Showing papers on "Orthotropic material published in 2002"
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25 Nov 2002TL;DR: In this paper, the authors discuss the use of composite materials in the manufacturing process of a composite piece and the characteristics of the composite material properties, such as anisotropic properties and anisotropy and elasticity.
Abstract: PART ONE PRINCIPLES OF CONSTRUCTION COMPOSITE MATERIALS, INTEREST AND PROPERTIES What is Composite Material Fibers and Matrix What can be Made Using Composite Materials? Typical Examples of Interest on the Use of Composite Materials Examples on Replacing Conventional Solutions with Composites Principal Physical Properties FABRICATION PROCESSES Molding Processes Other Forming Processes Practical Hints in the Manufacturing Processes PLY PROPERTIES Isotropy and Anisotropy Characteristics of the Reinforcement-Matrix Mixture Unidirectional Ply Woven Fabrics Mats and Reinforced Matrices Multidimensional Fabrics Metal Matrix Composites Tests SANDWICH STRUCTURES: What is a Sandwich Structure? Simplified Flexure A Few Special Aspects Fabrication and Design Problems Nondestructive Quality Control CONCEPTION AND DESIGN Design of a Composite Piece The Laminate Failure of Laminates Sizing of Laminates JOINING AND ASSEMBLY Riveting and Bolting Bonding Inserts COMPOSITE MATERIALS AND AEROSPACE CONSTRUCTION Aircraft Helicopters Propeller Blades for Airplanes Turbine Blades in Composites Space Applications COMPOSITE MATERIALS FOR OTHER APPLICATIONS: Composite Materials and the Manufacturing of Automobiles Composites in Naval Construction Sports and Recreation Other Applications PART TWO: MECHANICAL BEHAVIOR OF LAMINATED MATERIALS ANISOTROPIC ELASTIC MEDIA: Review of Notations Orthotropic Materials Transversely Isotropic Materials ELASTIC CONSTANTS OF UNIDIRECTIONAL COMPOSITES: Longitudinal Modulus Poisson Coefficient Transverse Modulus Shear Modulus Thermoelastic Properties ELASTIC CONSTANTS OF A PLY ALONG AN ARBITRARY DIRECTION: Compliance Coefficients Stiffness Coefficients Case of Thermomechanical Loading MECHANICAL BEHAVIOR OF THIN LAMINATED PLATES: Laminate with Miplane Symmetry Laminate without Miplane Symmetry PART THREE: JUSTIFICATIONS, COMPOSITE BEAMS, THICK PLATES ELASTIC COEFFICIENTS Elastic Coefficients in an Orthotropic Material Elastic Coefficients for a Transversely Isotropic Material Case of a Ply THE HILL-TSAI FRACTURE CRITERION: Isotropic Material: Von Mises Criterion Orthotropic Material: Hill-Tsai Criterion Evaluation of the Resistance of a Unidirectional Ply with Respect to the Direction of Loading COMPOSITE BEAMS IN FLEXURE: Flexure of Symmetric Beams with Isotropic Phases The Case of any Cross Section (Asymmetric) COMPOSITE BEAMS IN TORSION: Uniform Torsion Location of the Torsion Center FLEXURE OF THICK COMPOSITE PLATES: Preliminary Remarks Displacement Field Strains Constitutive Relations Equilibrium Equations Technical Formulation for Bending Examples PART FOUR: APPLICATIONS LEVEL 1 Simply Supported Sandwich Beam Poisson Coefficient of a Unidirectional Layer Helicopter Blade Transmission Shaft for Trucks Flywheel in Carbon/Epoxy Wing Tip Made of Carbon/Epoxy Carbon Fibers Coated with Nickel Tube Made of Glass/Epoxy Under Pressure Filament Wound Reservoir, Winding Angle Filament Wound Reservoir, Taking into Account the Heads Determination of the Volume Fraction of Fibers by Pyrolysis Lever Arm Made of Carbon/Peek Unidirectionals and Short Fibers Telegraphic Mast in Glass/Resin Unidirectional Ply of HR Carbon Manipulator Arm of Space Shuttle LEVEL 2 Sandwich Beam: Simplified Calculations of the Shear Coefficient Procedure for Calculation of a Laminate Kevlar/Epoxy Laminates: Evolution of Stiffness Depending on the Direction of the Load Residual Thermal Stresses Due to Curing of the Laminate Thermoelastic Behavior of a Tube Made of Filament Wound Glass/Polyester Polymeric Tube Loaded by Thermal Load and Creep First Ply Fracture of a Laminate Ultimate Fracture Optimum Laminate for Isotropic Stress State Laminate Made of Identical Layers of Balanced Fabric Wing Spar in Carbon/Epoxy Determination of the Elastic Characteristics of a Carbon/Epoxy Unidirectional Layer from Tensile Test Sail Boat Shell in Glass/Polyester Determination of the in-Plane Shear Modulus of a Balanced Fabric Ply Quasi-Isotropic Laminate Orthotropic Plate in Pure Torsion Plate made by Resin Transfer Molding (RTM) Thermoelastic Behavior of a Balanced Fabric Ply LEVEL 3 Cylindrical Bonding Double Bonded Joint Composite Beam with Two Layers Buckling of a Sandwich Beam Shear Due to Bending in a Sandwich Beam Column Made of Stretched Polymer Cylindrical Bending of a Thick Orthotropic Plate under Uniform Loading Bending of a Sandwich Plate Bending Vibration of a Sandwich Beam Appendix 1: Stresses in the Plies of a Laminate of Carbon/Epoxy Loaded in its Plane Appendix 2: Buckling of Orthotropic Structures Bibliography
678 citations
TL;DR: In this article, a generalized isoparametric formulation of graded finite elements is presented for boundary value problems involving continuously nonhomogeneous isotropic and orthotropic materials, and the performance of graded elements is compared to that of conventional homogeneous elements with reference to analytical solutions.
Abstract: Graded finite elements are presented within the framework of a generalized isoparametric formulation. Such elements possess a spatially varying material property field, e.g. Young's modulus (E) and Poisson's ratio () for isotropic materials; and principal Young's moduli (E11,E22), in-plane shear modulus (G12), and Poisson's ratio (12) for orthotropic materials. To investigate the influence of material property variation, both exponentially and linearly graded materials are considered and compared. Several boundary value problems involving continuously nonhomogeneous isotropic and orthotropic materials are solved, and the performance of graded elements is compared to that of conventional homogeneous elements with reference to analytical solutions. Such solutions are obtained for an orthotropic plate of infinite length and finite width subjected to various loading conditions. The corresponding solutions for an isotropic plate are obtained from those for the orthotropic plate. In general, graded finite elements provide more accurate local stress than conventional homogeneous elements, however, such may not be the case for four-node quadrilateral (Q4) elements. The framework described here can serve as the basis for further investigations such as thermal and dynamic problems in functionally graded materials. ©2002 ASME
380 citations
TL;DR: In this paper, a general constitutive theory of the stress-modulated growth of biomaterials is presented with a particular accent given to pseudo-elastic soft living tissues, and the governing equations of the mechanics of solids with a growing mass are revisited within the framework of finite deformation continuum thermodynamics.
284 citations
TL;DR: In this article, the structural behavior of composite thin-walled members made of laminated plates and displaying arbitrary orthotropy was analyzed and the main concepts and procedures involved in the available isotropic first-order generalized beam theory were revisited and adapted/modified to account for the specific aspects related to the member orthots.
Abstract: This paper presents the formulation of a Generalised Beam Theory (GBT) developed to analyse the structural behaviour of composite thin-walled members made of laminated plates and displaying arbitrary orthotropy. The main concepts and procedures involved in the available isotropic first-order GBT are revisited and adapted/modified to account for the specific aspects related to the member orthotropy. In particular, the orthotropic GBT fundamental equilibrium equations and corresponding boundary conditions are derived and their terms are physically interpreted, i.e., associated with the member mechanical properties. Moreover, different laminated plate material behaviours are dealt with and their influence on the GBT equations is investigated. Finally, in order to clarify the concepts involved in the formulated GBT and illustrate its application and capabilities, a thin-walled orthotropic beam is analysed and the results obtained are thoroughly discussed.
246 citations
TL;DR: This study has produced an orthotropic finite element model of a human femur and implies that it is possible to create a valid FE model by simply comparing the FE results with the measured resonant frequency of the CT scanned bone.
233 citations
TL;DR: In this paper, two new assumed strain finite element formulations of Reddy's higher-order theory are used to determine the natural frequencies of isotropic, orthotropic, and layered anisotropic composite and sandwich plates.
Abstract: Two new C0 assumed strain finite element formulations of Reddy's higher-order theory are used to determine the natural frequencies of isotropic, orthotropic, and layered anisotropic composite and sandwich plates. The material properties typical of glass fibre polyester resins for the skin and HEREX C70 PVC (polyvinyl chloride) foam materials for the core are used to show the parametric effects of plate aspect ratio, length-to-thickness ratio, degree of orthotropy, number of layers and lamination scheme on the natural frequencies. A consistent mass matrix is adopted in the present formulation. The results presented in this investigation could be useful for a better understanding of the behaviour of sandwich laminates under free vibration conditions and potentially beneficial for designers of sandwich structures.
215 citations
TL;DR: In this paper, an orthotropic damage model for brittle masonry subjected to in-plane loading is described, where four independent internal damage parameters, one in compression and one in tension for each of the two natural axes of the masonry, are defined allowing the stiffness recovery at crack closure as well as the different inelastic behaviour along each natural axis to be considered.
Abstract: An orthotropic damage model specifically developed for the analysis of brittle masonry subjected to in-plane loading is described. Four independent internal damage parameters, one in compression and one in tension for each of the two natural axes of the masonry, are defined allowing the stiffness recovery at crack closure as well as the different inelastic behaviour along each natural axis to be considered. The damage field of the material is defined in terms of four equivalent stresses and results, in the space of the in-plane effective stresses, in a double pyramid with a rectangular base where the slopes of the faces correspond to the internal friction angle of the material. The equivalent stresses also control the growth of the damage parameters. The returning path from the effective to the damaged stresses is given by multiplication by a fourth-rank damage effect tensor, which is a function of the damage parameters and of the effective stress state. Mesh size regularization is achieved by means of an enhanced local method taking into account the finite element size. Good agreement has been found in the comparison between numerical results and experimental data both for masonry shear panels and for a large-scale masonry holed wall. Copyright © 2002 John Wiley & Sons, Ltd.
194 citations
TL;DR: In this paper, a constitutive model is developed to characterize a general class of polymer and polymer-like materials that display hyperelastic orthotropic mechanical behavior and the strain energy function is derived from the entropy change associated with the deformation of constituent macromolecules.
Abstract: A constitutive model is developed to characterize a general class of polymer and polymer-like materials that displays hyperelastic orthotropic mechanical behavior. The strain energy function is derived from the entropy change associated with the deformation of constituent macromolecules and the strain energy change associated with the deformation of a representative orthotropic unit cell. The ability of this model to predict nonlinear, orthotropic elastic behavior is examined by comparing the theory to experimental results in the literature. Simulations of more complicated boundary value problems are performed using the finite element method. ©2002 ASME
192 citations
TL;DR: In this article, a three-dimensional mixed variational principle is used to derive a Kth-order two-dimensional line-artheory for an anisotropichomogeneous piezoelectric (PZT) plate.
Abstract: A three-dimensional mixed variational principle is used toderive a Kth-order two-dimensional lineartheory for an anisotropichomogeneouspiezoelectric(PZT)plate.Themechanicaldisplacements, theelectricpotential,theinplane components of the stress tensor, and the in-plane components of the electric displacement are expressed as a e niteseries of orderK inthethickness coordinate bytakingLegendrepolynomialsas thebasisfunctions. However, the transverse shear stress, the transverse normal stress, and the transverse electric displacement are expressed as a e nite series of order (K +2) in the thickness coordinate. The formulation accounts for the double forces without moments that may change the thickness of the plate. Results obtained by using the plate theory are given for the bending of a cantilever thick plate loaded on the top and the bottom surfaces by uniformly distributed 1) normal tractions and 2) tangential tractions. Results are also computed for the bending of a cantilever thick PZT beam loaded by 1) a uniformly distributed charge density on the top and the bottom surfaces and 2) equal and opposite normal tractions distributed uniformly only on a part of the beam. The seventh-order plate theory captures well the boundary-layer effects near the clamped and the free edges and adjacent to the top and the bottom surfaces of a thick orthotropic cantilever beam with the span to the thickness ratio of two. Also, through-the-thickness variation of the transverse shear and the transverse normal stresses agree well with those computed from the analytical solution of the three-dimensional elasticity equations. The governing partial differential equations are second order, so that Lagrange basis functions can be used to solve the problem by the e nite element method.
187 citations
TL;DR: In this paper, a six order differential equation governing the apparent bending of sandwich beams is derived using Hamilton's principle, and boundary conditions for free, clamped and simply supported beams are formulated.
167 citations
TL;DR: In this article, a finite element methodology is developed for fracture analysis of orthotropic functionally graded materials (FGMs) where cracks are arbitrarily oriented with respect to the principal axes of material orthotropy.
TL;DR: In this paper, a unified approach for the analysis and design of adhesive bonded joints is presented, where adherends are modelled as beams or wide plates in cylindrical bending, and are considered as generally orthotropic laminates using classical laminate theory.
TL;DR: In this article, a thorough investigation of the mechanical behavior of a closed-cell cellular foam (Divinycell) under multiaxial stress conditions was undertaken, and two types of Divinycell, H100 and H250, with densities of 100 and 250 kg/m3, respectively, were investigated.
Abstract: A thorough investigation of the mechanical behavior of a closed-cell cellular foam (Divinycell) under multiaxial stress conditions was undertaken. Two types of Divinycell, H100 and H250, with densities of 100 and 250 kg/m3, respectively, were investigated. The uniaxial tensile, compressive and shear stress–strain curves along the in-plane and the through-the-thickness directions of both materials were obtained. The materials showed quite different stress–strain behavior in tension and compression. The H100 material showed a nearly isotropic behavior, while the H250 material showed orthotropic behavior with a higher stiffness along the through-the-thickness than the in-plane direction. A series of biaxial tests were conducted, including: (i) constrained strip specimens in tension and compression with the strip axis along the through-the-thickness and in-plane directions; (ii) constrained thin-wall ring specimens in compression and torsion; (iii) thin-wall tube specimens in tension and torsion; and (iv) thin-wall tube specimens under axial tension, torsion and internal pressure. From these tests, biaxial strength results in the stress plane of the through-the-thickness and in-plane directions for different values of applied shear were obtained. Failure envelopes were constructed by the Tsai–Wu failure criterion based on the strength values in uniaxial tension, compression and shear. The experimental results were described well by the Tsai–Wu failure criterion.
TL;DR: In this article, a study on the influence of the through-the-thickness temperature profile T(z) on the thermomechanical response of multilayered anisotropic thick and thin plates has been conducted.
Abstract: A study on the influence of the through-the-thickness temperature profile T(z) on the thermomechanical response of multilayered anisotropic thick and thin plates has been conducted. The heat conduction problem is solved, and the temperature variation T c (z) is then calculated. The governing thermomechanical equations of multilayered plates are written considering a large variety of classical and advanced or zigzag theories into account. The principle of virtual displacement and the Reissner mixed variational theorem are employed. Linear, up to fourth-order expansions in z are retained for the assumed transverse stress and displacement fields. As a result, more than 20 plate theories are compared. The numerical investigation is restricted to orthotropic layered plates with harmonic in-plane distribution of both thermal loadings and unknown variables. Four sample plate problems are treated that are related to plates made of isotropic and/or orthotropic layers that are loaded by different top-bottom plate surface temperature conditions. Comparison is made to results related to a linear profile T a (z), which is usually assumed in open literature. The following is concluded: Thick plates could exhibit a layerwise form temperature profile T c (z). T a (z) case is approached for thin plate geometries. The use of linear temperature profile leads to large errors in tracing the response of thick plate geometries. The accuracy of plate theories is affected to great extent by the form of temperature variation T(z). Refinements of classical plate theories can be meaningless unless the calculated T c (z) is introduced. The layerwise form of T c (z) would require layerwise assumptions for stresses and/or displacements. Plate theories that neglect transverse normal strains lead to very inaccurate results in both thick and thin plates analysis. At least a parabolic expansion for transverse displacement is required to capture transverse normal thermal strains that vary linearly along the plate thickness.
TL;DR: In this article, the authors deal with the direct identification of mechanical parameters that govern the in-plane constitutive law of orthotropic materials, which are extracted from heterogeneous strain fields that occur in a short beam specimen tested in a Iosipescu fixture.
TL;DR: The aim of the present study was to determine in vitro the anisotropic elastic properties of cortical bones and Young's modulus E and Poisson's ratio nu, were deduced from the velocities measured considering the compact bone as transversely isotropic or orthotropic.
TL;DR: In this paper, the authors present a formulation of orthotropic elasto-plasticity at finite strains based on generalized stress-strain measures, which reduces for one special case to the so-called Green-Naghdi theory.
Abstract: In this paper we present a formulation of orthotropic elasto-plasticity at finite strains based on generalized stress–strain measures, which reduces for one special case to the so-called Green–Naghdi theory. The main goal is the representation of the governing constitutive equations within the invariant theory. Introducing additional argument tensors, the so-called structural tensors, the anisotropic constitutive equations, especially the free energy function, the yield criterion, the stress-response and the flow rule, are represented by scalar-valued and tensor-valued isotropic tensor functions. The proposed model is formulated in terms of generalized stress–strain measures in order to maintain the simple additive structure of the infinitesimal elasto-plasticity theory. The tensor generators for the stresses and moduli are derived in detail and some representative numerical examples are discussed.
TL;DR: An orthotropic material model is utilized to predict the proximal femur trabecular structure, and local directional stiffnesses, degree of anisotropy and density distribution are shown to conform to real femur morphology.
TL;DR: In this article, the effect of coalescence on shear band development and associated fracture mode in plane strain is analyzed numerically using a recent elastic-viscoplastic Gurson-like model that accounts for void shape evolution, coalescence and post-coalescence micromechanics along with isotropic hardening and orthotropic plasticity.
Abstract: The macroscopic fracture in plane strain is known to be shear-like in ductile materials. In most structural materials, fracture starts after diffuse necking, at the centre of the specimen, by micro-void coalescence giving rise afterwards to the macroscopic shear fracture mode. In this paper, the effect of coalescence on shear band development and on associated fracture mode in plane strain is analysed numerically. The calculations are performed using a recent elastic-viscoplastic Gurson-like model that accounts for void shape evolution, coalescence and post-coalescence micromechanics along with isotropic hardening and orthotropic plasticity for the matrix behaviour. The latter is introduced to represent the actual flow properties of hot-worked materials. No kinematic hardening or nucleation formulation is used in order to focus attention on coalescence effects and to discuss, with respect to experiments, published results based on kinematic hardening and nucleation effects. The most important finding is the synergistic effect of plastic anisotropy and post-coalescence yield surface curvature upon the onset of a shear band after the fracture sets in at the centre of the specimen.
TL;DR: In this article, the stability analysis of simply supported and cantilever, thin walled, open section, orthotropic composite beams subjected to concentrated end moments, concentrated forces, or uniformly distributed load is presented.
TL;DR: In this paper, the authors used the three-dimensional Hellinger-Reissner mixed variational principle to derive a K th order (K = 0, 1, 2,...) shear and normal deformable plate theory.
TL;DR: In this article, the radial deformation and the corresponding stresses in a non-homogeneous hollow elastic cylinder rotating about its axis with a constant angular velocity are investigated, and the results indicate that the effect of inhomogeneity is very pronounced.
Abstract: In this paper the radial deformation and the corresponding stresses in a non-homogeneous hollow elastic cylinder rotating about its axis with a constant angular velocity is investigated. The material of the cylinder is assumed to the non-homogeneous and cylindrically orthotropic. The system of fundamental equations is solved by means of a finite difference method and the numerical calculations are carried out for the temperature, the components of displacement and the components of stress with the time t and through the thickness of the cylinder. The results indicate that the effect of inhomogeneity is very pronounced.
TL;DR: In this article, a linear analysis of the vibratory behavior of initially tensioned cylindrical shells conveying a compressible inviscid fluid is presented based on the three-dimensional nonlinear theory of elasticity and the Eulerian equations.
TL;DR: In this paper, the transient internal crack problem for a functionally graded orthotropic strip was studied, where integral transforms and dislocation density functions were employed to reduce the problem to singular integral equations.
TL;DR: In this paper, a special procedure based on the spectral decomposition of the compliance tensor is proposed to obtain a closed formula for the elasticity tensor without explicit using the eigenvalue problem solution.
Abstract: Constitutive relations for incompressible (slightly compressible) anisotropic materials cannot (could hardly) be obtained through the inversion of the generalized Hooke's law since the corresponding compliance tensor becomes singular (ill-conditioned) in this case. This is due to the fact that the incompressibility (slight compressibility) condition imposes some additional constraints on the elastic constants. The problem requires a special procedure discussed in the present paper. The idea of this procedure is based on the spectral decomposition of the compliance tensor but leads to a closed formula for the elasticity tensor without explicit using the eigenvalue problem solution. The condition of nonnegative (positive) definiteness of the material tensors restricts the elastic constants to belong to an admissible value domain. For orthotropic and transversely isotropic incompressible as well as isotropically compressible materials the corresponding domains are illustrated graphically.
TL;DR: In this article, the validity of an orthotropic plasticity model of nonlinear stress-strain behavior in woven glass/epoxy laminates under off-axis tension has been investigated experimentally.
Abstract: Nonlinear stress–strain behavior in woven glass/epoxy laminates under off-axis tension has been investigated experimentally. The validity of an orthotropic plasticity model of such behavior, with three parameters, is discussed. The parameters have been determined from the experimental results. An attempt is also made to describe the nonlinear behavior of the woven composite as a cross-ply laminate using assumed unidirectional composite properties. The nonlinear behavior of the unidirectional laminate is assumed to be described by the one-parameter plasticity model. It is shown that there is a possibility that the one-parameter plasticity model can be used to predict the nonlinear behavior of woven composites.
TL;DR: Closed form solutions for the buckling loads of unidirectionally loaded rectangular orthotropic plates with free and built-in unloaded edges and free and rotationally restrained unloaded edges were derived in this paper.
Abstract: Closed form solutions are derived for the buckling loads of unidirectionally loaded rectangular orthotropic plates with (1) free and built-in unloaded edges and (2) free and rotationally restrained unloaded edges. These expressions can be used in the design of local buckling of the flanges of fiber-reinforced plastic beams. The accuracies of the formulas were determined and the usefulness of the formulas was demonstrated by numerical examples.
TL;DR: In this paper, two methodologies for the analysis of unidirectional fiber reinforced composite materials are presented: a generalized anisotropic large strains elasto-plastic constitutive model and a homogenization theory.
01 Jan 2002
TL;DR: In this paper, the state equation of a laminated thick orthotropic plate is established in the local coordinate system according to the knowledge which has been introduced in the paper by Sundara Raja Iyengar and Pandya (1983, Fiber Sci 7’echnof 18, 19-36).
Abstract: -h this study, the three-dimensional state equation for the jth ply of a laminated thick orthotropic plate is established in the local coordinate system according to the knowledge which has been introduced in the paper by Sundara Raja Iyengar and Pandya (1983, Fiber Sci 7’echnof 18, 19-36) Because all the physical quantities appearing in the state equation are just the compatible quantities of the interfaces, it is extremly convenient to develop the state equation of the whole plate Furthermore the number of unknowns included in the final equations has no relationship with that of the plies of the plate Exact solutions are presented for the statics and dynamics of a three-ply orthotropic thick plates with simply supported edges Numerical results are obtained and compared with those of Srinivas and Rao (1970, fnr J Solids Structures 6, 1463-1481) and thin plate theory
Book•
12 Apr 2002
TL;DR: In this article, the authors define definitions, assumptions and theorems in homogenization problems and apply cell functions for the calculation of binary composite elastic moduli for the homogenisation problem.
Abstract: 0 Introduction.- 1 Definitions, assumptions and theorems in homogenization problems.- 2 Application of cell functions for the calculation of binary composite elastic moduli.- 3 Asymptotic study of linear vibrations of a stretched beam with concentrated masses and discrete elastic supports.- 4 Reinforced plates.- 5 Problems of elasticity theory for reinforced orthotropic plates.- 6 Reinforced shells.- 7 Corrugated plates.- 8 Other periodic structures.- 9 Perforated plates and shells.- Concluding remarks. Perspectives and open problems.- References.