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Showing papers on "Plate theory published in 1974"


Journal ArticleDOI
TL;DR: In this article, a general-purpose computer program, VIPASA, is presented for determining the critical buckling stresses or natural frequencies of vibration of thin prismatic structures, consisting of a series of plates rigidly connected together along longitudinal edges.

312 citations



Journal ArticleDOI
T. Rock1, E. Hinton1
TL;DR: In this paper, an isoparametric quadrilateral plate bending element is used for the free and forced vibration analysis of both thick and thin plates, and the element performance is assessed by comparison with analytical solutions based on Mindlin's thick plate theory, three-dimensional elasticity solutions and solution based on thin plate theory.
Abstract: An isoparametric quadrilateral plate bending element is used for the free and forced vibration analysis of both thick and thin plates. Plates of rectangular, circular and triangular planform are analysed and excellent results are obtained. The element performance is assessed by comparison with analytical solutions based on Mindlin's thick plate theory, three-dimensional elasticity solutions and solutions based on thin plate theory.

69 citations


Journal ArticleDOI
TL;DR: In this paper, the series expansion of displacement in terms of simple thickness modes is used to obtain approximate two-dimensional equations of motion for crystal plates from the three-dimensional theory of elasticity.

45 citations


Journal ArticleDOI
TL;DR: In this article, a general forced-vibration analysis for laminated anisotropic rectangular plates including material damping is presented and applied to prediction of the resonant frequencies and associated nodal patterns and damping ratios for a series of rectangular plates with free edges.
Abstract: A general forced-vibration analysis is presented for laminated anisotropic rectangular plates including material damping. The theory used is the laminated version of the Mindlin plate theory and includes thickness-shear flexibility and rotatory and coupling inertia. A solution is obtained by the Rayleigh-Ritz method, extended to include the energy dissipated and the work done by the excitation. The analysis is applied to prediction of the resonant frequencies and associated nodal patterns and damping ratios of the first five modes for a series of rectangular plates with free edges. The plates considered consist of unidirectional boron-fiber/epoxy composite material with respective fiber orientations of 0, 10, 30, 45, 60, and 90 deg.

43 citations


Journal ArticleDOI
Isaac Fried1
TL;DR: In this paper, the residual shear balancing technique was applied to the generation of the stiffness matrix of a 12 degree-of-freedom rectangular plate bending element, and the results were compared with those obtained with elements of similar size.

40 citations



Journal ArticleDOI
TL;DR: Comparisons of experimental data and predicted results from the simple model provide a degree of confidence in the ability of a theoretical model to represent the actual deformations and show limitations of the simple beam model and the need for a more refined model such as a finite element representation.

29 citations



Journal ArticleDOI
TL;DR: A series of three-dimensional photoelastic experiments were conducted on plates containing through cracks which were loaded in bending with sufficient extension to prevent closure on the compressive side of the plate as discussed by the authors.
Abstract: A series of three-dimensional photoelastic experiments were conducted on plates containing through cracks which were loaded in bending with sufficient extension to prevent closure on the compressive side of the plate. Cracked plate geometries were selected so as to span the transitional “thin to thick” range. Slices were made parallel to the plate surfaces in the stress frozen material so as to remove the region around the crack tips. These slices were analyzed photoelastically and functions were evaluated experimentally corresponding to stress intensity factor distributions through the plate thickness. Results were compared with the theory of G. C. Sih. Agreement was excellent with theory for “thin” cracked plate geometries. For “thicker” cracked plate geometries results diverged progressively. For all cases studied, the use of a linear distribution of the stress intensity factor function through the plate thickness appeared to be satisfactory.

20 citations


Journal ArticleDOI
TL;DR: In this article, the flow of air between a plate at rest and another one falling onto it either vertically or by folding is studied, and the infrequency of breakage of glass plates colliding in this way is explained.
Abstract: The flow of air between a plate at rest and another one falling onto it either vertically or by folding is studied, and the infrequency of breakage of glass plates colliding in this way is explained The falling plate may be two‐dimensional, circular, or elliptic, and the results for an elliptic plate give bounds for the motion of a falling rectangular plate

Journal ArticleDOI
TL;DR: In this paper, a high precision triangular plate bending element for the analysis of thick plates is developed in thin paper, which has three nodes and 12 degrees of freedom per node, and explicit expressions for stiffness coefficients are derived.


Journal ArticleDOI
TL;DR: In this paper, the authors studied the vibration problem of generally orthotropic plates with particular attention to skew geometry and derived an approximate solution for frequencies and modes using products of appropriate beam characteristic functions as admissible functions.
Abstract: Vibration problem of generally orthotropic plates with particular attention to plates of skew geometry is studied. The formulation is based on orthotropic plate theory with arbitrary orientation of the principal axes of orthotropy. The boundary conditions considered are combinations of simply supported, clamped, and free‐edge conditions. Approximate solution for frequencies and modes is obtained by the Ritz method using products of appropriate beam characteristic functions as admissible functions. The variation of frequencies and modes with orientation of the axes of orthotropy is examined for different skew angles and boundary conditions. Features such as “crossings” and “quasi‐degeneracies” of the frequency curves are found to occur with variation of the orientation of the axes of orthotropy for a given geometry of the skew plate. It is also found that for each combination of skew angle and side ratio, a particular orientation of the axes gives the highest value for the fundamental frequency of the plate.

Journal ArticleDOI
TL;DR: In this paper, a review, correction, and extension of Vlasov and Leont'ev's analysis of beams, plates, and shells on elastic foundations is presented, and an improved theory for the motion of an elastic foundation is developed.

Journal ArticleDOI
TL;DR: In this paper, the phase velocity of flexural waves traveling along a l ¼ in.thick honeycomb sandwich panel has been experimentally determined from 170 Hz to 50 kHz using three techniques: measurement of resonant frequencies of beam-shaped samples in forced vibration, measurement of nodal spacing in standing-wave patterns on beam•shaped samples, and measurement of the change in time delay of a particular phase feature of a wave packet as a function of propagation distance in large plate samples.
Abstract: Honeycomb sandwich panels are highly anisotropic, layered media predicted to have unique dispersion characteristics for flexure wave frequencies above a few kilohertz. The phase velocity of flexural waves traveling along a l‐in.‐thick honeycomb sandwich panel has been experimentally determined from 170 Hz to 50 kHz using three techniques: measurement of resonant frequencies of beam‐shaped samples in forced vibration, measurement of nodal spacing in standing‐wave patterns on beam‐shaped samples, and measurement of the change in time delay of a particular phase feature of a wave packet as a function of propagation distance in large plate samples. The data are in good agreement with two models, a plate theory and an elasticity theory, each of which treats the core as a continuum. Above SO kHz, the predictions of the two models diverge and the experimental phenomena become more complex. A brief description of these results is given.

Book ChapterDOI
TL;DR: In this article, two test methods for determining the longitudinal or in-plane shear stress-strain response of a unidirectional composite material are presented, one of which is the uniaxial tension test on a ′45 deg laminate and the other one is the rail shear test on an 0/90 deg laminate.
Abstract: Two test methods for determining the longitudinal or in-plane shear stress-strain response of a unidirectional composite material are presented. These two methods are the uniaxial tension test on a ′45 deg laminate and the rail shear test on a 0/90 deg laminate. Although these tests are conducted on laminates, the laminates are special cases of geometric construction. It is shown that unidirectional shear properties can be found from the laminate test data. The stress-strain response for both methods agrees very well for glass-epoxy and graphite-epoxy composites. The nonisothermal viscoelastic shear response of a unidrectional composite is determined from tension creep tests on a ′45 deg laminate at temperatures of 81°, 125°, and 150° F. A master shear creep compliance curve is constructed by using the principle of time-temperature superposition. The other unidirectional creep compliances necessary for characterization of an orthotropic material under a state of plane stress are calculated from equations of micromechanics. Agreement is good for a comparison of the shear creep compliance calculated from micromechanics and the ′45 deg laminate. It was found that the behavior of the tensile relaxation modulus of the epoxy resin used in a typical graphite-epoxy composite is similar to the behavior of the epoxy resin used in a typical glass-epoxy. The creep behavior of any laminate can be predicted from laminated plate theory once the unidirectional material is characterized. Viscoelastic interconversion formulas are derived which relate the creep test, constant loading rate test, and dynamic test when the creep compliance can be approximated by a power law in time and linear viscoelasticity theory is valid.

Journal ArticleDOI
TL;DR: In this article, a new method for the numerical solution of Reissner-type plate equations is developed by deriving for an arbitrary edge of a polygonal plate a set of edge functions, which is possible to obtain accurate solutions to moderately thick plate problems.
Abstract: A new method for the numerical solution of Reissner-type plate equations is developed. By deriving for an arbitrary edge of a polygonal plate a set of edge functions, it is possible to obtain accurate solutions to moderately thick plate problems. To indicate the scope of the method, several problems of practical interest were solved, e.g., the torsion of a square plate, the uniformly-loaded clamped and simply-supported square plates. The accuracy achieved in these examples was remarkably good considering the number of unknowns in the formulation.



Journal ArticleDOI
James F. Wilson1
TL;DR: In this article, a plate strip of infinite length and constant width is cantilevered on a uniform elastic support along one edge and free along its opposite edge, and a normal line load of constant intensity applied across its width travels along the strip at constant speed.
Abstract: A plate strip of infinite length and constant width is cantilevered on a uniform elastic support along one edge and free along its opposite edge. A normal line load of constant intensity applied across its width travels along the strip at constant speed. Using plate theory, steady state solutions for the flexural waves are derived in terms of the generalized Fourier integral. Superposition is used to simulate responses to distributed transit loads. Results are applicable to the design of cantilevered guidance panels for air cushion vehicles and also in the design of the metal plates for the linear induction motors sometimes used to power these vehicles. /Author/

Journal ArticleDOI
TL;DR: In this paper, the behavior of unsymmetrically laminated anisotropic plates is investigated using the basic assumptions of linear plate theory and strain-displacement relations modified to account for small initial curvature.

Journal ArticleDOI
TL;DR: The buckling stiffness matrix of a refined plate bending element is derived for various continuous and non-uniform distributions of in-plane forces as discussed by the authors, which can be readily used in a finite element computer program for solving plate buckling problems with various loading and edge conditions.

01 Oct 1974
TL;DR: In this article, the behavior of an annular plate, free at its inner edge and simply supported at the outer one, was experimentally investigated and an approximate formula for the vibrations of the loaded annular plates was developed and compared with the experimental results.
Abstract: The behavior of an annular plate, free at its inner edge and simply supported at the outer one is experimentally investigated. A compressive inplane force is applied uniformly at the outer boundary. Deformations, strains frequencies, and mode shapes are explored over sub, trans, and post buckling regions. Experimental results for the buckling loads are compared. An approximate formula for the vibrations of the loaded annular plates is developed and compared with the experimental results. Good agreement is found between theory and experiments. The influence of initial geometrical imperfections on the behavior of the compressed plate is discussed. (Author)

Journal ArticleDOI
TL;DR: In this paper, a mathematical procedure for calculating the mean pole shift based on the plate theory was presented, and explicit expressions were obtained for the dependence of the secular polar shift on the dimensions and locations of the plate boundaries.
Abstract: The global plate motion indicates that changes in the products of inertia of the earth due to tectonic plate movement may provide a secular shift of the mean pole. A mathematical procedure for calculating this shift based on the plate theory is presented. Explicit expressions were obtained for the dependence of the secular polar shift on the dimensions and locations of the plate boundaries. Numerical results show that the secular motion of the mean pole is 0.0002 sec/year in the direction of 67 W. Hence, it is deduced that the influence of the plate motion on the secular polar shift may account for 10% of the observed value.

Journal ArticleDOI
TL;DR: In this paper, the curvature effects in the cochlea helical spiral of the mammalian inner ear were analyzed using classical plate theory, where the radii of the inner and outer edges are reciprocals of the average curvatures of the spiral edges over the segment of arc to be considered.
Abstract: In two recent contributions, Lieberstein [3,4] proposed a uniformly loaded plate, clamped on two lateral edges and on both ends, as a model of the basilar membrane in the spiral-shaped cochlea of the mammalian inner ear. The “replacement set” of problems suggested by Lieberstein [3], regarding the vibrational events in each segment of arc to be virtually the same as the events in a uniformly loaded circular annular plate clamped on both edges, where the radii of the inner and outer edges are reciprocals of the average curvatures of the spiral edges over the segment of arc to be considered, are analysed using classical plate theory. It is suggested that the results may be interpreted as an indication of the crucial importance of curvature effects in the cochlea helical spiral as the basis of any frequency selection principle, but the work must be presented at this time in a totally incomplete form because of a sad lack of data on the radii of curvature along the edges of the basilar membrane and even on the mass density per unit area as well as the flexural rigidity. We present such an incomplete study in an attempt to stimulate work on the determination of these factors. The direction of results is clearly encouraging.



Journal ArticleDOI
TL;DR: In this paper, the stress and strain distribution in a large plate containing a reinforced circular hole when loaded monotonically in uniaxial tension beyond the elastic range is investigated, where the hole is reinforced with a cylindrical member which is symmetrical with respect to the plate to which it is continuously joined.
Abstract: This investigation deals with the stress and strain distribution in a large plate containing a reinforced circular hole when loaded monotonically in uniaxial tension beyond the elastic range. The hole is reinforced with a cylindrical member which is symmetrical with respect to the plate to which it is continuously joined. Consideration is given to various degrees of plastic deformation of plate and reinforcement corresponding to various uniaxial tension loads. Whole-field analyses of the reinforcement in cylindrical co-ordinates and of the plate in plane polar co-ordinates are obtained by the finite-difference method in which the governing equilibrium equations are expressed in terms of displacements and plastic strains. Deformation theory of plasticity is employed. Limitations of the ‘compact’ reinforcement assumption result from the subsequent whole-field investigation.Results are obtained for material of a specific stress-strain curve so that strain-gauge results could be compared with the stra...

Journal ArticleDOI
TL;DR: In this article, the response of a finite three-dimensional standard linear viscoelastic solid to periodic excitation is investigated for a circular cylindrical body that is bonded to a rigid base at one end and shaken by a prescribed oscillation of a circular rigid plate that was bonded concentrically to the other end.