Showing papers on "Orthotropic material published in 1985"
TL;DR: In this article, a higher-order shear deformation theory for elastic shells was developed for shells laminated of orthotropic layers, which is a modification of the Sanders' theory and accounts for parabolic distribution of the transverse shear strains through thickness of the shell and tangential stress-free boundary conditions on the boundary surfaces.
1,009 citations
TL;DR: In this article, a higher-order shear deformation theory is used to demonstrate the natural frequencies and buckling loads of elastic plates, which accounts for parabolic distribution of the transverse shear strains through the thickness of the plate and rotary inertia.
629 citations
TL;DR: In this article, an analytical model is developed to assess the compressive strength criticality of near-surface interlaminar defects in laminated composites, where the growth conditions and growth behavior of this defect are studied by breaking the overall problem into an elastic stability problem and a fracture problem.
Abstract: An analytical model is developed to assess the compressive strength criticality of near-surface interlaminar defects in laminated composites. The delaminated region is elliptic in shape, separating a thick isotropic plate from a thin orthotropic layer whose material axes coincide with the ellipse axes. The growth conditions and growth behavior of this defect are studied by breaking the overall problem into an elastic stability problem and a fracture problem. Post-buckling solution for the elliptic section is obtained using the Rayleigh-Ritz method while an energy balance criterion based on a self-similar disbond growth governs the fracture. The parameters controlling the growth or arrest of the delamination damage are identified as the fracture energy, disbond depth and elastic properties of the materials from both sides of the delaminating interface. By varying the degree of material anisotropy relative to the loading axis a range in growth behavior was found including stable or unstable crack growth parallel to or normal to the loading axis.
311 citations
TL;DR: In this paper, the authors used Hill's theory of plastic anisotropy for both linear and non-linear strain paths in terms of the anisotropic coefficient measured during uniaxial tensile tensile stretching in three different directions referred to the rolling direction.
168 citations
01 Jun 1985
TL;DR: In this article, the technical literature dealing with buckling and post-buckling behavior of laminated composite plates and shell panels is summarized, and theoretical and experimental results are summarized in graphical and tabular form.
Abstract: : This work summarizes the technical literature dealing with buckling and post-buckling behavior of laminated composite plates and shell panels. Emphasis is given to modern materials used in the aerospace industry having fiber-matrix constituents (e.g., glass-epoxy, boron-epoxy, graphite-epoxy, boron-aluminum), but other applications are also considered (e.g., plywood, paperboard). Geometric configurations taken up are either flat (plates) or cylindrically curved (shells), and have rectangular planform. All possible types of loading conditions and edge constraint conditions are considered. Both symmetrically and unsymmetrically laminated configurations are included, with symmetrical laminates represented by orthotropic or anisotropic plate or shell theory. Complicating effects dealt with include: internal holes, shear deformation, sandwich plates with soft cores, local instability, inelastic materials, hygrothermal effects and stiffeners. Approximately 400 references are used. Extension numerical results are presented in graphical and tabular form. Both theoretical and experimental results are summarized. Keywords: Vibrations; Unsymmetric laminates.
115 citations
TL;DR: In this article, the acoustoelasticity equations of orthotropic elastic solids with initial stresses were formulated in both natural and initial frames of reference and applied to investigate the propagation of ultrasonic waves in orthotropic linear solids.
Abstract: The equations of acoustoelasticity are formulated in both natural and initial frames of reference and applied to investigate the propagation of ultrasonic waves in orthotropic elastic solids with initial stresses. The foundation of the equations is re‐examined for the purpose of applying them to the measurement of residual stresses.
107 citations
TL;DR: In this paper, a criterion for predicting the direction of crack extension in orthotropic composite materials is presented, based upon the normal stress and the anisotropic tensile strength on arbitrary planes about the tip of a crack.
Abstract: A criterion for predicting the direction of crack extension in orthotropic composite materials is presented. The criterion is based upon the normal stress and the anisotropic tensile strength on arbitrary planes about the tip of a crack. Results are obtained, via finite element solutions, for: (1) isotropic mixed mode fracture, (2) cracks in unidirectional off-axis slotted composite tensile coupons and (3) cracks in cross plied laminates. Comparisons are made with other theories and experimental results.
89 citations
TL;DR: In this article, the effects of pin elasticity, friction, and clearance on the stresses near the hole in a pin-loaded orthotropic plate are modeled as a contact elasticity problem using complex variable theory, the pin and the plate being two elastic bodies interacting through contact.
86 citations
TL;DR: In this article, a stress analysis of orthotropic beams subjected to concentrated loads is performed, within the framework of the classical theory of elasticity, on both three-point and four-point bending.
71 citations
TL;DR: In this article, the buckling coefficients of a simply supported rectangular symmetrical anisotropic sandwich plate under combined longitudinal compression and bending were evaluated using the Rayleigh-Ritz method.
Abstract: The small-deflection theory of orthotropic sandwich plates developed by Libove and Batdorf is extended to highly anisotropic sandwich plates with thin faces. Buckling coefficients of a simply supported rectangular symmetrical anisotropic sandwich plate under combined longitudinal compression and bending are evaluated using the Rayleigh-Ritz method. The results show that the multi-ply-faced orthotropic sandwich plate is stronger than a single-ply-fac ed anisotropic one and that the maximum longitudinal buckling strength occurs in plates with lower aspect ratios when the reinforcing fibers are longitudinal and in plates of higher aspect ratios when the fibers are oriented at about 40 deg with respect to the longitudinal axis.
67 citations
TL;DR: In this article, a higher-order plate theory was used to analyze a complete double cantilever beam specimen and the effect of specimen geometry on energy release rate was investigated numerically.
TL;DR: In this article, a nonlinear, thick, composite plate element is developed in which the usual Kirchhoff hypothesis of plane sections remaining plane and undeformed after loading is abandoned, and the displacement field is characterized by the sum of displacements with respect to a reference surface and displacements through the thickness.
Abstract: A nonlinear, thick, composite plate element is developed in which the usual Kirchhoff hypothesis of plane sections remaining plane and undeformed after loading is abandoned The displacement field is characterized by the sum of displacements with respect to a reference surface and displacements through the thickness The through-the-thickness deformations are modeled by imposing a cubic spline function and allowing the rotations at interlaminar boundaries to be degrees of freedom in the element The theory is developed by considering the Lagrangian strains in conjunction with the second Piola-Kirchhoff stress This formulation leads to a quasi-threedimensional element that encompasses large displacements with moderately large rotations but is restricted to small strains Comparisons of linear and nonlinear thick orthotropic plate solutions with those of previously published analytical and numerical results show the validity of the method
TL;DR: In this article, the effect of a constant thermal gradient on the free vibrations of an orthotropic rectangular plate whose thickness varies linearly in two directions is considered, and an approximate but quite convenient frequency equation is derived by using Rayleigh-Ritz techniques with a two-term deflection function.
TL;DR: In this article, a computer program developed for the three-dimensional finite element analysis of complex reinforced, prestressed, and refractory concrete systems is described, based on isotropic elastic, orthotropic elastic, and plasticity formulations, which are implemented in that program, are discussed in detail.
TL;DR: In this article, an analytic solution which satisfies the major displacement boundary conditions on the pin-loaded hole has been obtained, which is similar to the one used earlier by the authors, but extended into a more general fashion.
TL;DR: In this article, a polar orthotropic circular plate of variable thickness (linear as well as parabolic) resting on an elastic foundation of Winkler type is discussed on the basis of the classical theory of plates.
TL;DR: In this article, the transverse vibration of free elliptical plates with rectangular orthotropy is analyzed and a Ritz method analysis is carried out by use of a previously presented idea of taking a complete power series as a trial function.
TL;DR: In this article, the theoretical analysis of the compression panels is based on both wide column and simply supported orthotropic plate theory to predict overall buckling, on orthotropic buckling equations to predict local buckling and on a torsional instability theory for the blade-stiffened panels.
Abstract: Several tests were conducted on graphite/epox y hat-arid blade-stiffened panels under uniaxial compression and wing-box beams under pure bending to verify the accuracy of the theoretical analysis. Theoretical analysis of the compression panels is based on both wide column and simply supported orthotropic plate theory to predict overall buckling, on orthotropic buckling equations to predict local buckling, and on a torsional instability theory for the blade-stiffened panels. Adequate correlations with experimental results were obtained for uniaxial compression when the Euler or torsional buckling modes were critical; buckling occurred at lower strain values than predicted when the local buckling mode was critical. Indeed, simple compression tests cannot represent the load conditions of wing-box compression panels properly; in particular, the bending curvature causes a distributed load perpendicular to panels that can reduce the longitudinal load at which buckling occurs.
TL;DR: In this paper, the nonlinear large-deflection partial differential equations of von karman for orthotropic plates loaded in combined shear and compression are converted into a set of first-order nonlinear ordinary differential equations by assuming trigonometric functions in one direction.
Abstract: The nonlinear large-deflection partial differential equations of von karman for orthotropic plates loaded in combined shear and compression are converted into a set of first-order nonlinear ordinary differential equations by assuming trigonometric functions in one direction. These equations are solved numerically using a two point boundary problem solver which makes use of Newton's method. Results are obtained which determine the postbuckling behavior of rectangular plates with loading up to about three times the buckling load. Both isotropic and orthotropic composite plates are considered. Results show that orthotropic plates may behave quite differently than isotropic plates and that in-plane boundary conditions are important for plates loaded in shear.
TL;DR: In this paper, an approximate analytical solution of the large deflection axisymmetric response of polar orthotropic thin spherical caps resting on elastic foundations is presented, where the Winkler, nonlinear Winkler and Pasternak models of the foundations are considered.
TL;DR: In this article, the accuracy of Donnell's equations for the buckling analysis of imperfect (limit point instability), circular, cylindrical, thin orthotropic shells under axial compression is investigated by comparing critical loads obtained by employing Donnell-type kinematic equations with those based on the more accurate Sanders-type.
TL;DR: In this paper, a finite element formulation utilizing quadratic layer elements and linear interface elements is used to perform the analyses. And the effects of heat-transfer resistance at layer contact surfaces are illustrated through numerical examples.
TL;DR: In this paper, the von Karman type governing equations have been employed to deal with the large amplitude axisymmetric free vibrations of cylindrically orthotropic thin circular plates resting on elastic foundations.
TL;DR: In this article, a simplified method to solve the displacement boundary value problem by bianalytic function theory is given for certain situations of plane strain for an orthotropic elastic body, where the generalized Cauchy integral formula is used to obtain representation formulae.
Abstract: The plane strain problem for a two dimensional orthotropic elastic body is investigated. In particular analytic representations for the solution of the displacement boundary value problem and the stress boundary value problems are found. To this end, the Navier equations are reduced by means of composite transformations to normal form. These are the so-called equations for bianalytic function of the type (λk). The generalized Cauchy integral formula for this function theory is used to obtain representation formulae. A simplified method to solve these problems by bianalytic function theory is given for certain situations of plane strain for an orthotropic elastic body. AMS (MOS): 35A20, 35CO5, 35G15, 35J55.
TL;DR: In this article, the bending problem of a prismatic, orthotropic beam is treated by Saint-Venant's semi-inverse method, and it is shown that the anisotropy can be characterized by two parameters and that the shear stresses are of the same order of magnitude as in the isotropic case.
TL;DR: In this article, the contact behavior between a smooth rigid cylinder and a simply supported orthotropic beam under uniaxial initial stresses is studied, and the displacements are computed by superposing Mindlin plate solution with the solution obtained from Biot's theory of incremental deformation.
TL;DR: In this article, the amplitude-frequency response of an anisotropic rectangular plate with parallel edges having varying rotational constraints to the same degree is analyzed using the elliptic integral method.