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Showing papers on "Plate theory published in 1988"


Journal ArticleDOI
TL;DR: In this article, the problem of edge delamination at the -35/90 interfaces of an 8-ply composite laminate subjected to uniform axial strain was studied and the results showed that the imaginary part of the singularity is the cause of the nonconvergent behavior of the individual components.

328 citations


Journal ArticleDOI
TL;DR: In this paper, a simple isoparametric finite element formulation based on a higher-order displacement model for flexure analysis of multilayer symmetric sandwich plates is presented, which accounts for non-linear variation of inplane displacements and constant variation of transverse displacement through the plate thickness.

242 citations


Journal ArticleDOI
TL;DR: In this paper, a higher-order plate theory and a technique based on the state space concept are used to investigate free vibration and buckling problems of rectangular cross-ply laminated plates.

242 citations


Journal ArticleDOI
R.J. Nuismer1, S.C. Tan
TL;DR: In this article, an approximate elasticity theory solution for the stress-strain relations of a cracked composite lamina is given, which is written in the familiar form of two dimensional compliances appropriate for use with laminated plate theory, and include the effects of non-mechanical strains.
Abstract: An approximate elasticity theory solution is given for the stress-strain relations of a cracked composite lamina. These relations are written in the familiar form of two- dimensional compliances appropriate for use with laminated plate theory, and include the effects of non-mechanical strains. It is shown explicitly that the cracked lamina com pliances depend upon the overall laminate construction in which the lamina is contained.

223 citations


Journal ArticleDOI
TL;DR: In this paper, a method for calculating the locations and sizes of delaminations which occur in a rectangular, fiber reinforced composite plate subjected to non-penetrating (low velocity) impact of a solid object is presented.
Abstract: A method is presented for calculating the locations and sizes of delaminations which occur in a rectangular, fiber reinforced composite plate subjected to nonpenetrating (low velocity) impact of a solid object. The plate may be simply supported or clamped along its edges. In-plane loads or in-plane strains may be imposed on the plate during the impact. The method includes two steps. First, the stresses and strains in the plate are calculated by a three-dimensional, transient finite element method using 8-node brick elements with incompatible modes. Second, the locations, lengths, and widths of delaminations inside the plate are predicted by means of a proposed failure criterion, which is based on the concept of dimensional analysis. The finite element method and the failure criterion were implemented by a computer code which can be used to calculate the impactor position and velocity, the displacements of the plate, the stresses and strains inside the plate during the impact, and the locations and dimensions of the delaminations after the impact. Parametric studies were performed to illustrate the information which can be generated by the computer code.

126 citations


Book
01 Jul 1988
TL;DR: A detailed survey of elasticity theory can be found in this article, with a discussion of the basic equations and associated boundary conditions of the elasticity of transversely loaded and initially stressed plates.
Abstract: Mathematical preliminaries survey of elasticity theory fundamentals of plate theory basic equations and associated boundary conditions static deformation of transversely loaded plates dynamics of plates initially stressed plates - elastic instability numerical methods nonlinear considerations laminated plates.

119 citations


Journal ArticleDOI
Ahmed A. Khdeir1
TL;DR: In this article, an exact mathematical tool to analyze the free vibration and buckling of symmetric cross-ply laminated plates is developed, based on a generalized Levy type solution in conjunction with the state space concept, enabling one to solve exactly the equations governing the laminated anisotropic plate theory.

114 citations


Journal ArticleDOI
TL;DR: In this article, a finite element formulation for flexure of a symmetrically laminated plate based on a higher-order displacement model and a three-dimensional state of stress and strain is presented.
Abstract: A finite element formulation for flexure of a symmetrically laminated plate based on a higher-order displacement model and a three-dimensional state of stress and strain is presented here. The present higher-order theory incorporates linear variation of transverse normal strains and parabolic variation of transverse shear strains through the plate thickness, and as a result it does not require shear correction coefficients. A nine-noded Lagrangian parabolic isoparametric plate bending element is described. The applications of the element to bending of laminated plates with various loading, boundary conditions, and lamination types are discussed. The numerical evaluations also include the convergence study of the element used. The present solutions for deflections and stresses are compared with those obtained using the three-dimensional elasticity theory, closed-form solutions with another high-order shear deformation theory, and the Mindlin's theory. In addition, numerical results for a number of new problems, not available in the literature, are presented for future reference.

113 citations


Journal ArticleDOI
TL;DR: In this paper, a new triangular plate element is presented based on independent interpolations for slopes, displacement and shear forces, and it is shown that it does not suffer from any defect common to other Mindlin plate elements.
Abstract: A new triangular plate element is presented. This new element is based on independent interpolations for slopes, displacement and shear forces, and it is shown that it does not suffer from any defect common to other Mindlin plate elements. Several examples are presented to illustrate the behaviour of this new element.

100 citations


Journal ArticleDOI
TL;DR: In this paper, the influence of different parameters on the impact behavior of laminated composite plates is considered analytically, and the results indicate that the effective mass of the plate is often an important effect in the response to impact events.
Abstract: The influence of different parameters on the impact behavior of laminated composite plates is considered analytically. A Rayleigh-Ritz energy method was used to spatially discretize the time-varying boundary value problem and a set of coupled, ordinary differential equations in time were obtained based on the discretized system Lagrangian. The effects of shearing deformation, bending-twisting coupling, and nonlinear contact behavior were included in the model. The resulting equations were integrated using the implicit Newmark beta method without the effects of rotary inertia. The results indicate that the effective mass of the plate is often an important effect in the response to impact events. In general, the influence of the constitutive behavior dominates for very low velocity impact, whereas the target mass properties become more important as the impactor velocity increases. This importance of mass clearly shows that impactor kinetic energy is not sufficient to characterize the impactor as the impactor mass is shown to have a large influence on the resulting dynamic behavior. In addition to these parameters, the effects of preload and material properties are considered and discussed.

98 citations


Journal ArticleDOI
TL;DR: In this article, a general expression for the energy released at progressing delamination in plates consisting of an arbitrary distribution of layers of different material properties was derived for a delaminated member of circular shape and under transverse pressure.
Abstract: Potential energy theorems and associated bounds are derived for composite plates within the kinematical assumptions usually attributed to von Karman. Material properties are assumed Green elastic but otherwise unspecified. A general expression is derived for the energy released at progressing delamination in plates consisting of an arbitrary distribution of layers of different material properties. The advantages of different versions of the energy release rate expression based on dynamic or kinematic variables are discussed with application in mind. In particular the efficiency of different analytical and numerical means, including classical Rayleigh-Ritz and finite element methods, is investigated in detail for a delaminated member of circular shape and under transverse pressure. In addition to general conclusions drawn for this test case, results are obtained which have a direct practical significance relating to the so-called blister test used to determine adhesive and cohesive material properties.

Journal ArticleDOI
TL;DR: In this article, a general refined shell theory that accounts for the transverse deformation, small strains, and moderate rotations is presented, which can be reduced to various existing shell theories including: the classical (i.e., linear Kirchhoff-love) shell theory, the Donnell-Mushtari-Vlasov shell theory and the moderate rotation shell theory.
Abstract: A general refined shell theory that accounts for the transverse deformation, small strains, and moderate rotations is presented. The theory can be reduced to various existing shell theories including: the classical (i.e., linear Kirchhoff-Love) shell theory, the Donnell-Mushtari-Vlasov shell theory, the Leonard-Koiter-Sanders moderate rotations shell theory, the von Karman type shear-deformation shell theory and the moderate-rotation shear-deformation plate theory developed by Reddy. The present theory is developed from an assumed displacement field, nonlinear strain-displacement equations that contain small strain and moderate rotation terms, and the principle of virtual displacements. The governing equations exhibit strong coupling between the membrane and bending deformations, which should alter the bending, stability, and post-buckling behavior of certain shell structures predicted using the presently available theories.

Journal ArticleDOI
TL;DR: In this paper, a simple theory for bending composite anisotropic plates that are laminated symmetrically about their midplane is presented, which incorporates transverse shear deformation and transverse normal stress as well as the higher-order effects.

Journal ArticleDOI
TL;DR: In this paper, a mesh dependent energy norm was used for analyzing mixed finite element methods for the plate problem, which applies both to the Kirchhoff and to the Mindlin-Reissner formulation of the problem.
Abstract: We set up a framework for analyzing mixed finite element methods for the plate problem using a mesh dependent energy norm which applies both to the Kirchhoff and to the Mindlin-Reissner formulation of the problem. The analysis techniques are applied to some low order finite element schemes where three degrees of freedom are associated to each vertex of a triangulation of the domain. The schemes proceed from the Mindlin-Reissner formulation with modified shear energy.

Journal ArticleDOI
TL;DR: In this paper, a new mixed finite element formulation of Reissner-Mindlin theory is presented which improves upon the stability properties of the Galerkin formulation, and general convergence theorems are proved which are uniformly valid for all values of the plate thickness, including the Poisson-Kirchhoff limit.
Abstract: A new mixed finite element formulation of Reissner-Mindlin theory is presented which improves upon the stability properties of the Galerkin formulation. General convergence theorems are proved which are uniformly valid for all values of the plate thickness, including the Poisson-Kirchhoff limit. As long as the dependent variables are interpolated with functions of sufficiently high order, the formulation is convergent. No special devices are required.

Journal ArticleDOI
TL;DR: In this article, a direct boundary element formulation for Reissner's plate bending theory is reviewed and found to be also applicable to external problems in infinite plates, which bears close resemblance with the standard plane strain boundary element implementation producing singular integrals of the same order.

Book
31 Dec 1988
TL;DR: In this paper, the authors derived the governing equation for a plate with moment-curvature relations and integrated stress resultant-displacement relations and derived the equilibrium equation for the plate.
Abstract: 1. Equations of Linear Elasticity in Cartesian Coordinates.- 1.1 Stresses.- 1.2 Displacements.- 1.3 Strains.- 1.4 Isotropy and Its Elastic Constants.- 1.5 Equilibrium Equations.- 1.6 Stress-Strain Relations.- 1.7 Linear Strain-Displacement Relations.- 1.8 Compatibility Equations.- 1.9 Summary.- 1.10 References.- 1.11 Problems.- 2. Derivation of the Governing Equations for Beams and Rectangular Plates.- 2.1 Assumptions of Plate Theory.- 2.2 Derivation of the Equilibrium Equations for a Plate.- 2.3 Derivation of Plate Moment-Curvature Relations and Integrated Stress Resultant- Displacement Relations.- 2.4 Derivation of the Governing Equations for a Plate.- 2.5 Boundary Conditions.- 2.6 Stress Distribution within a Plate.- 2.7 References.- 2.8 Problems.- 3. Beams and Rods.- 3.1 General Remarks.- 3.2 Development of the Governing Equations.- 3.3 Solutions for the Beam Equation.- 3.4 Stresses in Beams - Rods - Columns.- 3.5 Example: Clamped-Clamped Beam with a Constant Lateral Load, q(x) = -q0.- 3.6 Example: Cantilevered Beam with a Uniform Lateral Load, q(x) = -q0.- 3.7 Example: Simply Supported Beam with a Uniform Load over Part of Its Length.- 3.8 Beam with an Abrupt Change in Stiffness.- 3.9 Beam Subjected to Concentrated Loads.- 3.10 Solutions by Green's Functions.- 3.11 Tapered Beam Solution Using Galerkin's Method.- 3.12 Problems.- 4. Solutions to Problems of Rectangular Plates.- 4.1 Some General Solutions to the Biharmonic Equation.- 4.2 Double Series Solution (Navier Solution).- 4.3 Single Series Solution (Method of M. Levy).- 4.4 Example of Plate with Edges Supported by Beams.- 4.5 Summary.- 4.6 References.- 4.7 Problems.- 5. Thermal Stresses in Plates.- 5.1 General Considerations.- 5.2 Derivation of the Governing Equations for a Thermoelastic Plate.- 5.3 Boundary Conditions.- 5.4 General Treatment of Plate Nonhomogeneous Boundary Conditions.- 5.5 Thermoelastic Effects on Beams.- 5.6 Self-Equilibration of Thermal Stresses.- 5.7 References.- 5.8 Problems.- 6. Circular Plates.- 6.1 Introduction.- 6.2 Derivation of the Governing Equations.- 6.3 Axially Symmetric Circular Plates.- 6.4 Solutions for Axially Symmetric Circular Plates.- 6.5 Circular Plate, Simply Supported at the Outer Edge, Subjected to a Uniform Lateral Loading, p0.- 6.6 Circular Plate, Clamped at the Outer Edge, Subjected to a Uniform Lateral Loading, p0.- 6.7 Annular Plate, Simply Supported at the Outer Edge, Subjected to a Stress Couple, M, at the Inner Boundary.- 6.8 Annular Plate, Simply Supported at the Outer Edge, Subjected to a Shear Resultant, Q0, at the Inner Boundary.- 6.9 General Remarks.- 6.10 Problems.- 7. Buckling of Columns and Plates.- 7.1 Derivation of the Plate Governing Equations for Buckling.- 7.2 Buckling of Columns Simply Supported at Each End.- 7.3 Column Buckling with Other Boundary Conditions.- 7.4 Buckling of Plates Simply Supported on All Four Edges.- 7.5 Buckling of Plates with Other Loads and Boundary Conditions.- 7.6 References.- 7.7 Problems.- 8. The Vibrations of Beams and Plates.- 8.1 Introduction.- 8.2 Natural Vibrations of Beams.- 8.3 Natural Vibrations of Plates.- 8.4 Forced Vibrations of Beams and Plates.- 8.5 References.- 8.6 Problems.- 9. Energy Methods in Beams, Columns and Plates.- 9.1 Introduction.- 9.2 Theorem of Minimum Potential Energy.- 9.3 Analysis of Beams Subjected to a Lateral Load.- 9.4 The Buckling of Columns.- 9.5 Vibration of Beams.- 9.6 Minimum Potential Energy for Rectangular Plates.- 9.7 The Buckling of a Plate under Uniaxial Load, Simply Supported on Three Sides, and Free on an Unloaded Edge.- 9.8 Functions to Assume in the Use of Minimum Potential Energy for Solving Beam, Column, and Plate Problems.- 9.9 Problems.- 10. Cylindrical Shells.- 10.1 Cylindrical Shells under General Loads.- 10.2 Circular Cylindrical Shells under Axially Symmetric Loads.- 10.3 Edge Load Solutions.- 10.4 A General Solution for Cylindrical Shells under Axially Symmetric Loads.- 10.5 Sample Solutions.- 10.6 Circular Cylindrical Shells under Asymmetric Loads.- 10.7 Shallow Shell Theory (Donnell'1. Equations of Linear Elasticity in Cartesian Coordinates.- 1.1 Stresses.- 1.2 Displacements.- 1.3 Strains.- 1.4 Isotropy and Its Elastic Constants.- 1.5 Equilibrium Equations.- 1.6 Stress-Strain Relations.- 1.7 Linear Strain-Displacement Relations.- 1.8 Compatibility Equations.- 1.9 Summary.- 1.10 References.- 1.11 Problems.- 2. Derivation of the Governing Equations for Beams and Rectangular Plates.- 2.1 Assumptions of Plate Theory.- 2.2 Derivation of the Equilibrium Equations for a Plate.- 2.3 Derivation of Plate Moment-Curvature Relations and Integrated Stress Resultant- Displacement Relations.- 2.4 Derivation of the Governing Equations for a Plate.- 2.5 Boundary Conditions.- 2.6 Stress Distribution within a Plate.- 2.7 References.- 2.8 Problems.- 3. Beams and Rods.- 3.1 General Remarks.- 3.2 Development of the Governing Equations.- 3.3 Solutions for the Beam Equation.- 3.4 Stresses in Beams - Rods - Columns.- 3.5 Example: Clamped-Clamped Beam with a Constant Lateral Load, q(x) = -q0.- 3.6 Example: Cantilevered Beam with a Uniform Lateral Load, q(x) = -q0.- 3.7 Example: Simply Supported Beam with a Uniform Load over Part of Its Length.- 3.8 Beam with an Abrupt Change in Stiffness.- 3.9 Beam Subjected to Concentrated Loads.- 3.10 Solutions by Green's Functions.- 3.11 Tapered Beam Solution Using Galerkin's Method.- 3.12 Problems.- 4. Solutions to Problems of Rectangular Plates.- 4.1 Some General Solutions to the Biharmonic Equation.- 4.2 Double Series Solution (Navier Solution).- 4.3 Single Series Solution (Method of M. Levy).- 4.4 Example of Plate with Edges Supported by Beams.- 4.5 Summary.- 4.6 References.- 4.7 Problems.- 5. Thermal Stresses in Plates.- 5.1 General Considerations.- 5.2 Derivation of the Governing Equations for a Thermoelastic Plate.- 5.3 Boundary Conditions.- 5.4 General Treatment of Plate Nonhomogeneous Boundary Conditions.- 5.5 Thermoelastic Effects on Beams.- 5.6 Self-Equilibration of Thermal Stresses.- 5.7 References.- 5.8 Problems.- 6. Circular Plates.- 6.1 Introduction.- 6.2 Derivation of the Governing Equations.- 6.3 Axially Symmetric Circular Plates.- 6.4 Solutions for Axially Symmetric Circular Plates.- 6.5 Circular Plate, Simply Supported at the Outer Edge, Subjected to a Uniform Lateral Loading, p0.- 6.6 Circular Plate, Clamped at the Outer Edge, Subjected to a Uniform Lateral Loading, p0.- 6.7 Annular Plate, Simply Supported at the Outer Edge, Subjected to a Stress Couple, M, at the Inner Boundary.- 6.8 Annular Plate, Simply Supported at the Outer Edge, Subjected to a Shear Resultant, Q0, at the Inner Boundary.- 6.9 General Remarks.- 6.10 Problems.- 7. Buckling of Columns and Plates.- 7.1 Derivation of the Plate Governing Equations for Buckling.- 7.2 Buckling of Columns Simply Supported at Each End.- 7.3 Column Buckling with Other Boundary Conditions.- 7.4 Buckling of Plates Simply Supported on All Four Edges.- 7.5 Buckling of Plates with Other Loads and Boundary Conditions.- 7.6 References.- 7.7 Problems.- 8. The Vibrations of Beams and Plates.- 8.1 Introduction.- 8.2 Natural Vibrations of Beams.- 8.3 Natural Vibrations of Plates.- 8.4 Forced Vibrations of Beams and Plates.- 8.5 References.- 8.6 Problems.- 9. Energy Methods in Beams, Columns and Plates.- 9.1 Introduction.- 9.2 Theorem of Minimum Potential Energy.- 9.3 Analysis of Beams Subjected to a Lateral Load.- 9.4 The Buckling of Columns.- 9.5 Vibration of Beams.- 9.6 Minimum Potential Energy for Rectangular Plates.- 9.7 The Buckling of a Plate under Uniaxial Load, Simply Supported on Three Sides, and Free on an Unloaded Edge.- 9.8 Functions to Assume in the Use of Minimum Potential Energy for Solving Beam, Column, and Plate Problems.- 9.9 Problems.- 10. Cylindrical Shells.- 10.1 Cylindrical Shells under General Loads.- 10.2 Circular Cylindrical Shells under Axially Symmetric Loads.- 10.3 Edge Load Solutions.- 10.4 A General Solution for Cylindrical Shells under Axially Symmetric Loads.- 10.5 Sample Solutions.- 10.6 Circular Cylindrical Shells under Asymmetric Loads.- 10.7 Shallow Shell Theory (Donnell's Equations).- 10.8 Inextensional Shell Theory.- 10.9 Membrane Shell Theory.- 10.10 Examples of Membrane Theory.- 10.11 References.- 10.12 Problems.- 11. Elastic Stability of Shells.- 11.1 Buckling of Isotropic Circular Cylindrical Shells under Axially Symmetric Axial Loads.- 11.2 Buckling of Isotropic Circular Cylindrical Shells under Axially Symmetric Axial Loads and an Internal Pressure.- 11.3 Buckling of Isotropic Circular Cylindrical Shells under Bending.- 11.4 Buckling of Isotropic Circular Cylindrical Shells under Lateral Pressures.- 11.5 Buckling of Isotropic Circular Cylindrical Shells in Torsion.- 11.6 Buckling of Isotropic Circular Cylindrical Shells under Combined Axial Loads and Bending Loads.- 11.7 Buckling of Isotropic Circular Cylindrical Shells under Combined Axial Load and Torsion.- 11.8 Buckling of Isotropic Circular Cylindrical Shells under Combined Bending and Torsion.- 11.9 Buckling of Isotropic Circular Cylindrical Shells under Combined Bending and Transverse Shear.- 11.10 Buckling of Isotropic Circular Cylindrical Shells under Combined Axial Compression, Bending and Torsion.- 11.11 Buckling of Isotropic Spherical Shells under External Pressure.- 11.12 Buckling of Anisotropic and Sandwich Cylindrical Shells.- 11.13 References.- 11.14 Problems.- 12. The Vibration of Cylindrical Shells.- 12.1 Governing Differential Equations for Natural Vibrations.- 12.2 Hamilton's Principle for Determining the Natural Vibrations of Cylindrical Shells.- 12.3 Reference.- Appendix 1. Properties of Useful Engineering Materials.- Appendix 2. Answers to Selected Problems.

Journal ArticleDOI
TL;DR: In this paper, a finite element formulation for flexure of a generally orthotropic plate based on a higher-order displacement model and a three-dimensional state of stress and strain is presented.

Journal ArticleDOI
C.T. Sun1, H. Chin1
TL;DR: In this article, the von Karman plate theory was used to analyze composite laminates under in-plane and transverse loadings, and the governing equations were reduced to linear differentia with nonlinear boundary conditions yielding a simple solution procedure.
Abstract: Linear laminated plate theory is shown to be inadequate for analysis of asymmetric composite laminates, even in the small deflection range. The von Karman plate theory was used to analyze composite laminates under in-plane and transverse loadings. For cylindrical bending problems, the governing equations were reduced to linear differentia} equations with nonlinear boundary conditions yielding a simple solution procedure. Cross-plied laminates were used as examples.

Journal ArticleDOI
TL;DR: In this article, a corner type constitutive equation was developed using the general quadratic anisotropic yield function, and the wrinkling point of square plates subjected to diagonal tension was obtained by the bifurcation and Mindlin type plate theories in conjunction with the finite element approximation.

Book ChapterDOI
TL;DR: In this article, a cumulative damage model for the prediction of stiffness loss in graphite/epoxy laminates applies a thermomechanical constitutive theory for elastic composites with distributed damage.
Abstract: The present cumulative damage model for the prediction of stiffness loss in graphite/epoxy laminates applies a thermomechanical constitutive theory for elastic composites with distributed damage. The model proceeds from a continuum mechanics and thermodynamics approach in which the distributed damage is characterized by a set of second-order tensor-valued internal state variables. A set of damage-dependent laminated plate equations is obtained; this is developed by modifying classical Kirchhoff plate theory.

Journal ArticleDOI
TL;DR: In this paper, a simple isoparametric finite element formulation based on a higher-order displacement model for dynamic analysis of multi-layer symmetric composite plates is presented with an explicit time marching scheme.

Journal ArticleDOI
Ahmed A. Khdeir1
TL;DR: In this paper, the free vibration of angle-ply laminated plates is investigated and a powerful analytical procedure based on a generalized Levy-type solution in conjunction with the state space concept enables one to solve exactly the equations governing the laminated anisotropic plate theory.

Journal ArticleDOI
TL;DR: In this article, the equilibrium configurations of a thin circular plate supported on an elastic foundation of the Winkler type that reacts in compression only are investigated, where the plate is assumed to be subjected to eccentric concentrated load and moment as well as a uniformly distributed load.
Abstract: The equilibrium configurations of a thin circular plate supported on an elastic foundation of Winkler type that reacts in compression only are investigated. The plate is assumed to be subjected to eccentric concentrated load and moment as well as a uniformly distributed load. The solution is accomplished by minimizing the total potential energy of the system. As the coordinate functions for the displacement function of the plate, the free vibration mode shapes of the completely free plate are used by including a rigid translation and a rigid rotation. It is found out that the plate will lift-off when the foundation stiffness is low. The results for the plate on a conventional and tensionless Winkler foundations are given in figures and compared.

Journal ArticleDOI
TL;DR: In this paper, an extension of recent analyses for the transverse motion of an elastic plate under a transverse load is given which shows that the problem of the loading of a thin plate is a singular perturbation one.

Journal ArticleDOI
TL;DR: In this paper, boundary conditions for the interior solution of circular plate problems with edgewise nonuniform boundary data are discussed in detail and then applied to two specific problems, one of them is concerned with a circular plate compressed by two equal and opposite point forces at the plate rim.
Abstract: 1 Necessary conditions have been established recently for the prescribed data along the cylindrical edge(s) of an elastic flat plate to induce only an exponentially decaying elastostatic state. The present paper describes how these conditions may be used to determine the interior solution (or its various thin and thick plate theory approximations) of plate problems. The results in turn show that the necessary conditions for a decaying state are also sufficient conditions. Boundary conditions for the interior solution of circular plate problems with edgewise nonuniform boundary data are discussed in detail and then applied to two specific problems. One of them is concerned with a circular plate compressed by two equal and opposite point forces at the plate rim. The solution process for this problem illustrates for the first time how the stretching action in the plate interior induced by transverse loads can be I properly analyzed.

Journal ArticleDOI
TL;DR: In this paper, a shear-deformable two-layer plate theory with built-in interlayer slip was developed, based upon the principle of virtual work and Reissner's mixed variational principle.
Abstract: Layered plates that experience interlayer slip at a precracked interface such as a construction joint of reinforced concrete slabs or the interface of nailed wooden plates may exhibit significant stiffness degradation. In order to furnish increased simulation capability of stiffness degradation of layered plate structures, a shear‐deformable two‐layer plate theory with built‐in interlayer slip has been developed. Based upon the principle of virtual work and Reissner's mixed variational principle, well‐posed boundary‐value problems of the proposed theory are defined. The theory is tested by examining the cylindrical bending of two‐layer plates consisting of like material layers. Comparisons with the exact elasticity solution for a linear interface slip law and with the numerical result of plane‐strain finite‐element analysis for a nonlinear interface slip law indicate that the present theory accurately simulates important in‐plane responses of the plates. Also, it is observed that the interlayer slip can h...

Book ChapterDOI
01 Jan 1988
TL;DR: In this paper, shear deformation and rotary inertia are included in plate theory to determine the dispersion curves for flexural waves propagating in laminated composite plates, and the results of a unidirectional laminate are compared with the elasticity solutions for flexurys traveling in transversely isotropic plates to determine shear correction factors in the low frequency, long wavelength range.
Abstract: Shear deformation and rotary inertia are included in plate theory to determine the dispersion curves for flexural waves propagating in laminated composite plates. The results of a unidirectional laminate are compared with the elasticity solutions for flexural waves traveling in transversely isotropic plates to determine the shear correction factors in the low frequency, long wavelength range. The values of the shear correction factors for the unidirectional composite laminate are in good agreement with the theoretical values calculated from static cylindrical bending. An acousto-ultrasonic technique using narrowband excitation frequencies is used to obtain experimental data for flexural waves. By measuring the phase velocities for different excitation frequencies, dispersion curves are generated. There is excellent agreement between the experimentally determined values and the theoretical results for aluminum and unidirectional composite plates. For symmetric cross-ply and quasi-isotropic laminates, the data definitely have the characteristic of a dispersion curve for flexural waves, although the agreement between analytic and experimental results is not quite as good. The results of the present work indicate that the inclusion of shear deformation and rotary inertia in plate theory improves the prediction of dispersion curves for flexural waves propagating in composite laminates and suggest that the acousto-ultrasonic technique can be used to characterize composite plates with and without damage since each material and stacking sequence gives distinct dispersion curves.

Journal ArticleDOI
TL;DR: In this paper, a non-monotone multivalued law is introduced in order to describe the interlaminar bonding forces and the existence and the approximation of the solution of this inequality are investigated.
Abstract: In this paper the delamination problem for laminated plates is studied. A nonmonotone multivalued law is introduced in order to describe the interlaminar bonding forces. This law is written as the generalized gradient in the sense of F. H. Clarke of an appropriately defined nonconvex superpotential. Moreover, monotone boundary conditions of the subdifferential type are assumed to hold. The problem is formulated as a variational-hemivariational inequality expressing the principle of virtual work in inequality form. By using compactness and monotonicity arguments, the existence and the approximation of the solution of this inequality are investigated.

Journal ArticleDOI
TL;DR: In this article, a finite strip method is presented for the determination of buckling stresses and natural frequencies of vibration of prismatic plate structures assembled from plate flats, which generally are laminates of fiber-reinforced composite material.