Showing papers on "Plate theory published in 1997"
Book•
01 Jan 1997
TL;DR: In this paper, the authors present a one-dimensional analysis of fiber-reinforced composite materials and their properties, including the properties of the components of a Lamina and their relationship with other components.
Abstract: Introduction and Mathematical Preliminaries Fiber-Reinforced Composite Materials. Vectors and Tensors. Matrices. Transformation of Vector and Tensor Components. Integral Relations. Equations of Anisotropic Elasticity Classification of Equations. Kinematics. Kinetics. Constitutive Equations. Equations of Thermoelasticity and Electroelasticity. Summary. Virtual Work Principles and Variational Methods Virtual Work. The Variational Operator and Functionals. Extrema of Functionals. Virtual Work Principles. Variational Methods. Summary. Introduction to Composite Materials Basic Concepts and Terminology. Constitutive Equations of a Lamina. Transformation of Stresses and Strains. Plane Stress Constitutive Relations. Classical and First-Order Theories of Laminated Composite Plates Introduction. An Overview of ESL Laminate Theories. The Classical Laminated Plate Theory. The First-Order Laminated Plate Theory. Stiffness Characteristics for Selected Laminates. One-Dimensional Analysis of Laminated Plates Introduction. Analysis of Laminated Beams Using CLPT. Analysis of Laminated Beams Using FSDT. Cylindrical Bending Using CLPT. Cylindrical Bending Using FSDT. Closing Remarks. Analysis of Specially Orthotropic Plates Using CLPT Introduction. Bending of Simply Supported Plates. Bending of Plates with Two Opposite Edges Simply Supported. Bending of Rectangular Plates with Various Boundary Conditions. Buckling of Simply Supported Plates Under Compressive Loads. Buckling of Rectangular Plates Under Inplane Shear Load. Vibration of Simply Supported Plates. Buckling and Vibration of Plates with Two Parallel Edges Simply Supported. Closure. Analytical Solutions of Rectangular Laminates Using CLPT Governing Equations in Terms of Displacements. Admissible Boundary Conditions for the Navier Solutions. Navier Solutions of Antisymmetric Cross-Ply Laminates. The Navier Solutions of Antisymmetric Angle-Ply Laminates. The LTvy Solutions. Analysis of Midplane Symmetric Laminates. Transient Analysis. Summary. Analytical Solutions of Rectangular Laminates Using FSDT Introduction. Simply Supported Antisymmetric Cross-Ply Laminates. Simply Supported Antisymmetric Angle-Ply Laminates. Antisymmetric Cross-Ply Laminates with Two Opposite Edges Simply Supported. Antisymmetric Angle-Ply Laminates with Two Opposite Edges Simply Supported. Transient Solutions. Summary. Finite Element Analysis of Composite Laminates Introduction. Laminated Beams and Plate Strips by CLPT. Timoshenko Beam/Plate Theory. Numerical Results for Beams and Plate Strips. Finite Element Models of Laminated Plates (CLPT). Finite Element Models of Laminated Plates (FSDT). Summary. Refined Theories of Laminated Composite Plates Introduction. A Third-Order Plate Theory. Higher-Order Laminate Stiffness Characteristics. The Navier Solutions. LTvy Solutions of Cross-Ply Laminates. Displacement Finite Element Model. Layerwise Theories and Variable Kinematic Models In troduction. Development of the Theory. Finite Element Model. Variable Kinematic Formulations. Nonlinear Analysis of Composite Laminates Introduction. Nonlinear Stiffness Coefficients. Solution Methods for Nonlinear Algebraic Equations. Computational Aspects and Numerical Examples. Closure. Index Most chapters include Exercises and References for Additional Reading
1,344 citations
Book•
20 Jun 1997
TL;DR: In this paper, Bessel functions have been used to detect and detect longitudinal and shortitudinal waves in Rods, and to propagate and reconstructing the wave motion in a 3D model.
Abstract: 1 Spectral Analysis of Wave Motion.- 1.1 Continuous Fourier Transforms.- 1.2 Discrete Fourier Transform.- 1.3 Examples Using the FFT Algorithm.- 1.4 Experimental Aspects of Wave Signals.- 1.5 Spectral Analysis of Wave Motion.- 1.6 Propagating and Reconstructing Waves.- Problems.- 2 Longitudinal Waves in Rods.- 2.1 Elementary Rod Theory.- 2.2 Basic Solution for Waves in Rods.- 2.3 Dissipation in Rods.- 2.4 Coupled Thermoelastic Waves.- 2.5 Reflections and Transmissions.- 2.6 Distributed Loading.- Problems.- 3 Flexural Waves in Beams.- 3.1 Bernoulli-Euler Beam Theory.- 3.2 Basic Solution for Waves in Beams.- 3.3 Bernoulli-Euler Beam with Constraints.- 3.4 Reflection of Flexural Waves.- 3.5 Curved Beams and Rings.- 3.6 Coupled Beam Structure.- Problems.- 4 Higher-Order Waveguides.- 4.1 Waves in Infinite Media.- 4.2 Semi-Infinite Media.- 4.3 Doubly Bounded Media.- 4.4 Doubly Bounded Media: Lamb Waves.- 4.5 Hamilton's Principle.- 4.6 Modified Beam Theories.- 4.7 Modified Rod Theories.- Problems.- 5 The Spectral Element Method.- 5.1 Structures as Connected Waveguides.- 5.2 Spectral Element for Rods.- 5.3 Spectral Element for Beams.- 5.4 General Frame Structures.- 5.5 Structural Applications.- 5.6 Waveguides with Varying Cross Section.- 5.7 Spectral Super-Elements.- 5.8 Impact Force Identification.- Problems.- 6 Waves in Thin Plates.- 6.1 Plate Theory.- 6.2 Point Impact of a Plate.- 6.3 Wavenumber Transform Solution.- 6.4 Waves Reflected from a Straight Edge.- 6.5 Scattering of Flexural Waves.- 6.6 Lateral Boundary Conditions.- 6.7 Curved Plates and Shells.- Problems.- 7 Structure-Fluid Interaction.- 7.1 Acoustic Wave Motion.- 7.2 Plate-Fluid Interaction.- 7.3 Double Panel Systems.- 7.4 Waveguide Modeling.- 7.5 Radiation from Finite Plates.- 7.6 Cylindrical Cavity.- Problems.- 8 Thin-Walled Structures.- 8.1 Membrane Spectral Elements.- 8.2 Spectral Elements for Flexure.- 8.3 Folded Plate Structures.- 8.4 Structural Applications.- 8.5 Segmented Cylindrical Shells.- 8.6 Future of Spectral Elements.- Problems.- Afterword.- Appendix: Bessel Functions.- References.
391 citations
TL;DR: In this article, a derivation of the shear and peeling stresses in the adhesive layer of a beam with a strengthening plate bonded to its soffit and loaded with an arbitrary point load is presented.
Abstract: At Lulea University of Technology, Sweden, research has been carried out in the area of plate bonding, i.e., the problems that can arise when concrete members need to be strengthened using epoxy-bonded plates. Both comprehensive experimental and theoretical work have been done. In this paper a derivation of the shear and peeling stresses in the adhesive layer of a beam with a strengthening plate bonded to its soffit and loaded with an arbitrary point load are presented. The results from both theory and finite-element analysis show that the stresses are very large at the end of the plate, but they quickly diminish as we move nearer the center of the beam. The magnitude of the stresses is influenced not only by the geometrical and material parameters of the beam, but also by the adhesive and the strengthening material.
338 citations
TL;DR: In this paper, a finite element model based on the classical laminated plate theory is developed for the active vibration control of a composite plate containing distributed piezoelectric sensors and actuators.
Abstract: A finite-element model based on the classical laminated plate theory is developed for the active vibration control of a composite plate containing distributed piezoelectric sensors and actuators. The formulation is derived from the variational principle. The piezoelectrics' mass and stiffness are taken into account in the present model. A simple negative velocity feedback control algorithm coupling the direct and converse piezoelectric effects is used to actively control the dynamic response of an integrated structure through a closed control loop. The static analysis and active vibration suppression of a cantilever composite plate are performed as a numerical example to verify the proposed model. The modal superposition technique and the Newmark- method are used in the numerical simulation to calculate the dynamic response of the laminated composite plate.
209 citations
Book•
[...]
01 Jan 1997
TL;DR: Linear plate theory as mentioned in this paper has been used to model the von Karman equations of linearly elastic plates and shallow shells in Cartesian coordinates, as well as other nonlinear plate models.
Abstract: Part A. Linear Plate Theory. 1. Linearly elastic plates. 2. Junctions in linearly elastic multi-structures. 3. Linearly elastic shallow shells in Cartesian coordinates. Part B. Nonlinear Plate Theory. 4. Nonlinearly elastic plates. 5. The von Karman equations.
209 citations
TL;DR: In this article, the authors investigated the stability and vibration properties of two-dimensional axially moving plates and showed that the speed at the onset of instability increases as the ratio of the length to the width of the plate decreases and as the flexural stiffness increases.
133 citations
TL;DR: In this article, the effects of initial geometric imperfections of the plate are included in the present study which also includes the thermal effects, and the analysis uses a mixed Galerkinperturbation technique to determine thermal buckling loads and postbuckling equilibrium paths.
Abstract: Karman-type nonlinear large deflection equations are derived according to the Reddy's higher-order shear deformation plate theory and used in the thermal postbuckling analysis. The effects of initial geometric imperfections of the plate are included in the present study which also includes the thermal effects. Simply supported, symmetric cross-ply laminated plates subjected to uniform or nonuniform parabolic temperature distribution are considered. The analysis uses a mixed Galerkinperturbation technique to determine thermal buckling loads and postbuckling equilibrium paths. The effects played by transverse shear deformation, plate aspect ratio, total number of plies, thermal load ratio and initial geometric imperfections are also studied.
122 citations
TL;DR: In this article, the performance of various shear-deformation laminated-plate theories was compared for two problems for which an exact elasticity solution has been given by Pagano.
91 citations
TL;DR: In this article, the theory of scattering for flexural waves is developed for an elastic heterogeneity in a flat thin plate in the context of Mindlin's theory, and some new results are derived for energy flux and contrasted with the equivalent results in Kirchhoff plate theory.
90 citations
TL;DR: In this paper, a B-spline Rayleigh-Ritz method is proposed for free vibration analysis of skew fiber-reinforced composite laminates which may have arbitrary lay-ups, admitting the possibility of coupling between in-plane and out-of-plane behaviour and general anisotropy.
87 citations
TL;DR: In this article, an approximate analytical model for the behavior of a laminated composite plate in the presence of delaminations and other local effects is presented, which is based on a generalized displacement formulation implemented at the layer level.
TL;DR: In this paper, the authors employed consistent truncation procedures to both the Mindlin and the exact Rayleigh-Lamb frequency equations, valid for long wavelength and low phase velocity, and found that the 1mode agreement is achieved when the shear coefficient takes the valuek=5/(6?v); the 2mode prediction is then less than?0·5% in error when the wavelength is equal to the plate thickness, and less than + 1% as wavelength approaches zero.
TL;DR: In this paper, a geometrically nonlinear theory of anisotropic multilayered plates of general layups featuring interlayer slips is discussed, and the pertinent equations of motion and consistent boundary conditions are derived by means of the dynamic version of virtual work.
Abstract: The formulation of a geometrically nonlinear theory of anisotropic multilayered plates of general layups featuring interlayer slips is discussed. The theory rests on a displacement field, which accounts for an arbitrary distribution of the tangential displacements through the laminate thickness, fulfills a priori the static continuity conditions of tangential stresses at the layer interfaces, and allows for jumps in the tangential displacements so as to provide the possibility of incorporating effects of interfacial imperfection. For the interlayer displacement jump, a linear shear slip law is postulated. No a priori assumption is made on the type and order of the expansion in the thicknesswise direction of the tangential displacements. The pertinent equations of motion and consistent boundary conditions are derived by means of the dynamic version of the principle of virtual work. These are given in terms of force and moment stress resultants and in terms of generalized displacements. The generalization achieved by the proposed approach is shown by deriving, as particular cases, the recently proposed first-order and third-order models for laminated plates featuring interlayer slips
TL;DR: In this article, an unsymmetric double cantilever beam test is described and its suitability for the determination of interfacial fracture toughness is evaluated; the test specimen consists of a beam type geometry comprised of two materials, one 'top' and one 'bottom' with a crack at one end along the bimaterial interface.
TL;DR: In this article, an analytical procedure is developed to assess the stresses and deformations of filament-wound structures under loading conditions particular to centrifuge rotors and assess the effects of wind angle variation through the centrifuge wall.
Abstract: An analytical procedure is developed to assess the stresses and deformations of filament-wound structures under loading conditions particular to centrifuge rotors and to assess the effects of wind angle variation through the centrifuge wall. This procedure is based on classical laminated plate theory and models both plane stress and plane strain states of a cylindrical shell comprising a number of cylindrical sublayers, each of which is cylindrically orthotropic. Available loading conditions are: radial body force due to rotation about the cylinder axis, internal and external pressures and axial force. The analysis is applied to three examples: a pressure vessel, a centrifuge rotor and a flywheel. It is shown that the benefit of wind angle variation is more significant for applications in which there is no axial loading to the cylindrical shell. It is also shown that, where axial loading is present, the benefits of wind angle variation are more significant under the last ply failure criterion than under the first ply failure criterion.
TL;DR: In this paper, a cubic polynomials for approximation of displacements and a quadratic polynomial for approximating rotations were provided for thin plates and shells.
TL;DR: In this paper, a high-order sandwich plate theory is introduced for the analysis of hard points in the form of inserts, and special attention is focused on the problem of sandwich plates with inserts of the "through-the-thickness" and "fully potted" types.
TL;DR: In this paper, a complete set of shell field equations and side conditions (boundary and jump conditions) is derived from the basic laws of continuum mechanics, including the so-called drilling couples as well as the drilling rotation.
TL;DR: In this paper, a variational-asymptotic method was used to derive a linear, asymptotically correct theory for inhomogeneous orthotropic plates, for example, laminated plates with orthotropic laminae.
Abstract: The focus of this paper is the development of linear, asymptotically correct theories for inhomogeneous orthotropic plates, for example, laminated plates with orthotropic laminae. It is noted that the method used can be easily extended to develop nonlinear theories for plates with generally anisotropic inhomogeneity. The development, based on variational-asymptotic method, begins with three-dimensional elasticity and mathematically splits the analysis into two separate problems: a one-dimensional through-the-thickness analysis and a two-dimensional “plate” analysis. The through-the-thickness analysis provides elastic constants for use in the plate theory and approximate closed-form recovering relations for all truly three-dimensional displacements, stresses, and strains expressed in terms of plate variables. In general, the specific type of plate theory that results from variational-asymptotic method is determined by the method itself. However, the procedure does not determine the plate theory uniquely, and one may use the freedom appeared to simplify the plate theory as much as possible. The simplest and the most suitable for engineering purposes plate theory would be a “Reissner-like” plate theory, also called first-order shear deformation theory. However, it is shown that construction of an asymptotically correct Reissner-like theory for laminated plates is not possible in general. A new point of view on the variational-asymptotic method is presented, leading to an optimization procedure that permits a derived theory to be as close to asymptotical correctness as possible while it is a Reissner-like. This uniquely determines the plate theory. Numerical results from such an optimum Reissner-like theory are presented. These results include comparisons of plate displacement as well as of three-dimensional field variables and are the best of all extant Reissner-like theories. Indeed, they even surpass results from theories that carry many more generalized displacement variables. Although the derivation presented herein is inspired by, and completely equivalent to, the well-known variational-asymptotic method, the new procedure looks different. In fact, one does not have to be familiar with the variational-asymptotic method in order to follow the present derivation.
TL;DR: In this paper, an absolute nodal co-ordinate dynamic formulation is developed for the large deformations and rotations of three-dimensional plate elements, which does not require the use of coordinate transformation to define the global inertia properties of the plates.
Abstract: In this investigation, an absolute nodal co-ordinate dynamic formulation is developed for the large deformations and rotations of three-dimensional plate elements. In this formulation, no infinitesimal or finite rotations are used as nodal co-ordinates, instead global displacements and slopes are used as the plate coordinates. Using this interpretation of the plate coordinates the new method does not require the use of co-ordinate transformation to define the global inertia properties of the plates. The resulting mass matrix is the same constant matrix that appears in linear structural dynamics. The stiffness matrix, on the other hand, is a non-linear function of the nodal co-ordinates of the plate even in the case of a linear elastic problem. It is demonstrated in this paper that, unlike the incremental finite element formulations, the proposed method leads to an exact modelling of the rigid body inertia when the plate element moves as a rigid body. It is also demonstrated that by using the proposed method the conventional plate element shape function has a complete set of rigid body modes that can describe an exact arbitrary rigid body displacement. Using this fact, plate elements in the proposed new formulation can be considered as isoparametric elements. As a consequence, an arbitrary rigid body motion of the element results in zero strain. © 1997 John Wiley & Sons, Ltd.
01 Nov 1997
TL;DR: In this article, an improved version of a previously reported simple theoretical model for predicting the premature (ie peeling) failure of plates is presented in some detail, which extends the range of applicability to cases when the portion of the plate within the critical shear span (where it terminates) can be as long as is desired and unlike the previous model, which assumed a uniform state of shear stresses at the plate/concrete interface.
Abstract: A review of the literature on various structural characteristics of reinforced concrete strongly suggests that, despite extensive research which dates back to the late 1960s, many unresolved problems still remain in the field The purpose of the present paper is twofold Firstly, for the simpler case when full bond may be assumed between the reinforced concrete beam and externally bonded plate up to ultimate load when the plate yields, a non-linear finite element method in conjunction with large scale test data from another source is used to throw some light on the influence of certain design variables such as the ratio of plate area to embedded steel reinforcement area on the beam's ultimate strength plus the effect of plate area on ductility at failure, and to investigate increases in the beam's overall stiffness in the presence of external plate in the case of both under- and over-reinforced designs In the latter part of the paper, an improved version of a previously reported simple theoretical model for predicting the premature (ie peeling) failure of plates will be presented in some detail This model extends the range of applicability to cases when the portion of the plate within the critical shear span (where it terminates) can be as long as is desired and unlike the previous model, which (for short enough lengths of plates within the shear span) assumed a uniform state of shear stresses at the plate/concrete interface, the present version can handle cases when non-uniform variations of shear stresses can exist Most importantly it is argued that the plate peeling phenomenon is controlled by the spacings of the stabilized flexural cracks in the concrete cover, and, owing to large variations (by a factor of, say, two) in spacings of flexural cracks in practice, wide scatter is to be expected in the test data from even closely controlled experiments (A)
TL;DR: In this paper, a finite element based micromechanical method is developed for computing the plate stiffness coefficients (A, B, D matrices) and coefficients of thermal expansion (α's and β's) of a textile composite modeled as a homogeneous plate.
Abstract: A novel finite element based micromechanical method is developed for computing the plate stiffness coefficients (A, B, D matrices) and coefficients of thermal expansion (α's and β's) of a textile composite modeled as a homogeneous plate. Periodic boundary conditions for the plate model, which are different from those for the continuum model, have been derived. The micromechanics methods for computing the coefficients of thermal expansion are readily extended to compute the thermal residual stresses due to curing. The methods are first verified by applying to several examples for which solutions are known, and then applied to the case of woven composites. The plate stiffness coefficients computed from direct micromechanics are compared with those derived from the homogenized elastic constants in conjunction with the classical plate theory. It is found that the plate stiffness coefficients of textile composites, especially the B and D matrices, cannot be predicted from the homogenized elastic constants and ...
TL;DR: In this article, the Ritz method combined with a variational formulation and Mindlin plate theory is used to investigate the effects of elastic spring stiffness, relative thickness and aspect ratio upon the natural frequencies of flexural vibration of rectangular Mindlin plates.
TL;DR: In this paper, a finite element model is used for the analysis of thermal postbuckling and natural vibration of thermally postbuckled anisotropic plates, and the initial nonlinear stiffness is determined from estimated deflection of scaled buckling mode shape.
TL;DR: In this article, the authors developed relationships for the determination of the first-order residual stress in a multi-layer system using beam-based analysis based on beam theory, and they also introduced the bi-axial modulus for isotropic stresses when the thin plate theory (the width-to-thickness ratio of the system being less than 5).
Abstract: Internal residual stresses significantly influence the overall mechanical properties of multi-layer systems and consequently affect the coated material's performance. The determination of residual stresses within coatings has been extensively carried out for thin (the coating thickness being less than the substrate thickness) films (Stoney, Roll, etc.) and for thick (the coating thickness being approximately equal to the substrate thickness) films (Timoshenko, Inoue, etc.). This work extends currently existing models to cover cases where the coating thickness approaches that of the sheet substrate. We developed relationships for the determination of the first-order residual stress. The construction of these models was carried out using a one-dimensional analysis based on beam theory (the width-to-thickness ratio of the system being less than 5). As suggested by Timoshenko and later on by Hoffman, we also introduced the bi-axial modulus for isotropic stresses when the thin plate theory (the width-to-thickn...
TL;DR: In this paper, a set of fundamental equations of a two-dimensional higher-order plate theory is derived through the principle of virtual displacements, and several sets of truncated approximate theories are applied to solve the eigenvalue problems of a simply supported square plate.
TL;DR: In this paper, a B-spline Rayleigh-Ritz method based on first-order shear deformation plate theory 1,2 (SDPT) was proposed for buckling analysis of skew fiber-reinforced composite laminates.
TL;DR: In this paper, a critical review of analytic solutions for bending and buckling of flat, rectangular, orthotropic thin plates is presented, and the validity of the thin plate theory solutions over a range of plate thicknesses is also examined.
TL;DR: In this paper, a method for substantially improving the performance of the higher-order plate and shell theories in connection with the accurate stress analysis of homogeneous and laminated composite structural elements is presented.
Abstract: This paper proposes a method for substantially improving the performance of the higher-order plate and shell theories in connection with the accurate stress analysis of homogeneous and laminated composite structural elements. The presentation of the method is based on the equations of the “general five-degrees-of-freedom” shear deformable plate theory. Since the method is entirely new, it is initially applied to the solution of the problem of simply supported plates deformed by cylindrical bending, for which there exists an exact elasticity solution [12]. Hence, its reliability is substantially validated by means of appropriate comparisons between numerical results based on the present plate theory and this exact elasticity solution. Moreover, the one-dimensional version of the present plate theory, employed for the cylindrical bending of plates, is considered as a general three-degrees-of-freedom shear deformable beam theory. This advanced beam theory is used for an accurate stress analysis of two-layered composite beams having one of their edges rigidly clamped and the other either rigidly clamped, free of tractions or simply supported. This final set of applications can be thought of alternatively as a stress analysis of two-layered plates deformed in cylindrical bending and subjected to several, different sets of edge boundary conditions.
TL;DR: In this paper, the Timoshenko beam B-spline Rayleigh-Ritz method (TBkSRRM) is formulated for vibration analysis of beams based on Timoshenkobeam theory and vibration and buckling analysis of isotropic plates or fiber-reinforced composite laminates based on the first-order shear deformation plate theory.
Abstract: First, the shear-locking phenomenon in the wψBkSRRM1–3 is investigated and the shear-locking terms are identified in both one-dimensional beam and two-dimensional plate analyses. Subsequently the shear-locking free conditions are proposed and under the guidance of these conditions the Timoshenko beam B-spline Rayleigh–Ritz method, designated as TBkSRRM, is formulated for vibration analysis of beams based on Timoshenko beam theory and vibration and buckling analysis of isotropic plates or fibre-reinforced composite laminates based on the first-order shear deformation plate theory (SDPT). In TBkSRRM the number of degrees of freedom is exactly the same as that when the Bernoulli–Euler beam theory or classical plate theory (CPT) is used. However, the TBkSRRM includes the through-thickness shearing and rotary inertia effects in full. Several numerical applications are presented and they show that this unified approach is extremely efficient for both thick and thin beams and plates. © 1997 by John Wiley & Sons, Ltd.