Showing papers on "Orthotropic material published in 1969"

Exact solutions for composite laminates in cylindrical bending

Abstract: Limitations of classical laminated plate theory are investigated by comparing solutions of several specific boundary value problems in this theory to the corresponding theory of elasticity solutions. The general class of problems treated involves the geometric configuration of any number of isotropic or orthotropic layers bonded together and subjected to cylindrical bending. In general it is found that conventional plate theory leads to a very poor description of laminate response at low span-to-depth ratios, but converges to the exact solution as this ratio increases. The analysis presented is also valid in the study of sandwich plates under cylindrical bending.

A Method of Predicting the Nonlinear Behavior of Laminated Composites

Abstract: This paper presents an analytical technique for determining the stress-strain response up to ultimate laminate failure for a laminated composite consisting of orthotropic lamina with nonlinear stress-strain behavior. The procedure, which has been programmed for a digital computer, will produce a laminate stress-strain curve up to ultimate failure. The technique is restricted to the prediction of ultimate strength for plane anisotropic laminates with midplane symmetry sub jected to biaxial membrane loads. Comparisons are made between analytical predictions and experimental results. The basic concepts of ultimate and limit strength design as applied to an advanced com posite structure are discussed.

Buckling of Light-Gage Corrugated Metal Shear Diaphragms

Abstract: Formulas for the elastic buckling loads of shear diaphragms are derived. They are obtained from an analysis of light-gage, corrugated-metal diaphragms of the type that occur in pre-engineered metal buildings. The formulas are applicable to any rectangular, orthotropic plate loaded in pure shear, and they are derived using orthotropic plate theory and the Ritz energy method. Small deflection theory is used first to establish critical loads and buckling modes. Then, large deflection theory is used to predict post-buckling load versus lateral deflection relationships. The results of experiments that were designed to verify the accuracy of the formulas are presented in the form of load versus lateral deflection curves covering the pre and post-buckling ranges. Several light-gage, corrugated-metal diaphragms of different size and corrugation shape were tested to determine their buckling behavior. The results of the experiments compare favorably with the formulas derived.

Free Vibrations of Unsymmetrically Laminated Anisotropic Plates with Clamped Edges

Abstract: A linear analysis is presented for determining the natural frequen cies of vibration of laminated anisotropic rectangular plates. The plate may consist of an arbitrary number of thin orthotropic layers, the major material-symmetry axis of each layer oriented arbitrarily with respect to the longer plate edge. An approximate solution is obtained by the Rayleigh-Ritz energy method. Numerical results are presented for fully clamped boundary conditions and compared with experimental results for symmetrically and unsymmetrically laminated plates.

Photoelastic Analysis of Anisotropic Fiber Reinforced Composites

Abstract: A theoretical and experimental investigation was made of the integrated photoelastic effect in a transparent fiber glass reinforced epoxy resin. Vacuum impregnation techniques were developed to render the material transparent. The integrated effect of the isochro matics and isoclinics in the material when subjected to both uniaxial and biaxial stresses was observed and compared to the predicted data. Isochromatic data proved to be representable by a proposed orthotropic stress-optic law. Isoclinics were predictable, but at a given point in a stressed model the isoclinic angle depends on both the fiber orienta tion with respect to the principal stress directions and the ratio of principal stress magnitudes. Thus, the isoclinics do not directly give the principal stress directions. At this point, the anisotropic photo elasticity solution has not been determined.

A method for computation of vibration modes and frequencies of orthotropic thin shells of revolution having general meridional curvature

Abstract: Finite element method for computing natural frequencies and mode shapes of thin shells of revolution

Application of birefringent coatings to glass-fiber-reinforced plastics

Abstract: The application of birefringent coatings to plane-stress problems associated with orthotropic-glassreinforced plastic materials is treated. The improvement in the sensitivity of the birefringent-coating method due to the high strength and low modulus of the glassfiber-reinforced plastic materials is noted. Next, the effect of a mismatch in Poisson's ratio between the specimen material and coating is examined and a correction factor is developed which permits determination of boundary stresses even when the mismatch is large. Finally, the stress-strain relations for an orthotropic material are reviewed and an example of a nonsymmetric stress distribution associated with a symmetric fringe pattern is covered.

Experimental Study of the Stability of Composite Plates

Abstract: An experimental study of the uniaxial compressive stability of rectangular boron-epoxy laminated plates is presented. The plates are clamped on the loaded edges and either clamped or simply- supported on the sides. The buckling loads are determined by means of Southwell plots and are compared to analytical results obtained with a previously published method. Experimental results are presented for twenty composite plates and four metal plates. Good agreement between the experimental and analytical results is shown for both symmetrical and unsymmetrical plates, and for plates strongly aniso tropic as well as orthotropic and isotropic.

Analysis of orthotropic steel plate bridge decks

Abstract: A computer-oriented method for the analysis of orthotropic bridge decks is presented. The structure is idealized as a rectangular orthotropic plate which is continuous over simply supported, deformable floor beams. A finite element method is developed for the analysis of the idealized structure. An efficient and easy to use computer program is described, and results are presented.

Shear Buckling of Unsymmetrical Cross-Ply Plates

Abstract: Recently solutions have been obtained [1, 2, 3] for the bending, vibrations, and buckling of laminated plates in which coupling between bending and stretch ing is important. However, buckling results were limited to unsymmetric angle- ply laminates under biaxial compression. Thus, there are no solutions available for the buckling of coupled laminates subjected to shear loading.This paper is concerned with the stability of unsymmetric cross-ply rectangular plates under uniform shear. These composites consist of an even number of layers all of the same thickness and elastic properties with the orthotropic axes of symmetry in each ply alternately oriented at 0° and 90° to the plate axes. Hinge- support boundary conditions are considered. The effect of coupling is ascertained by comparing coupled solutions to those obtained by neglecting the coupling coefficients in the governing equations. Applicability of the reduced bending stiffness approximation to shear buckling of cross-ply composites is also in vestig...

Behavior of stiffened curved plate model

Abstract: The solution of the orthotropic plate equation, in polar coordinates, is obtained by the finite difference technique. The boundary conditions are imposed such that simple supports along the radial edges and free supports along the angular edges are prescribed. Fifteen various mesh pattern equations are developed; six of these patterns are described. The solution of these equations, representing a particular subdivided plate sector, is solved by a computer program. The internal forces throughout the plate are also evaluated by the finite difference method, utilizing the deflection data and a computer program. To evaluate the validity of the technique, a stiffened curved steel plate model was tested. Separate stiffness model tests were also conducted to evaluate experimentally the angular and radial stiffnesses and torsional stiffness, which were compared to the calculated stiffnesses. Proper evaluation of the plate stiffnesses resulted in analytical deflections and strains, which correlated very well with the experimental data.

Buckling of stiffened two-layered shells of revolution with a circumferentially cracked unbonded layer.

Abstract: Orthotropic stiffness layer models are derived for buckling of eccentrically stiffened shells of revolution with two unbonded orthotropic layers: 1) both of which are uncracked, and 2) one of which is circumferentially cracked. The two models are used in conjunction with a theory for buckling of eccentrically stiffened, circular cylindrical shells with multiple orthotropic layers to assess the importance of including the ablative layer in design calculations for two-layered (metallic plus ablative) re-entry vehicle shells. It is demonstrated in the present analysis that the ablative layer, even when circumferentially cracked and not bonded to the metallic layer, actually dominates the buckling stiffness of a re-entry vehicle shell and, hence, provides an already available source of stiffness for design calculations. However, the current treatment of the ablative layer is to either ignore it completely (an unduly conservative approach) or to regard it as uncracked and perfectly bonded to the metallic layer (an unconservative approach).

Two-Dimensional Bi-Linear Orthotropic Elastic Materials

Abstract: The constitutive equations have been obtained [1] for the most general anisotropic bi-linear materials. These are the materials with different elastic properties in tension and compression. Such considerations are of special interest in composite materials. Since in most composite materials the Young’s moduli in tension and compression are considerably different in the filament direction. As examples, we might cite wire or cord reinforced rubber, reinforced plastic and others. In this paper the constitutive equations are given, without derivation, for orthotropic bi-linear materials in plane-stress case. Examinations of these equations throw some light on some of the basic physical problems of this class of materials. Some interesting features are discussed with emphasis on unidirectional composites.

Torsion testing for shear modulus of thin orthotropic sheet

Abstract: O materials have nine independent elastic constants, of which three are shear moduli for three orthogonal planes. The simpler transversely isotropic materials have five distinct constants, of which only one is a shear constant, the remaining shear properties being determined by the uniaxial moduli. In each of these material classes shear tests are required to evaluate completely the elastic constants, and methods are needed for extracting these constants from test data. Although a procedure is available for obtaining all the elastic constants bf orthotropic materials from a series of uniaxial tensile or compression tests alone such a method requires that the tests be made in a wide variety of orientations. For thin sheet this is not possible, but torsion tests provide a suitable alternative. Although an analysis of orthotropic torsion has existed since the last century no practical use has been made of it, with the significant exception of the work of Trayer and March who studied the behavior of wood. This Note demonstrates a method of shear testing and of data reduction based on the torsion analysis which can be used for obtaining the elastic shear constants of thin orthotropic sheets. The method has been applied to a study of a cross-rolled beryllium sheet.

Non-linear theory for axisymmetric deformations of heterogeneous shells of revolution

Abstract: A general nonlinear theory, based on the Euler—Bernoulli hypothesis, is established for heterogeneous orthotropic shells of revolution that are subject to rotationally symmetric mechanical and thermal loads. Two simultaneous second-order ordinary differential equations are developed, in terms of a deformation variable and a stress-resultant variable, which exhibit a stronger coupling of these two basic variables, than occurs in the corresponding equations for homogeneous shells of revolution. The general theory is specialized for small finite deformations, and specific equations for large finite deflections of circular heterogeneous plates are shown. The possibility of using a modified system of shell equations, resulting from a simplified compatibility relation, is indicated.

Large deflections of multisandwich shells of arbitrary shape

Abstract: A system of nonlinear differential equations governing the statical behavior of multisandwich shells built up of stiff and weak layers is derived in this contribution. The stiff layers are assumed to be elastic, isotropic, and obeying the Kirchoff-Love hypothesis. The weak layers are assumed to be elastic, orthotropic, and deformable in tangential directions. The thickness of the shell is small compared to its radii of curvature. The shell may be of arbitrary shape. The derived system of equations is specialized to cylindrical shells and compared with the equations of Kurshin for sandwich shells and the equations of Bolotin for multisandwich plates with infinitesimal deflections.

Structural behavior of an orthotropic steel deck bridge

Abstract: THE AUTHORS PRESENT THE MAJOR RESULTS OF EXTENSIVE EXPERIMENTAL AND ANALYTICAL STUDIES ON THE STRUCTURAL BEHAVIOR OF AN ORTHOTROPIC STEEL PLATE DECK BRIDGE. THE RESULTS OF A NUMBER OF DIFFERENT METHODS OF ANALYSIS, WHICH ARE DISCUSSED, COMPARED RELATIVELY AS WELL WITH EACH OTHER AS WITH EXPERIMENTAL RESULTS OBTAINED FROM FIELD STUDIES. RESULTS INDICATE THAT ANALYTICAL METHODS ARE AVAILABLE FOR STUDIES OF DIFFERENT PARTS OF ORTHOTROPIC STEEL DECK BRIDGES. GENERAL AGREEMENT BETWEEN EXPERIMENT AND THEORY-- PARTICULARLY WITH A GRID METHOD OF ANALYSIS--IS NOTED TO BE EXCELLENT. SEVERAL IMPORTANT FEATURES OF THE STRUCTURAL ACTION OF ORTHOTROPIC DECK BRIDGES HAVE BEEN EXPOSED. /AUTHOR/

Mechanical Property Tests for Cylindrically Orthotropic Materials

Abstract: Experiments for the determination of the elastic properties of cylindrically orthotropic materials are suggested. Analyses, which neglect end effects, are presented for the tests, consideration is given to the importance of this approximation. Because of the cylindrical orthotropy two of the tests even in the absence of end effects result in very complicated strain states; a special procedure is presented for the interpretation of the results of these tests. Lastly, for a particular cylin drically orthotropic material an example of the application of the interpretation procedure is presented.