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Showing papers on "Orthotropic material published in 1986"


Journal ArticleDOI
TL;DR: In this paper, a piecewise linear displacement field which allows the contact conditions for the displacements and the transverse shearing stresses at the interfaces to be satisfied simultaneously, the nonlinear (in the von Karman sense) equations of motion for thick multilayered orthotropic plates are developed.

372 citations


Journal ArticleDOI
TL;DR: In this article, the relationship between the overall stiffness properties and the intensity of damage in composite laminates is determined using a vectorial representation of damage as internal variables in a phenomenological theory.

205 citations


Journal ArticleDOI
TL;DR: In this article, the differential equation governing buckling of symmetrically laminated composite plates loaded in compression is presented in nondimensiona l form, and a nondimensional parameter is presented that is used to assess when anisotropic bending stiffnesses can be neglected in a buckling analysis.
Abstract: The differential equation governing buckling of symmetrically laminated composite plates loaded in compression is presented in nondimensiona l form. From this equation, nondimensional material coefficients are obtained, and a nondimensional parameter is presented that is used to assess when anisotropic bending stiffnesses can be neglected in a buckling analysis. Results obtained using finite element analyses are presented that show how boundary conditions, aspect ratio, fiber orientation, stacking sequence, and thickness affect the importance of the anisotropic bending stiffnesses.

186 citations


Journal ArticleDOI
TL;DR: In this article, orthogonal polynomial functions are used in the Rayleigh-Ritz method to generate results for a number of flexural vibration and buckling problems for rectangular isotropic and orthotropic plates.

169 citations


Journal ArticleDOI
TL;DR: In this article, the results of a finite element analysis of a corrugated sheet subjected to constant strain states reveal an inadequacy in some of the classical expressions in use today.

167 citations


Journal ArticleDOI
TL;DR: In this paper, a SiC particle-reinforced aluminum-alloy composite was modeled as prolate spheroids distributed randomly, both in position and orientation, and wave speeds of plane waves, both longitudinal and shear, were calculated in the longwavelength limit.
Abstract: Plane‐wave propagation in an SiC‐particle‐reinforced aluminum‐alloy composite was studied. Considering the composite to possess orthotropic symmetry (nine independent elastic constants), by a pulse‐echo method, nine independent ultrasonic velocities were measured. Measured elastic stiffnesses departed negatively up to 40% from a rule‐of‐mixture model. Using ensemble‐average, scattered‐plane‐wave methods, the composite was modeled as SiC particles represented as prolate spheroids distributed randomly, both in position and in orientation. Wave speeds of plane waves, both longitudinal and shear, were calculated in the long‐wavelength limit. These wave speeds lead to equations for the effective static bulk and shear moduli of the composite. Further, a nonhomogeneous particle distribution was considered. Wave‐speed equations were derived for the case where the composite contains particle‐free aluminum‐alloy regions that were represented by oblate spheroids. The resulting anisotropic composite behaves transvers...

97 citations


Journal ArticleDOI
TL;DR: In this paper, a variational model for a laminated plate consisting of an arbitrary number of fiber-reinforced composite material layers has been developed, using the variational principles.
Abstract: Governing equations of motion for a laminated plate consisting of an arbitrary number of fiber-reinforced composite material layers have been developed, using the variational principles. Each layer was considered to be of an orthotropic material with its directional elastic properties depending on the fiber orientation. The extension, bending, inplane shear, and transverse shear deformations in each separate layer were considered. The analytical results were verified with the literature-reported data. A study of the optimum fiber orientations in a criss-cross laminated plate has shown that different fiber orientations lead to the maximum frequency and the maximum damping. For a cross-ply laminated plate, the maximum flexural frequency ratio has been obtained for large aspect ratio plates and with large values of elastic modular ratio E11/E22. The maximum loss factor for a cross-ply plate was obtained with square plate and with small values of E11/E22. 15 references.

96 citations


Journal ArticleDOI
TL;DR: In this paper, an elasticity solution is used to analyze an orthotropic fiber in an isotropic matrix under uniform thermal load and the analysis reveals that stress distributions in the fiber are singular in the radial coordinate when the radial fiber stiffness is greater than the hoop stiffness.
Abstract: An elasticity solution is utilized to analyze an orthotropic fiber in an isotropic matrix under uniform thermal load. The analysis reveals that stress distributions in the fiber are singular in the radial coordinate when the radial fiber stiffness (C-rr) is greater than the hoop stiffness (C-theta-theta). Conversely, if C-rr is less than C-theta-theta the maximum stress in the composite is finite and occurs at the fiber-matrix interface. In both cases the stress distributions are radically different than those predicted assuming the fiber to be transversely isotropic (C-rr = C-theta-theta). It is also shown that fiber volume fraction greatly influences the stress distribution for transversely isotropic fibers, but has little effect on the distribution if the fibers are transversely orthotropic.

71 citations


Journal ArticleDOI
TL;DR: In this article, the authors considered the flexural vibration of symmetrically laminated rectangular plates, based upon the adoption of a shear-deformation plate theory, which is an extension of Mindlin's theory for isotropic plates and includes the effects of both transverse shear deformation and rotary inertia.

50 citations


Journal ArticleDOI
TL;DR: In this article, an arbitrarily laminated, anisotropic cylindrical shell of finite length, under uniform internal pressure, is analyzed using Love-Timoshenko's kinematic relations and under the framework of classical lamination theory.
Abstract: An arbitrarily laminated, anisotropic cylindrical shell of finite length, under uniform internal pressure, is analyzed using Love-Timoshenko's kinematic relations and under the framework of classical lamination theory. The previously obtained solutions for asymmetrically laminated orthotropic (cross-ply) as well as unbalanced-symmetric and balanced-unsymmetric (angle-ply) cylindrical shells under the same loading conditions have been shown to be special cases of the present closed-form solution. Numerical results have been presented for a two-layer cylindrical shell and compared with those obtained using finite element solutions based on the layerwise constant shear-angle theory. These are expected to serve as benchmark solutions for future comparisons and to facilitate the use of unsymmetric lamination in design.

42 citations


Journal ArticleDOI
TL;DR: In this article, the problem of cracked bodies in the form of an infinite strip subjected to antiplane stresses or displacements was solved within the context of the linear and anisotropic theory of elasticity.

Journal ArticleDOI
TL;DR: The thermodynamic restrictions on the elastic coefficients of linear orthotropic elasticity and linear transversely isotropy elasticity are recorded and it is shown that previously reported data for the elastic orthotropic constants of bone satisfy these thermodynamics restrictions.

Journal ArticleDOI
TL;DR: In this paper, an analytical analysis of free vibrations of a heated orthotropic rectangular thin plate under various boundary conditions is presented; the nonlinear governing equations are derived from von Karman plate theory and Berger's analysis separately; from them the Duffing-type nonlinear ordinary equations are then obtained by employing Galerkin's method using one-term approximation.

Journal ArticleDOI
TL;DR: In this article, the authors investigated the elastodynamic response of a finite crack in an infinite orthotropic strip under normal impact, where the crack is situated symmetrically and oriented in a direction normal to the edges of the strip.
Abstract: The elastodynamic response of a finite crack in an infinite orthotropic strip under normal impact is investigated in this study. The crack is situated symmetrically and oriented in a direction normal to the edges of the strip. Laplace and Hankel transforms are used to reduce the transient problem to the solution of a pair of dual integral equations in the Laplace transform plane. The solution to the dual integral equations is then expressed in terms of a Fredholm integral equation of the second kind. Numerical values on the dynamic stress intensity factor for some fiber-reinforced composite materials are obtained and the results are graphed to display the influence of the material orthotropy.

Journal ArticleDOI
TL;DR: In this paper, a classical elasticity solution for the stress and displacement fields in loaded orthotropic beams is presented and the corresponding stress equations, derived from a stress function which satisfies the orthotropic analogue of the biharmonic equation, are written as Fourier series.

Journal ArticleDOI
TL;DR: In this article, the free vibration of point supported elliptical plates is studied analytically with consideration of rectangular orthotropy, and an analytical method used is an accurate variational approach, the Ritz-Lagrange multiplier method which constitutes an extension of the classical Ritz method.

01 Feb 1986
TL;DR: In this paper, an approximate analysis for predicting buckling of rectangular orthotropic composite plates with centrally located cutouts is presented, which is based on linear differential equations with variable coefficients, expressed as series with each element containing a trigonometric function of one coordinate and a coefficient that is an arbitrary function of the other coordinate.
Abstract: An approximate analysis for predicting buckling of rectangular orthotropic composite plates with centrally located cutouts is presented. In this analysis, prebuckling and buckling problems are converted from a two-dimensional to a one-dimensional system of linear differential equations with variable coefficients. The conversion is accomplished by expressing the displacements as series with each element containing a trigonometric function of one coordinate and a coefficient that is an arbitrary function of the other coordinate. Ordinary differential equations are then obtained from a variational principle. Analytical results obtained from the approximate analysis are compared with finite element analyses for isotropic plates and for specially orthotropic plates with central circular cutouts of various sizes. Experimental results for the specially orthotropic plates are also presented. In nearly all cases, the approximate analysis predicts the buckling mode shapes correctly and predicts the buckling loads to within a few percent of the finite element and experimental results.

Journal ArticleDOI
TL;DR: In this article, near-tip stress and strain fields for power-law hardening orthotropic materials under plane-strain conditions are presented, and the applicability of these fields in the context of a fiber-reinforced composite containing a macroscopic flaw is discussed.

Journal ArticleDOI
TL;DR: In this paper, the effects of anisotropy and the profile of the disks on stresses and strains have been carried out employing the method of successive approximations, and five different cases of material anisotropic have been considered.

Journal ArticleDOI
TL;DR: In this article, the influence of the state of stress in the equilibrium configuration of the Earth (i.e. the pre-stress) upon its adiabatic perturbations is examined.
Abstract: Summary. In this paper we examine the influence of the state of stress in the equilibrium configuration of the Earth (i.e. the pre-stress) upon its adiabatic perturbations. The equations governing these perturbations to the first order (Woodhouse & Dahlen; Dahlen) are re-derived using a Lagrangian approach. Different expressions of the sesquilinear form associated to the elastic-gravitational operator are given. One of these provides a way to extend to hydrostatically pre-stressed solids the criterion of local stability given by Friedman & Schutz for uniformly rotating fluids. Then the propagation in the Earth of seismic wavefronts is considered. It is shown that the nature of these different wavefronts is entirely determined by the quadratic coefficients of the development of the specific internal energy variation, corresponding to isentropic evolution, with respect to the Lagrangian finite deformation tensor. Expressions for the velocities of the various waves are given as functions of incidence angle and pre-stress for orthotropic elastic material. In the particular case where the elastic parameters depend only on one coordinate of a curvilinear system and the axis of orthotropy of the material coincides with the corresponding natural base vector, the elastodynamic equations are reduced to a simple system for a displacement stress vector, using surface operators. In particular for spherical geometry, equations are obtained which generalize to orthotropic pre-stress those given by Alterman et al. and Takeuchi & Saito.

Journal ArticleDOI
TL;DR: In this paper, a nonlinear analysis of symmetric anisotropic panels is presented, where the authors use three-field mixed models having independent interpolation (shape) functions for stress resultants, strain components, and generalized displacements.
Abstract: A computational procedure is presented for the efficient nonlinear analysis of symmetric anisotropic panels. The three key elements of the procedure are: 1) use of three-field mixed models having independent interpolation (shape) functions for stress resultants, strain components, and generalized displacements, with the stress resultants and strain components allowed to be discontinuous at interelement boundaries; 2) decomposition of the material stiffness matrix into the sum of an orthotropic and a nonorthotropic (anisotropic) part; and 3) successive application of the finite element method and the classical Rayleigh-Ritz technique. The finite element method is first used to generate a few global approximation vectors (or modes). Then the amplitudes of these modes are computed by using the Rayleigh-Ritz technique. The global approximation vectors are taken to be various-order derivatives of the strain components, stress resultants, and generalized displacements with respect to an anisotropic tracing parameter and a load parameter; they are evaluated at zero values of the two parameters. The size of the analysis model used in generating the global approximation vectors is identical to that of the corresponding orthotropic structure. The effectiveness of the proposed computational procedure is demonstrated by means of a numerical example, and its potential for solving quasi-symmetric nonlinear problems of composite structures is discussed.

Journal ArticleDOI
TL;DR: In this paper, the authors developed an efficient boundary element method (BEM) for use in the analysis of composite structures, principally loaded holes in mechanically fastened composites, and verified the validity of the method by computing the stress concentration factor in a double lap joint for different hole sizes and various boundary conditions.
Abstract: The purpose of this paper is to develop an efficient boundary element method (BEM) for use in the analysis of composite structures, principally loaded holes in mechanically fastened composites. The idea is to modify the BEM by an analytical scheme to evaluate boundary stresses and deformations accurately. The validity of the method is verified by computing the stress concentration factor in a double lap joint for different hole sizes and various boundary conditions.

Journal ArticleDOI
Jwo Pan1
TL;DR: In this paper, a plane-strain crack-tip stress solution for anisotropic perfectly-plastic materials is presented using the slip-line theory developed by Rice (1973), which is described by the Hill quadratic yield condition.
Abstract: Plane-strain crack-tip stress solutions for anisotropic perfectly-plastic materials are presented. These solutions are obtained using the plane-strain slip-line theory developed by Rice (1973). The plastic anisosotropy is described by the Hill quadratic yield condition. The crack-tip stress solutions under symmetric (Mode I) and anti-symmetric (Mode II) conditions agree well with the low-hardening solutions for the corresponding power-law hardening materials. The crack-tip stress solutions under mixed Mode I and II conditions are also presented. All the solutions indicate that the general features of the slip-line field near a crack tip in orthotropic plastic materials with the elliptical yield contours in the Mohr plane are the same as those associated with isotropic plastic materials. However, the angular variations of the crack-tip stress fields for the materials with large plastic orthotropy differ substantially from those for isotropic plastic materials. Modifications due to polygonal yield contours are outlined and implications of solutions to the fracture analysis of ductile composite materials containing macroscopic flaws are discussed.

Journal ArticleDOI
TL;DR: In this article, the stiffness of a strain gage can produce a significant reinforcement error when it is installed on a low-modulus material such as a plastic, which raises the question of errors due to the same effect when strain measurements are made on some types of orthotropic materials which are characterized by a low elastic modulus in at least the minor principal material direction.
Abstract: There is both experimental and analytical evidence that the stiffness of a strain gage can produce a significant reinforcement error when it is installed on a low-modulus material such as a plastic.1–4 This raises the question of errors due to the same effect when strain measurements are made on some types of orthotropic materials (e.g., unidirectionally reinforced plastics) which are characterized by a low elastic modulus in at least the minor principal material direction. Actually, as indicated by the goniometric distribution of mechanical properties plotted in Fig. 1, the elastic modulus of such a material is typically low in most directions, and not far from that of the plastic matrix, except for an angular range of about ± 30 deg from the major principal material axis.

Journal ArticleDOI
TL;DR: A transfer matrix method was used to obtain numerical solutions to the linearized von Karman plate equations, and to determine critical angles of twist per unit length which buckle the plate as mentioned in this paper, in a compact nondimensional form, for a range of material, geometric and loading parameters.

Journal ArticleDOI
TL;DR: In this article, the effect of an hydrostatic in-plane force, together with the orthotropy, on the axisymmetric vibrations of an annular plate of linearly varying thickness in the radial direction has been analyzed on the basis of classical theory of plates.


Journal ArticleDOI
TL;DR: In this article, the minimum weight of a honeycomb sandwich cylinder with the facings in composite material is obtained by an optimization method with the ply angles and the thicknesses of the ply and honeycomb as the design variables.

Journal ArticleDOI
TL;DR: In this paper, the effects of material orthotropy, foundation parameters and shell-material damping on the deflection response are determined for the clamped and the simply-supported immovable edge conditions accurately.
Abstract: Governing non-linear integro-differential equations for cylindrically orthotropic shallow spherical shells resting on linear Winkler-Pasternak elastic foundations, undergoing moderately large deformations are presented. Three problems, namely, non-linear static deflection response, non-linear dynamic deflection response and dynamic snap-through buckling of orthotropic shells have been investigated. The influences of material orthotropy, foundation parameters and shell-material damping on the deflection response are determined for the clamped and the simply- supported immovable edge conditions accurately. Orthotropy, foundation interaction and material damping play significant roles in improving the load carrying capacity of the shell structures.

Journal ArticleDOI
TL;DR: In this paper, a computer oriented "exact" method of solution is presented for the bending problem of orthotropic rectangular plates, where two opposite edges are clamped or simply supported, or one edge clamped and the other simply supported.
Abstract: A computer oriented "exact" method of solution is presented for the bending problem of orthotropic rectangular plates. The method requires that two opposite edges be clamped or simply supported, or one edge clamped and the other simply supported. Any combination of boundary conditions could exist along the other edges. The plate could be subjected to any combination of patch, uniform, line, and concentrated loads. The plate is divided into strips whose number depends on the types and number of loads. The solution for the deflection of each plate strip is expressed as a Levy type single Fourier series, and the loads are expressed as a corresponding series. The advantage of the analytical strip method is that it overcomes the limitations of the previous "exact" methods (Navier's and Levy's), it is easy to program on a computer, and it provides an alternative to numerical, semi-numerical, and other approximate methods. Results are presented for isotropic and orthotropic plates with different loading and boundary conditions.