Showing papers on "Orthotropic material published in 1999"

The Behavior of Sandwich Structures of Isotropic and Composite Materials

Abstract: SANDWICH STRUCTURES: ORIGINS, ADVANTAGES, AND USES Description of Various Sandwich Constructions Advantages of Sandwich Construction over Construction Monocoque Thin Walled Construction Origins of Sandwich Construction Uses of Sandwich Construction Present Approach to Analysis Problems References ANISTROPIC ELASTICITY AND COMPOSITE LAMINATE THEORY Introduction Derivation of the Anisotropic Elastic Stiffness and Compliance Matrices The Physical Meaning of the Components of the Orthotropic Elasticity Tensor Methods to Obtain Composite Elastic Properties from Fiber and Matrix Properties Thermal and Hygrothermal Considerations Time-Temperature Effects on Composite Materials High Strain Rate Effects on Material Properties Laminae of Composite Materials Laminate Analysis [A], [B], and [D] Stiffness Matrices for a Mid-Plane Symmetric Sandwich Structure Piezoelectric Effects Problems References DERIVATION OF THE GOVERNING EQUATIONS FOR SANDWICH PLATES (PANELS) Introduction Plate Equilibrium Equations The Bending of Composite Material Laminated and/or Sandwich Plates: Classical Theory Classical Plate Theory Boundary Conditions Analysis of Composite Materials Laminated and/or Sandwich Panels Including Transverse Shear Deformation Effects Boundary Conditions for a Plate Using the Refined Plate Theory Laminated or Sandwich Plate on an Elastic Foundation Laminated or Sandwich Plates Subjected to Dynamic Loads Problems References BEAMS, COLUMNS, AND RODS OF COMPOSITE MATERIALS Development of Classical Beam Theory Some Simplified Sandwich-Beam Solutions Eigenvalue Problems of Sandwich Beams: Natural Vibrations and Elastic Stability Other Considerations Problems References ENERGY METHODS FOR SANDWICH STRUCTURES Introduction Theorem of Minimum Potential Energy Analysis of a Beam in Bending Using the Theorem of Minimum Potential Energy Reissner's Variational Theorem and Its Applications Static Deformation of Moderately Thick Beams Flexural Vibrations of Moderately Thick Beams Flexural Natural Frequencies of a Simply Supported Beam Including Transverse Shear Deformation and Rotatory Inertia Effects Minimum Potential Energy for Rectangular Plates A Rectangular Composite Material Plate Subjected to Lateral and Hygrothermal Loads In-Plane Shear Strength Determination of Composite Materials in Laminated and Sandwich Panels Problems References SOLUTIONS FOR RECTANGULAR SANDWICH PLATES Introduction Navier Solutions for Rectangular Sandwich Plates Levy Solutions for Plates of Composite Materials Perturbation Solutions for the Bending of a Composite Material Sandwich Plate, with Mid-Plane Symmetry and No Bending-Twisting Coupling Isotropic Sandwich Panels Subjected to a Uniform Lateral Load Minimum Weight Optimization for a Sandwich Panel Subjected to a Distributed Lateral Load Analysis of an Isotropic Sandwich Plate on an Elastic Foundation Subjected to a Uniform Lateral Load Static Analysis of Sandwich Plates of Composite Materials Including Transverse Shear Deformation Effects Exact Solution Other Considerations Problems References DYNAMIC EFFECTS ON SANDWICH PANELS Introduction Natural Flexural Vibrations of Sandwich Plates: Classical Theory Natural Flexural Vibrations of Sandwich Plates Including Transverse Shear Deformation Effects Forced-Vibration Response of a Sandwich Plate Subjected to a Dynamic Lateral Load Dynamic Response of Sandwich Plates to Localized Loads Large Amplitude Nonlinear Oscillations of Sandwich Plates Simply Supported on All Edges Linear and Nonlinear Oscillations of Specially Orthotropic Sandwich Panels with Various Boundary Conditions Vibration Damping Problems References THERMAL AND MOISTURE EFFECTS ON SANDWICH STRUCTURES General Considerations Derivation of the Governing Equations for a Thermoplastic Isotropic Plate Boundary Conditions General Treatment of Plate Nonhomogeneous Boundary Conditions Thermoelastic Effects on Beams Self-Equilibrium of Thermal Stress Rectangular Composite Material Plate Subjected to Lateral and Hygrothermal Loads References ELASTIC INSTABILITY (BUCKLING) OF SANDWICH PANELS General Considerations The Buckling of an Orthotropic Sandwich Plate Subjected to In-Plane Loads Classical Theory Elastic Stability of a Composite Sandwich Panel Including Transverse Shear Deformation and Hygrothermal Effects The Buckling of an Isotropic Plate on an Elastic Foundation Subjected to Biaxial In-Plane Compressive Loads The Buckling of Honeycomb Core Sandwich Panels Subjected to In-Plane Compressive Loads The Buckling of Solid- or Foam-Core Sandwich Panels Subjected to In-Plane Compressive Loads Buckling of a Truss-Core Sandwich Panel Subjected to Uniaxial Compression Elastic Stability of a Web-Core Sandwich Panel Subjected to a Uniaxial Compressive In-Plane Load Buckling of Honeycomb-Core Sandwich Panels Subjected to In-Plane Shear Loads Buckling of Solid-Core or Foam-Sandwich Panel Subjected to In-Plane Shear Loads Buckling of a Truss-Core Sandwich Panel Subjected to In-Plane Shear Loads Buckling of a Web-Core Sandwich Panel Subjected to an In-Plane Shear Load Other Considerations Problems References STRUCTURAL OPTIMIZATION TO OBTAIN MINIMUM-WEIGHT SANDWICH PANELS Introduction Minimum Weight Optimization of Honeycomb-Core Sandwich Panels Subjected to a Unidirectional Compressive Load Minimum Weight Optimization of Foam-Core Sandwich Panels Subjected to a Unidirectional Compressive Load Minimum Weight Optimization of Truss-Core Sandwich Panels Subjected to a Unidirectional Compressive Load Minimum Weight Optimization of Web-Core Sandwich Panels Subjected to a Unidirectional Compressive Load Minimum Weight Optimization of Honeycomb-Core Sandwich Panels Subjected to In-Plane Shear Loads Minimum Weight Optimization of Solid- and Foam-Core Sandwich Panels Subjected to In-Plane Shear Loads Minimum Weight Optimization of Truss-Core Sandwich Panels Subjected to In-Plane Shear Loads Minimum Weight Optimization of Web-Core Sandwich Panels Subjected to In-Plane Shear Loads Optimal Stacking Sequences for Composite Material Laminate Faces for Various Sandwich Panels Subjected to Various Loads Problems References SANDWICH SHELLS Introduction Analysis of Sandwich Cylindrical Shells under Axially Symmetric Loads A General Solution for Orthotropic-Sandwich Cylindrical Shells under Axially Symmetric Loads Shells with Mid-Plane Asymmetry Other Considerations Problems References BUCKLING OF SANDWICH CYLINDRICAL SHELLS Buckling of a Solid- or Foam-Core Sandwich Cylindrical Shell with Isotropic Faces Subjected to an Axially Symmetric Compressive End Load Buckling of a Solid- or Foam-Core Sandwich Cylindrical Shell with Orthotropic Composite Faces Subjected to an Axially Symmetric Compressive Load Buckling of a Honeycomb-Core Sandwich Cylindrical Shell with Composite Faces Subjected to an Axially Symmetric Compressive End Load Overall Buckling of Sandwich Cylindrical Shells Subjected to an Overall Bending Moment Buckling of a Sandwich Cylindrical Shell Due to External Pressure Buckling of a Sandwich Cylindrical Shell Due to Torsion Dynamic Buckling Problems References MINIMUM WEIGHT OPTIMIZATION OF SANDWICH CYLINDRICAL SHELLS General Discussion Minimum Weight Optimization of a Solid Foam-Core Sandwich Cylindrical Shell with Isotropic Faces Subjected to an Axially Compressive Load Minimum Weight Optimization of a Solid- or Foam-Core Sandwich Cylindrical Shell with Orthotropic Composite Material Faces Subjected to an Axially Compressive Load Minimum Weight Optimization of a Honeycomb-Core Sandwich Cylindrical Shell with Composite Material Faces Subjected to an Axially Symmetric Compressive Load Problems References APPENDIX 1: Core Materials APPENDIX 2: Face Materials APPENDIX 3: American Society for Testing Materials (ASTM) Standards for Sandwich Structures and Materials INDEX

Numerical Analysis of Moisture-Related Distortion in Sawn Timber

Abstract: In timber exposed to moisture variations such as in wood drying, shape distortions are often a serious problem since it can make the wood products obtained unsuitable for construction purposes. Two characteristics of wood are that its behaviour is strongly orthotropic and that it is very sensitive to variation in moisture. In addition, wood is characterized by variation in its properties from pith to bark. A further important property of wood affecting its behaviour is its spiral grain. In addition, in timber containing much compression wood, drying distortion is highly dependent upon where the compression wood is located in the board. In the present thesis, a finite element method is used to simulate deformations and stresses in wood during drying. A three-dimensional theory for the numerical simulation of deformations and stresses in wood during moisture variation is described. The constitutive model employed assumes the total strain rate to be the sum of the elastic strain rate, the moisture-induced strain rate, the mechano-sorption strain rate and the creep strain rate. Wood is assumed to be an orthotropic material with large differences in properties between the longitudinal, radial and tangential directions regarding the stiffness parameters as well as the moisture shrinkage and mechano-sorption parameters. The influence of moisture content and temperature on the material parameters is likewise taken into account. In addition, the effect of inhomogeneity in the internal structure of the wood material is considered. The influence of the growth rings, the spiral grain and the conical shape of the log on the orthotropic directions in the wood is also taken account of in the model. Variations in the wood properties with distance from the pith are considered as well. The three-dimensional theory used for analysing the shape stability of sawn timber was implemented in a finite element program. To illustrate the types of results that can be obtained, the behaviour of boards during drying was simulated. These simulations yield information on unfavourable deformations and stresses that can develop during the drying process. Boards without external constraint during drying are analysed, as well as boards from different positions in the timber log, boards with deviations in the pith and boards with external constraints. The finite element model is also used to clarify how the material properties and the internal structure affect stiffness properties in sawn timber. The influence of the stiffness parameters, the spiral grain and the annual ring orientation are of particular interest. To investigate factors that influence drying deformations, a parameter study was performed in which the influence of different constitutive models and different material parameters was examined. Numerical simulations were performed to investigate how the annual ring orientation, the cross sectional size and the drying profiles affect the shape stability of sawn timber. The influence of radial variations in the basic properties, the spiral grain and the conical angle was analysed as well. The study involves an experimental investigation of density, grain angles, shrinkage parameters and the longitudinal elastic modulus of a number of spruce boards containing compression wood. On the basis of the data obtained, numerical simulations are carried out to determine deformations that develop in the boards during changes in moisture. Shape stability of sawn timber can often be improved by gluing pieces of wood together. To study how the internal location and orientation of the pieces influence the drying deformations of glued products, numerical simulations for different products were performed. The knowledge obtained can contribute to more effective use of the raw material through allowing boards with properties resulting in poor shape stability or poor stiffness to be sorted out. Possibilities for improving the shape stability through gluing pieces of wood together are examined as well.

Water Entry of a Wedge by Hydroelastic Orthotropic Plate Theory

Abstract: Water entry of a hull with wedge-shaped cross sections is analyzed. The stiffened platings between two transverse girders on each side of the keel are separately modeled. Orthotropic plate theory is used. The effect of structural vibrations on the fluid flow is incorporated by solving the two-dimensional Laplace equation in the cross-sectional fluid domain by a generalized Wagner's theory. The coupling with the plate theory provides three-dimensional flow effects. The theory is validated by comparison with full-scale experiments and drop tests. The importance of global ship accelerations is pointed out. Hydrodynamic and structural error sources are discussed. Systematic studies on the importance of hydroelasticity as a function of deadrise angle and impact velocity are presented. This can be related to the ratio between the wetting time of the structure and the greatest wet natural period of the stiffened plating. This ratio is proportional to the deadrise angle and inversely proportional to the impact velocity. A small ratio means that hydroelasticity is important and a large ratio means that hydroelasticity is not important.

Transverse Normal Stress Effects in Multilayered Plates

Abstract: An evaluation of transverse normal stress σ zz effects in multilayered plate modeling is given in this paper. Mixed theories with continuous interlaminar transverse shear and normal stresses have been formulated on the basis of Reissner's theorem (Reissner, 1984). The case in which the number of the displacement variables preserves independence by the number of constitutive layers, N 1 , has been investigated. Classical models based on standard displacement formulations have been discussed for comparison purposes. The analysis of transverse stress effects has been conducted by allowing a constant, linear, and higher-order distribution of the transverse displacement components in the plate thickness directions. Related two-dimensional models are compared for the static response of symmetrically and unsymmetrically layered, simply supported plates made of isotropic as well as orthotropic layers. The conducted numerical investigation and comparison with available results have above all led to the following conclusions. The possibility of including σ zz makes the used mixed theories more attractive that other available modelings. σ zz plays a fundamental role in thick laminate plates analysis. Such a role increases in transversely anisotropic multilayered plate analysis. With an increase of the plate thickness, a very accurate description of σ zz requires modelings whose number of independent variables depends on N 1 .

Analytical Solution for Rectangular Thick Laminated Plates Subjected to Arbitrary Boundary Conditions

Abstract: Three-dimensional deformations of a multilayered, linear elastic, anisotropic rectangular plate subjected to arbitrary boundary conditions at its edges are analyzed by the generalized Eshelby-Stroh formalism. The rectangular laminate consists of anisotropic and homogeneous laminae of arbitrary thicknesses. Perfect bonding is assumed between the adjoining laminae in the sense that both surface tractions and displacements are assumed to be continuous across their interfaces. The analytical solution is in terms of infinite series, and the effect of truncating the series on the accuracy of the solution is scrutinized. The method is also applicable to rectangular laminated plates, with edges of each lamina subjected to different boundary conditions. Results are presented for thick plates with different sets of edge boundary conditions, e.g., two opposite edges simply supported and the other two subjected to eight different conditions or all four edges clamped.

The mixed mode crack problem in an inhomogeneous orthotropic medium

Abstract: The mixed mode crack problem in plane elasticity for a graded and oriented material is considered. The material property grading is intentional, whereas the property orientation or orthotropy is usually the consequence of material processing. It is assumed that the crack is located in a plane perpendicular to the direction of property grading and the principal axes of orthotropy are parallel and perpendicular to the crack. The four independent engineering constants E11, E22, G12, and ν12 are replaced by a stiffness parameter, E = √E11 E22, a stiffness ratio, δ = (E11/E22)1/4, a Poisson's ratio, ν = √ν12 ν21, and a shear parameter κ0 = (E/2G12) - ν. The corresponding mixed boundary value problem is reduced to a system of integral equations which is solved for various loading conditions and material parameters. The results presented consist of the strain energy release rate, the stress intensity factors and the crack opening displacements. It is found that generally the stress intensity factors increase with increasing material inhomogeneity parameter and shear parameter and with decreasing stiffness ratio.

Novel procedure for complete in-plane composite characterization using a single T-shaped specimen

Abstract: This paper deals with the direct identification of the in-plane elastic properties of orthotropic composite plates from heterogeneous strain fields. The shape of the tested specimen is that of a T subjected to a complex stress state. As a result, the entire set of unknown parameters is directly involved in the strain and displacement responses of the sample. No exact analytical solution is available for such a geometry, and a specific strategy is used to identify the different stiffness components from the whole-field displacements measured over the tested specimen with a suitable optical method. The paper focuses mainly on the experimental aspects of the procedure, and an example of mechanical characterization of a fabric-reinforced composite plate is given.

On free vibration of a rotating truncated circular orthotropic conical shell

Abstract: This article presents a method to study the free vibration of a rotating truncated circular orthotropic conical shell with simply-supported boundary conditions at both ends. Based on the Love first approximation theory and considering the centrifugal and Coriolis accelerations as well as the initial hoop tension, this article studies the frequency characteristics for various geometric and material properties. A detailed discussion is also made for the effects of material orthotropy and cone angle on the frequency characteristics. The present method proves to be reliable and accurate by comparing with available results in the literature.

On radiation-free transonic motion of cracks and dislocations

Abstract: Eshelby has shown that a glide dislocation can move without radiation of energy at 2 of the shear wave speed. It is also known that the same velocity plays a special role in shear crack propagation. This result has not received wide attention in the past due to lack of experiments and numerical simulations of transonic defects. Recent experiments on transonic shear fracture and molecular dynamics simulations of dislocation motion have stimulated renewed interest in the behavior of cracks and dislocations beyond the subsonic regime. We attempt to provide a unified treatment of transonic cracks and dislocations by elaborating on the fundamental result of Eshelby. We develop a unified treatment of radiation-free transonic motion of both cracks and dislocations. We use Stroh’s method to generalize the Eshelby theorem to orthotropic and anisotropic elastic solids. In the case of orthotropic solids, we provide a proof of existence of the radiation-free speed. In the case of general anisotropic solids, there are three wave speeds c3

Ultrasonic evaluation of stresses in orthotropic materials using Rayleigh waves

Abstract: The characterization of stress states in materials is often necessary in mechanical construction. The realization of aeronautical structures increasingly needs knowledge concerning the initial states of the internal stresses, because they induce bending or twisting deformations on the pieces during the tooling. Several non-destructive methods for the determination of stresses have been developed. As the material being characterized here is an aluminum alloy in which the size of grains is very important (order of 150 μm) and, moreover, that the control must be performed on-line, the ultrasonic techniques seem to be more convenient. In this paper, we present a method based on the measurement of ultrasonic Rayleigh wave velocity variations versus the stress state in the thickness of sheets. We show some residual stress profiles obtained by this method. These are then compared with other profiles determined using a destructive technique that makes it possible to check our results. Finally, we discuss various factors that could affect the acoustic measurement of stress profiles in sheets with our method.

Impact response of a finite crack in an orthotropic piezoelectric ceramic

Abstract: The transient dynamic stress intensity factor and dynamic energy release rate were determined for a cracked piezoelectric ceramic under normal impact in this study. A plane step pulse strikes the crack and stress wave diffraction takes place. Laplace and Fourier transforms are employed to reduce the transient problem to the solution of a pair of dual integral equations in the Laplace transform plane. The solution of the dual integral equations is then expressed in terms of a Fredholm integral equation of the second kind. A numerical Laplace inversion technique is used to compute the values of the dynamic stress intensity factor and the dynamic energy release rate for some piezoelectric ceramics, and the results are graphed to display the electroelastic interactions.

Applications of thermoelastic stress analysis to composite materials

Abstract: A number of applied thermoelastic stress analysis (TSA) studies on composite components and assemblies are described, for the purpose of illustrating the potential of the technique for use with composite materials.

Buckling of composite cylindrical shells under mechanical and thermal loads

Abstract: In this article the buckling of specially orthotropic laminated composite cylindrical shells is investigated The nonlinear equilibrium equations based on the Sander's assumption of simplified nonlinear strain-displacement relations and the linearized stability equations for a circular cylindrical thin shell are considered The equations include the rotations and transverse shear force The resulting equations are improved compared to the Donnell stability equations The mechanical and thermal buckling loads of a thin composite circular cylindrical shell based on Donnell and improved stability equations are obtained

The interface crack problem for bonded piezoelectric and orthotropic layers under antiplane shear loading

Abstract: The primary objective of this paper is to study the influence of the electroelastic interactions on the stress intensity factor in bonded layers of piezoelectric and orthotropic materials containing a crack along the interface under antiplane shear. Attention is given to a two-layer hybrid laminate formed by adding a layer of piezoelectric ceramic to a unidirectional graphite/epoxy composite or an aluminum layer. Electric displacement or electric field is prescribed on the surfaces of the piezoelectric layer. The problem is formulated in terms of a singular integral equation which is solved by using a relatively simple and efficient technique. A number of examples are given for various material combinations. The results show that the effect of the electroelastic interactions on the stress intensity factor and the energy release rate can be highly significant.