Showing papers on "Orthotropic material published in 1993"
TL;DR: In this paper, a gspeneral expression for the yield surface of polycrystalline materials is developed, which can describe both isotropic and anisotropic materials.
Abstract: A gspeneral Expression for the yield surface of polycrystalline materials is developed. The proposed yield surface can describe both isotropic and anisotropic materials. The isotropic surface can be reduced to either the Tresca or von Mises surface if appropriate, or can be used to capture the yield behavior of materials (e.g. aluminum) which do not fall into either category. Anisotropy can be described by introducing a set of irreducible tensorial state variables. The introduced linear transformation is capable of describing different anisotropic states, including the most general anisotropy (triclinic) as opposed to existing criteria which describe only orthotropic materials. Also, it can successfully describe the variation of the plastic strain ratio (R-ratio), where polycrystalline plasticity models usually fail. A method for obtaining the material constants using only uniaxial test data is described and utilized for the special case of orthotropic anisotropy. Finally, the use of tensorial state variables together with the introduced mathematical formulation make the proposed yield function a very convenient tool for numerical implementation in finite element analysis.
622 citations
TL;DR: In this paper, a solution to the plane elasticity problem for a symmetrically laminated composite panel with spatially varying fiber orientations has been obtained, and the effects of the variable fiber orientation on the displacement fields, stress resultants and global stiffness are analyzed.
Abstract: A solution to the plane elasticity problem for a symmetrically laminated composite panel with spatially varying fiber orientations has been obtained. The fiber angles vary along the length of the composite laminate, resulting in stiffness properties that change as a function of location. This work presents an analysis of the stiffness variation and its effects on the elastic response of the panel. The in-plane response of a variable stiff ness panel is governed by a system of coupled elliptic partial differential equations/Solving these equations yields the displacement fields, from which the strains, stresses, and stress resultants can be subsequently calculated. A numerical solution has been obtained using an iterative collocation technique. Corresponding closed-form solutions are presented for three sets of boundary conditions, two of which have exact solutions, and therefore serve to validate the numerical model. The effects of the variable fiber orientation on the displacement fields, stress resultants, and global stiffness are analyzed.
474 citations
TL;DR: In this article, the in-plane and flexural stiffness of a laminated composite plate are modeled as functions of the lamination parameters that are the functions of their stacking sequences.
Abstract: When laminated composite plates are symmetric and orthotropic, their in-plane and flexural stiffnesses become the functions of the lamination parameters that are the functions of their stacking sequences. We use the lamination parameters as fundamental design variables in designing laminates. The feasible region of the lamination parameters is obtained on a two-dimensional plane. Optimum design points can be obtained from the geometric relations between the feasible region and an objective function
179 citations
Book•
01 Jan 1993TL;DR: In this paper, the elasticity of a composite medium in Orthogonal Curvilinear Coordinates has been analyzed for thin-walled composite materials, including Fibers and Matrix Materials.
Abstract: INTRODUCTION TO STRUCTURAL PROPERTIES OF COMPOSITE MATERIALS Fibers Matrix Materials Structural Features and Mechanical Properties of Composite Materials Elastic Properties of Composite Ply Elastic Properties of Angle-Ply Laminate EQUATIONS OF COMPOSITE STRUCTURE MECHANICS Equations of the Elasticity of Theory for an Orthotropic Medium in Orthogonal Curvilinear Coordinates Preliminary Analysis - Basic Assumptions Equations of Engineering Mechanics for Thin-Walled Composite Structures General and Simplified Forms of Governing Equations and Boundary Conditions Composite Structures of Variable Thickness Hygrothermal Effects Nonlinear Stress-Strain Behavior of Composite Materials Geometric Nonlinearity Buckling Dynamic Response COMPOSITE BEAMS, COLUMNS, AND RINGS Governing Equations for Laminated Beams Lateral Bending Buckling Under Axial Compression Dynamic Behaviour Circular Rings THIN-WALLED BEAMS Single-Cell Beams Beams with Open Cross-Section Contour Analysis of Thin-Walled Beams with Multi-Cell Cross-Section Contour COMPOSITE PANELS AND PLATES Equations of the Theory of Laminated Plates Symmetrically Laminated Panels Generally Laminated Plates Axisymmetric Deformation of Circular Plates and Disks CIRCULAR CYLINDRICAL SHELLS Equations of the Theory of Circular Cylindrical Orthotropic Shells Circular Cylindrical Shells with Stress-Strain State Independent of Longitudinal Coordinate Axisymmetric Deformation of Cirular Cylindrical Shells General Case of Circular Cylindrical Shell Loading: Solutions in the Form of Trigonometric Series Simplified Theories of Circular Cylindrical Shells Buckling of Circular Cylindrical Shells Circular Cylindrical Shell Vibrations Buckling and Vibrations of Circular Cylindrical Panels AXISYMMETRIC DEFORMATION OF SHELLS OF REVOLUTION Governing Equations Linear Membrane Theory Boundary-Layer Theory Composite Pressure Vessels
156 citations
TL;DR: In this paper, a fully nonlinear theory for the dynamics and active control of elastic laminated plates with integrated piezoelectric actuators and sensors undergoing large-rotation and small-strain vibrations is presented.
155 citations
TL;DR: In this article, a refined finite-rotation theory with seven independent displacement variables is developed, approximating the displacement field by a cubic series expansion of thickness coordinates, which allows a quadratic shear deformation distribution across the thickness.
137 citations
TL;DR: In this paper, a nonlinear finite element procedure is presented for the analysis of reinforced-concrete shell structures, where cracks are treated as an orthotropic material using a smeared rotating crack approach, and the constitutive model adopted for concrete compression response accounts for reductions in strength and stiffness due to the presence of transverse cracks.
Abstract: Nonlinear finite element procedures are presented for the analysis of reinforced‐concrete shell structures. Cracked concrete is treated as an orthotropic material using a smeared rotating crack approach. The constitutive model adopted for concrete compression response accounts for reductions in strength and stiffness due to the presence of transverse cracks. The model used for concrete in tension represents the tension stiffening effects that significantly influence postcracking response. A heterosis‐type degenerate isoparametric quadrilateral element is developed using a layered‐element formulation, which rigorously considers out‐of‐plane shear response. Selective integration is used to avoid shear‐locking and zero‐energy problems. Good stability and convergence characteristics are provided by the iterative, full‐load secant stiffness solution procedure employed. Simple test elements are used to confirm the analytical procedure's ability to accurately model behavior under conditions of membrane load, fle...
114 citations
TL;DR: In this article, a strength of materials approach is used to derive a closed form solution for the compliance and energy release rate of a double cantilever beam specimen with an adhesive layer and cohesive cracks.
Abstract: A simple, yet accurate, strength of materials approach is used to derive a closed form solution for the compliance and energy release rate of the double cantilever beam specimen with an adhesive layer and cohesive cracks. Such capability currently is not available in the literature. The results are valid for either isotropic or orthotropic mate nals in plane stress or plane strain. The specimen is modelled as a beam partially free and partially supported by an elastic foundation. The solution is an extension of previous work by Kanninen [1] for the special case of a homogeneous material (e.g., no adhesive layer). The closed form results are subsequently verified using the finite element method. Ex cellent agreement is found for a variety of crack lengths and material properties. It is shown that, for composite adherends, shear deformation must be taken into account in ad dition to elastic foundation effects. The present results are useful in analyzing test results to determine the fracture toughness of ad...
105 citations
TL;DR: In this article, the structural tensors of anisotropic symmetry groups are derived based on available properties of Kronecker products of orthogonal transformations, and a simple method of determining the structural Tensor with respect to any given symmetry group is developed.
100 citations
TL;DR: In this article, a simple and exact solution procedure for linear free vibration of isotropic and orthotropic conical shells is presented, in the form of a power series in terms of a particularly convenient coordinate system, obtained directly from the governing equations for the three displacements.
99 citations
TL;DR: In this paper, a metric for the strain rate potential for plastically deforming metals is defined in six-dimensional deviatoric strain rate space, and its gradient provides deviateic stresses in the flowing material.
TL;DR: In this article, a simple and exact solution was obtained directly for the Donnell-type governing equations of the free vibration of composite laminated conical shells, with orthotropic stretching-bending coupling.
TL;DR: In this article, the complete and irreducible representations for two-dimensional orthotropic functions and two and three-dimensional relative isotropic functions of symmetric tensors, skew-symmetric tensor and vectors are derived.
TL;DR: In this article, a numerical method based on the Rayleigh method for predicting the natural frequencies of a rectangular plate with a centrally located crack is presented, and the effects of transverse shear deformation and rotary inertia are included by applying the dynamic equivalent of the simplified Reissner theory.
TL;DR: In this paper, the authors present a method for the approximate analysis of local bending effects in sandwich plates with specially orthotropic face layers subjected to localised external loads, which is based on the assumption that the relative deflection of the loaded face against the face not loaded can be modelled by application of an elastic foundation model.
TL;DR: In this article, a compound finite element model is developed to investigate eccentrically stiffened plates in free vibration, where the plate elements and beam elements are treated as integral parts of a compound section, and not as independent bending components.
TL;DR: In this paper, the four independent elastic constants (longitudinal and transverse Young's moduli, in-plane shear modulus and major Poisson's ratio) of an orthotropic material may be extracted from the modal resonance data of a freely-supported rectangular thin plate made from the material, using the classical lamination theory and an optimized threemode Rayleigh formulation with a suitably formed least-squares objective function.
TL;DR: In this paper, a general solution for the collinear interface cracks between dissimilar anisotropic media is applied to the near tip of an interface crack, which can be reduced to the classical stress intensity factors for a crack tip in homogeneous media.
TL;DR: In this technical note a different approach is presented, based on the use of a digital image technique for the measurement of nonhomogeneous strain distributions, finite element modeling and theUse of a minimum-variance estimator.
TL;DR: In this paper, the elastic constants of an orthotropic material were determined by studying the free vibrations of a rectangular plate in completely free boundary conditions, based on series expansions of the deformed plate shape and requiring the boundary conditions to be satisfied.
TL;DR: In this article, the stress-strain rate relations for an anisotropic, incompressible viscous body that is orthotropic, transversely isotropic, are drawn from symmetry considerations.
TL;DR: In this paper, the effect of fiber and interfacial layer morphologies on thermal fields in metal matrix composites (MMCs) was examined. But the authors focused on the thermal properties of the SCS6 silicon carbide fiber and the use of multiple compliant layers at the fiber/matrix interface.
TL;DR: In this paper, a finite element analysis of the Iosipescu shear tests for unidirectional and cross-ply composites is presented and the correction factors which are needed to compensate for the nonuniformity of stress distribution in calculating shear modulus are shown to be dependent on the material orthotropic ratio and the finite element loading models.
TL;DR: In this article, the authors proposed phenomenological potentials to describe the plastic behavior of orthotropic metals, which can be used for any type of loading condition applied to materials with orthotropic anisotropy.
Abstract: Recently, some potentials were proposed to analytically describe the plastic behavior of orthotropic metals. These potentials were expressed either in six-dimensional stress space (yield function) or in six-dimensional strain rate space (strain rate potential). It was shown that these phenomenological potentials provide a good approximation of the plastic potentials calculated with polycrystal models. They can be used for any type of loading condition applied to materials with orthotropic anisotropy. In the paper, both potentials are presented under the same theoretical framework. The determination of the constants that characterize the anisotropy is explained. The application of these potentials in finite-element method (FEM) codes is discussed.
TL;DR: In this article, the analysis of homogeneous and laminated doubly curved shells made of an orthotropic material using the three-dimensional elasticity equations is presented by utilising the assumption that the ratio of the shell thickness to its middle surface radius is negligible as compared to unity.
TL;DR: In this paper, second-order boundary conditions (B.C) are introduced to model an anisotropic interfacial layer when the layer is thin compared to the wavelength, which greatly improves the accuracy and consistency of approximation and at the same time preserve the same order of simplicity.
Abstract: In this paper, using a transfer matrix method, second‐order asymptotic boundary conditions (B.C.) are introduced to model an anisotropic interfacial layer when the layer is thin compared to the wavelength. Compared with the first‐order asymptotic B.C. which have previously been introduced by Rokhlin and Huang [J. Acoust. Soc. Am. 92, 1729–1742 (1992)], the second‐order B.C. greatly improve the accuracy and consistency of approximation and at the same time preserve the same order of simplicity. Other attractive features are that unlike the first‐order approximation the wave solutions for the second‐order B.C. exactly satisfy energy balance and give zero scattering from a homogeneous substrate/layer/substrate system. Furthermore, for decoupled symmetric and antisymmetric problems, the second‐order B.C. can be simplified through lower‐order stiffness matrices so that the rank of the system of equations is reduced by half. Here the second‐order B.C. are presented for a thin orthotropic layer between two solid...
TL;DR: In this article, the authors derived the canonical representations for first, second, third and fourth order Kronecker powers of any two- or three-dimensional orthogonal tensor and applied these results to construct the micropolar elasticity matrices for micropolastic elastic tensors under the 13 anisotropic mechanics symmetry groups C n n = 1, 2, …, 13 as well as the isotropic symmetry group C 0.
TL;DR: In this article, the free vibration of completely free orthotropic rectangular plates was investigated using the method of superposition, and the results were obtained for a particular set of problems, representative of reinforced concrete and similar materials.