propagation problem follows the usual lines of harmonic analysis. Numerical results prove that the effects emerging from the dependence of the Poisson ratio on the microstructure are negligible for both fresh water ice and sea ice. On the basis of the plate theory, it should thus be extremely difficult to experimentally detect the dependence of the Poisson ratio on brine content for sea ice.

Influence of rotary inertia and shear deformation on acoustic transmission through a plate

Abstract: The reflection and transmission of a harmonic acoustic plane wave from a fluid‐loaded plate is investigated using the Timoshenko–Mindlin plate equation. In contrast to the classical plate theory, the effects of rotary inertia and shear deformation are included in the Timoshenko–Mindlin theory. The usual acoustic coincidence frequency and angle based on the classical theory are shown to depart from the present results based on the Timoshenko–Mindlin theory as the frequency–plate thickness product increases. Furthermore, an additional acoustic coincidence frequency and angle are also noted in the present analysis for large frequency‐plate thickness products. Several numerical results are presented to illustrate the effects of the incident angle, frequency, plate thickness, and damping on the transmission of an incident acoustic plane wave through a steel plate in water.Subject Classification: 20.60; 40.24; 20.30.

A general nonlinear viscoelastic plate theory and its application to floating ice

Abstract: On the basis of the general theory for floating ice plates, as presented in Ref. [6], a viscoelastic plate theory is constructed which is analogous to a Reissner—von Karman theory in elasticity. The nonuniform distribution of temperature across the depth of the plate is accounted for by assuming that ice satisfies the postulates of thermorheologically simple solids. It is shown how the plate relaxation functions may be obtained from the relaxation functions of three dimensional viscoelasticity and the temperature-time-shifting functional. The paper concludes by demonstrating that a theory of such complexity is required to explain certain behavior of sea ice plates.

Flutter of laminated plates in supersonic flow

Abstract: A solution procedure was developed using linear small deflection theory for the flutter of simply supported laminated plates. For such plates, the bending and extensional governing equations are coupled and have cross-stiffness terms which do not appear in classical plate theory. An extended Galerkin method is used to obtain approximate solutions to the governing equations, and the aerodynamic pressure loading used in the analysis is that given by linear piston theory with flow at arbitrary cross-flow angle. A limited parametric study was conducted for typical laminated composite plates. The calculations show that both the bending-extensional coupling and the cross-stiffness terms have a large destabilizing effect on flutter. Since classical plate theory does not consider bending-extensional coupling and cross stiffness terms, it usually gives inaccurate and nonconservative flutter boundaries for laminated plates.

On an integro-differential equation model for the study of the response of an acoustically coupled panel

Abstract: The response of a clamped panel to supersonically convected turbulence is considered. A theoretical model in the form of an integro-differential equation is employed that takes into account the coupling between the panel motion and the surrounding acoustic medium. The kernels of the integrals, which represent induced pressures due to the panel motion, are Green's functions for sound radiations under various moving and stationary sources. An approximate analysis is made by following a finite-element Ritz-Galerkin procedure. Preliminary numerical results, in agreement with experimental findings, indicate that the acoustic damping is the controlling mechanism of the response.

Approximate Method for the Bending of Rectangular Plate with Nonuniform Thickness

Abstract: An approximate method using a double trigonometric series for the bending of a plate with nonuniform thickness is proposed. The convergency of solutions with this method is examined to be satisfactory. Furthermore, simple approximate formulae to estimate the maximum deflection and surface stresses of the plate with the linearly varying thickness in one direction under uniform pressure are derived. The error of these formula for typical cases here treated is found to be less than 2 per cent.

Steel Orthotropic Plates under Alternate Loads

Abstract: An experimental study of the behavior of a model on an orthotropic steel bridge deck is reported. The orthotropic plate was acted upon by static repeated loads capable of stressing the structure beyond the elastic range. The tests performed showed alternate yielding in the ribs which were directly loaded, for a P value quite lower than the static collapse; the latter was found to be very high compared to the elastic limit, confirming a well-known fact. The behavior of the model tested is finally reproduced by means of two theoretical schemes: (1) For the lower values of P the loaded ribs were considered to be an elastic-plastic beam with strain hardening. This beam is considered to be continuous on elastic supports, i.e., on transverse beams. (2) for the higher values of P, up to collapse, the orthotropic plate was considered to be a rigid-plastic grid connected to an elastic-plastic membrane, i.e., the deck plate.

Modal Analysis for Impact of Layered Plates

Abstract: An analysis is presented of the plane strain response of an arbitrarily layered elastic plate to surface impact loads of specified distribution over the plate surface and in time. Each layer has specified orthotropic material properties, with coincident material and plate axes. The method is based on the extended Ritz technique and employs a normal mode procedure to accurately predict the motion through the plate thickness of stress waves generated by the impact load. The case of impact on an isotropic plate is studied in detail, both with the present method and other methods based on the exact elasticity theory to indicate the accuracy and convergence properties of this method. The procedure is applied to the case of a two-layer plate, where each layer is assigned orthotropic elastic properties typical of a unidirectional boron-epoxy composite. The stress waves generated by a normal surface impact are presented to indicate both the quality and quantity of information that can be generated by the analysis. A tension wave that trails the initial compression wave is shown to exist.