Showing papers on "Orthotropic material published in 1976"

Radial Tire Cord-Rubber Composites

Abstract: Experimental and theoretical results are presented in terms of the elements of the compliance matrix for the material properties which are needed to characterize a calendered ply of various cord-rubber composites commonly used in the body and belt of radial tires. It is shown that a single ply can be represented as a linear, elastic, homogeneous, orthotropic material to a level of accuracy sufficient for modeling inflated, but otherwise unloaded, radial tires. Cord load distributions in the body, belt, and turnup ply endings are predicted and plotted from the bead to the crown of inflated radial tires using principles of structural mechanics to represent the laminated material properties of the tire and finite element techniques to calculate the stresses in the cords. Predictions are also made for rubber strains and tire growth at the crown due to inflation pressure loading. The effects of changing various tire construction and/or material property parameters on such responses are assessed; these...

Interlaminar Stresses in Laminated Cylindrical Shells of Composite Materials

Abstract: Many existing analysis methods for laminated composite material structural components assume structural integrity between laminae and predict load carrying capabilities considerably higher than those sometimes obtained experimentally These methods do not include the means to determine accurately the interlaminar shear and normal stresses, which can cause premature structural failure Methods of analysis are presented herein for a laminated circular cylindrical shell composed of generally orthotropic materials subjected to arbitrary axially symmetric loadings Elastic shell theory, including transverse shear deformation, is utilized By treating each lamina individually, in conjunction with imposing stress and displacement boundary conditions between laminae, the governing equations for the individual laminae are combined, yielding the interlaminar shear and normal stresses as explicit dependent variables A parametric study for a generally othotropic circular cylindrical shell, subjected to a uniform pressure with both clamped and simple supported end boundary conditions is presented Variables include laminate geometry, fiber orientation, stacking sequence and material properties The solutions obtained provide insight into the interlaminar stress fields of shells with any number of plies, and provide a baseline for finite element and finite difference solutions for the same problem A computer program has been formulated to expedite calculations with the analytical solution

Stress intensity factors in anisotropic plates using singular isoparametric elements

Abstract: A conformable displacement model is presented for the finite element analysis of stress intensity factors in linear elastic fracture mechanics. The method is an extension to anisotropic materials of the one developed by Benzley for isotropic materials. Very good agreement is shown for the case of inclined cracks in an orthotropic plate between finite element results and those obtained by least squares collocation of stress functions.

Stress concentrations in anisotropic plates by the method of caustics

Abstract: The optical method of caustics has been extended to study, theoretically and experimentally, the stress fields developed around discontinuities or singularities in anisotropic plates. The equations of the caustic to be expected from illuminating the anisotropic plate by a coherent light beam were derived in terms of the two complex stress functions used in the complex formulation of the plane anisotropic stress problem, the coefficients of the optical anisotropy of the material and the characteristics of the optical arrangement. The particular case of the singular stress field developed at the tip of a crack in an orthotropic plate was studied in detail. A series of experiments was then undertaken with slotted plates taken from the neck region of a polycarbonate plate which had been necked in tension and therefore showed a significant amount of anisotropy. The experimental data corroborated the theoretical predictions. It was concluded that singular or discontinuous stress fields can be successful...

Material Models for Nonlinear Deformation of Graphite

Abstract: ATJ-S graphite is a transversely isotropic granular composite material with different nonlinear stress-strain behavior under tension loading than under compression loading. A model for nonlinear deformation behavior is extended from initial loading under biaxial tension stresses to initial loading under mixed tension and compression stresses. The principal basis of the model is that the material properties are expressed as a function of the strain energy of an equivalent elastic material. Thus, interaction between the various components of a multiaxial stress state is accounted for. Different moduli in tension and compression are excited and are included in the analysis. Both the Jones weighted compliance matrix (WCM) material model and the Isabekian and Khachatryan restricted compliance matrix (RCM) material model are extended to nonlinear deformation.

Design of Composite-Material Plates for Maximum Uniaxial Compressive Buckling Load

Abstract: A major potential advantage claimed for fibrous composite materials in structural applications is that the material can be "tailored" by proper orientation of the fibers in the various layers so as to optimize the desired structural behavior. Yet the very nature of fibrous composites with their anisotropic elastic behavior has kept such optimal tailoring beyond the reach of most design engineers. In comparison to the numerous analyses available in the literature on buckling of anisotropic plates, very few optimal-design syntheses have been published for this problem. In 1960, Gerard (1) gave a synthesis for uniaxially compressed structurally orthotropic plates, but it was devoted only to longitudinally, transversely, or grid stiffened plates. For composite-material plates, Rothwell (2) presented a crude synthesis using netting analysis for the composite layers. Such an analysis completely neglects the contribution of the matrix material and is known to be in considerable disagreement with experimental results for laminated composite-material plates (3). Recently Hayashi (4) synthesized for maximum uniaxial buckling load in both symmetric cross-ply and symmetric angle-ply plates. However, his synthesis was based on the treatment of the number of axial half waves as a continuous rather than discrete variable. The present synthesis considers both symmetric and unsymmetric laminates subjected to uniaxial compressive loading parallel to two of the plate edges.

On the wrinkling of honeycomb sandwich columns with laminated cross-ply faces

Abstract: In the theoretical and experimental work on the buckling of sandwich panels with laminated faces reported in Refs. 1 and 2, panels which had certain coupling terms present in the constitutive equations for the faces were solved in an approximate manner. The previous theoretical solution for angle-ply lay-ups assumed that there were sufficient layers present to treat the faces as orthotropic, with the Bij coupling terms in the constitutive equations put equal to zero. Further simplifying assumptions were made when comparing theoretical and experimental results in Ref. 2 where tests were carried out on three different types of carbon fibre faces; orthotropic, balanced angle-ply and unbalanced cross-ply. It was only in the first case that an exact theoretical analysis was carried out, and the second case was again treated as an orthotropic panel neglecting coupling between direct and shear deformations and bending and twisting curvatures. The unbalanced cross-ply lay-up, which consisted of two fibre reinforced plastic orthotropic layers, one at 0° to the plate axis and one at 90°, gave rise to large B11 and B22 coupling terms which were taken into account approximately using “reduced stiffness” terms with the orthotropic equations. However, the disparity between theory and experiment was greatest in this case, particularly as far as wrinkling was concerned, where the experimental failure load was 78% higher than the theoretical wrinkling load. This type of cross-ply layup is important since it is used when making carbon fibre sandwich floor panels; it being chosen from the point of view of manufacturing convenience rather than from considerations of strength and stiffness. Furthermore, the bending stresses in the faces, which result from the normal loads, predominate in one direction so that one face is subjected to essentially a uniaxial compressive stress which might cause the faces to wrinkle. In order to study this problem in greater depth, it was decided to carry out further theoretical and experimental work on the simpler problem of the wrinkling of sandwich columns with carbon fibre cross-ply faces.

Finite Element Analysis of Doubly Corrugated Shells

Abstract: The basic structural components of the shells are doubly corrugated steel panels fabricated of thin sheet steel that is first deformed into a U-shaped big corrugation. Then, to obtain the proper curvature, small corrugations are rolled into the bottom and into the sides of the big corrugation. The proposed finite element model consists of an assemblage of curved rectangular elements with boundaries parallel to lines of principal curvature of the shell. Sanders' linearized strain-displacement equations are chosen for the description of the kinematics of deformation of the middle surface of a finite element. The small corrugations are replaced by an equivalent orthotropic material of uniform thickness. Suitable constitutive equations are developed. Static analyses are performed for two different doubly corrugated shells. Some of the predictions of the analysis are compared with experimental results.

Creep of Thick-Walled Orthotropic Cylinders Subject to Combined Internal and External Pressures:

Abstract: A creep analysis of a thick-walled anisotropic cylinder subject to combined internal and external pressures is presented. The elastic strains are also taken into account. By considering the creep r...

Torsion of Frame-Tube Structures

Abstract: In an earlier paper, a method was presented for the simplified analysis of frame-tube structures under bending actions. By replacing the discrete structure by an equivalent orthotropic tube, and by making simplifying assumptions regarding the stress distributions in the structure, design curves were derived for rapid approximate analysis of the dominant behavior. A similar analysis is presented in this paper for the torsional analysis of frame-tube structures. Closed-form solutions are obtained and design curves are developed for three standard torsional loading cases, corresponding to those considered in the bending analysis, i.e., a point torque at the top, and uniformly and triangularly distributed twisting moments, Design curves are found to be identical in form to those derived for the bending case.

The analysis of rotational shells using a curved ring element and the mixed variational formulation

Abstract: A finite element for the analysis of rotational shells using a mixed variational formulation is proposed. The element has arbitrary curvature in the meridional plane, its geometry being given by the values of the axial and radial co-ordinates, slope and meridional curvature at the nodal circles. A linear variation in the thickness was included in the formulation as was an orthotropic material. Test cases of flat plates and spherical shells indicate that a high degree of accuracy is obtainable with relatively small number of elements.

Postbuckling of angle-ply and anisotropic plates

Abstract: An analysis based on the von Karman-type large-deflection equations of plates is presented for the postbuckling behavior of homogeneous and symmetrically laminated anisotropic rectangular plates. Boundary conditions for both simply supported and clamped edges are considered. A solution is obtained by expressing the force function and transverse deflection as double series involving the appropriate beam eigen-functions. Numerical results are presented for graphite-epoxy angle-ply laminates and homogeneous anisotropic plates. In the cases of buckling of anisotropic plates and postbuckling of isotropic and orthotropic plates, the present solution is in good agreement with existing solutions.

Finite element computer program to analyze cracked orthotropic sheets

Abstract: A two dimensional orthotropic sheet with through-the-thickness cracks and temperature gradient was analyzed The program includes special crack tip elements that account for singular stress fields associated with crack opening and crack sliding displacements at the crack tip The program also includes a linear spring element and a constant strain, triangular element A number of problems for which closed form solutions exist were analyzed to demonstrate the capabilities of the program