Showing papers on "Orthotropic material published in 1974"

Finite element bending analysis of multilayer plates

Abstract: The development of a general quadratic multilayer plate element is presented for the analysis of arbitrarily layered curved plates. In the formulation, each layer of the multilayer plate can have different orthotropic properties and can deform locally. Examples of bending problems are presented which demonstrate the applicability of the formulation.

Transverse Compressive Moduli and Yield Behavior of Some Orthotropic, High-Modulus Filaments

Abstract: An account is given of the experimental determination of the transverse elastic moduli and yield behavior of some commercially available organic and graphite high-modulus filaments. The experimental technique involves transverse compression of single cylindrical filaments between two parallel flat platens and concurrent measurement of the platen- relative displacements and contact forces on the filaments. A theoretical discussion of the transverse compressional behavior of a linear elastic, homogeneous, orthotropic cylinder is presented. Using the theoretical results and the trans verse load-displacement measurements, a technique is developed for calculating the elastic moduli and maximum shear stresses at yield or fracture.

Fracture resistance of paper

Abstract: An attempt has been made to apply the concepts of fracture mechanics to describe the behaviour of a paper sheet with a crack. Considering paper as an orthotropic homogeneous continuum, the critical strain energy release rate, G c, for eight different papers has been measured using linear elastic fracture mechanics. Also, a direct measurement of work of fracture, R, has been made for these samples by using the quasi-static crack propagation technique. For both techniques, results independent of specimen dimensions were obtained. G c and R were found to be experimentally equivalent. The fracture toughness of paper has been compared with that of other engineering materials.

On the distribution of tree growth stresses — Part I: An anisotropic plane strain theory

Abstract: Growth stress distributions in trees are derived using the hypothesis that longitudinal and circumferential growth strains are continuously induced at the periphery of the growing stem. An axisymmetric plane deformation model serves as a basis for the cylindrically orthotropic analysis. By accounting for the influence on the total stress distribution of the strains in each new growth increment, a self-equilibriating distribution of growth stresses develops in the stem. In regions away from the central core of the stem, a simple closed form solution of the general anisotropic problem is given. The growth stress results of Kubler can be recovered from the present results by assuming isotropy in the cross section of the stem and avoiding the central region near the pith. The transition point where the peripheral longitudinal tension zone ends is shown to remain essentially unchanged in the more general theory from that given by Kubler. However, the point where the compression circumferential stress zone ends is shown to be a function of the ratio of the modulii in the radial and circumferential directions whereas in Kublers' theory it was independent of the elastic constants. Detailed results are given for the development of growth stresses as the stem grows and comparisons with the earlier theory noted.

Semi‐analytical finite element procedure for conduction in anisotropic axisymmetric solids

Abstract: Through the use of complex series representations and the properties of adjoint differential operators, a semi-analytical finite element procedure is developed which can analyse the steady state and transient temperature fields of thermally anisotropic axisymmetric bodies with complete circumferential properties. Due to its generality, the procedure can handle arbitrary laminate construction with possible meridional and radial variations in locally or globally thermally anisotropic materials. In this respect, the procedure developed herein supercedes the classical semi-analytical treatment which is limited to specially orthotropic materials. Furthermore, in contrast with the classical procedure, the present treatment reveals several important effects of material anisotropy which are entirely missed by the specially orthotropic assumption.

Vibration Anaylysis of Clamped Square Orthotropic Plate

Abstract: An approximate method is presented for the determination of the natural frequencies and mode shapes of a square orthotropic plate with all sides clamped. The presentation of the clamped plate's frequency in a form analogous to the corresponding frequency of a simply supported plate is postulated, considering the wave numbers as unknown quantities. These are determined from a system of two transcendental equations, obtained from the solution of two auxiliary Levy's type problems. It is shown, that our method reduces to Bolotin's asymptotic method for large wave numbers. The solution is given for the case of equal coefficients of orthotropy and mode shapes with double symmetry. The results are compared with those known from the literature.

Elastic stability of laminated, flat and curved, long rectangular plates subjected to combined inplane loads

Abstract: A method is presented to predict theoretical buckling loads of long, rectangular flat and curved laminated plates with arbitrary orientation of orthotropic axes each lamina. The plate is subjected to combined inplane normal and shear loads. Arbitrary boundary conditions may be stipulated along the longitudinal sides of the plate. In the absence of inplane shear loads and extensional-shear coupling, the analysis is also applicable to finite length plates. Numerical results are presented for curved laminated composite plates with boundary conditions and subjected to various loadings. These results indicate some of the complexities involved in the numerical solution of the analysis for general laminates. The results also show that the reduced bending stiffness approximation when applied to buckling problems could lead to considerable error in some cases and therefore must be used with caution.

A study of cracks in orthotropic crystals using dislocation layers

Abstract: The method of dislocation layers is used to study the stress field of a loaded Griffith-type elastic strip crack in an orthotropic crystal. Three fundamental modes of tractions applied to the crack faces are discussed. Formal solutions are derived for the stress components and the distribution of stress near a crack tip is deduced, before representative numerical results are presented graphically. Finally, the method is applied to the BCS model of elastoplastic cracks. In particular, the results are convenient for studying certain orientations of elastic and elastoplastic cracks in hexagonal and cubic crystals.

Elastic constants of B-A1 composites by ultrasonic velocity measurements

Abstract: The complete orthotropic elastic-stiffness matrix of unidirectional, Borsic-filament-reinforced aluminum composites was experimentally evaluated for three different volume fractions by ultrasonic velocity measurements on thin plates. Longitudinal- and shear-velocity measurements were made in appropriate symmetry directions by direct contact or liquid-immersion techniques. The elastic constants determined by this pulsed through-transmission method were in agreement with micromechanical theories based on the properties of the constituent materials. Agreement was also found between engineering constants determined by mechanical testing and those calculated from the ultrasonic data. Finally, measurement of the ultrasonic-wave velocity has also been shown to be a rapid nondestructive-test method for determining filament-volume fraction in a fabricated part.

On the effect of orthotropy in a cracked cylindrical shell

Abstract: A pressurized cylindrical shell containing a longitudinal crack is considered. The shear modulus of the sheet may be evaluated from the measured Young's moduli and the Poisson's ratios rather than being an independent material constant. Two examples, one for a mildly orthotropic (titanium) and the other for a strongly orthotropic (graphite) material approximately satisfying the condition of special orthotropy are given. The results show that the stress intensity factors are rather strongly dependent on the degree of orthotropy.

Measurement of the Elastic Moduli of Continuous-Filament and Eutectic Composite Materials

Abstract: Continuous filaments and eutectic composite materials have been treated as homogeneous and orthotropic and transversely isotropic elastic materials, respectively, in stress analysis problems. Based on these assump tions the elastic moduli of boron-epoxy and Al-Al3Ni eutectic composite materials are measured using pulse-echo techniques. The shear wave measurements show that the elastic anisotropy assumed for each material is only an approximation. The measurements are also influenced by defects in the fiber arrangement and, m the eutectic composite, by the presence of a solidification substructure.

Effects of Transverse Normal and Shear Strains in Orthotropic Shells

Abstract: Introduction P and shell structures in missile, space, and nuclear applications are often subjected to severe operational conditions. Classical methods of analysis based on the Kirchhoff-Love (K-L) hypothesis (implying neglect of transverse shear deformation and transverse normal stress) may not be applicable in such cases. This is especially true for certain composite and refractory materials which show a high degree of anisotropy in physical and mechanical properties. Typical of such materials is pyrolytic graphite (PG), perhaps the best known of the many pyrolytic refractory materials. Noteworthy among its unusual properties are the following: 1 ) PG is transversely isotropic. 2) The ratio of in-plane Young's modulus to transverse shear modulus (E/G\3) for PG varies between 20-50, as compared to E/G of 2.6 for an isotropic material with v = 0.3. 3) The ratio of transverse to in-plane thermal expansion coefficients (a33/an) varies approximately between 10 and 30. 4) The in-plane Poisson's ratio for PG is negative (v = 0.21) while the transverse ratio (v13 = 0.90-1.0) is quite high. The purpose of the present Note is to illustrate the significance of transverse shear, normal stress effects, and edge conditions on the stress and displacement computations for thin shells subjected to thermal loading and also to point out the hazards of employing classical shell theories for analysis of structures of pyrolytic graphite-type materials.

Three-Dimensional Mechanical Characterization of Anisotropic Composites

Abstract: The problem of complete characterization of a general linearly elastic, anisotropic material is discussed. An experimental procedure of testing a normally oriented and an obliquely oriented cubical specimen of the material is proposed, from which the 36 constants in the compliance matrix can be determined. A multiaxial test cell for applying homogeneous compressive stresses to the cubical specimen is described and the procedure is applied to Scotchply, a reinforced plastic. The compliance matrix for Scotchply is determined and it is shown to be orthotropic.

Elastic Analysis of Zoned Orthotropic Continua

Abstract: A method is presented for determining the stresses and displacements, under plane strain or plane stress conditions, in a linear elastic multizoned continuum having an irregular boundary geometry. Each zone is homogeneous and consists in general of a different orthotropic material, with one plane of elastic symmetry parallel to the problem plane, and the other two planes orientated arbitrarily. The singular solution used is that for a point load acting within a homogeneous orthotropic infinite lamina. The derivation of this new solution is given. Since the principle of superposition applies, the numerical integration of multiples of such singular solutions around zone boundaries produces a result satisfying both the governing equations and the zone boundary conditions on discrete boundary elements. The main advantage of the method is that, since only the boundary is discretized, the system of equations is small compared with other numerical methods.

Analysis for Tire Mold Design

Abstract: An analysis is presented for determining tire deformation due to shrinkage. The analysis uses composite theory and the finite element technique in modeling the material properties and the structural behavior. The constant strain toroidal shell element developed by Wilson for small displacement and isotropic properties is modified for orthotropic properties which depend on the element location. Temperature history and the buildup of shrink forces during cure are determined experimentally. The shrink forces are represented by a set of equivalent loads applied at the nodes. Good correlation is obtained between calculated and experimental displacements. The analysis is applied in relating the mold shape to the final shape of the tire.

Vibration of generally orthotropic skew plates

Abstract: Vibration problem of generally orthotropic plates with particular attention to plates of skew geometry is studied. The formulation is based on orthotropic plate theory with arbitrary orientation of the principal axes of orthotropy. The boundary conditions considered are combinations of simply supported, clamped, and free‐edge conditions. Approximate solution for frequencies and modes is obtained by the Ritz method using products of appropriate beam characteristic functions as admissible functions. The variation of frequencies and modes with orientation of the axes of orthotropy is examined for different skew angles and boundary conditions. Features such as “crossings” and “quasi‐degeneracies” of the frequency curves are found to occur with variation of the orientation of the axes of orthotropy for a given geometry of the skew plate. It is also found that for each combination of skew angle and side ratio, a particular orientation of the axes gives the highest value for the fundamental frequency of the plate.