Showing papers on "Orthotropic material published in 1984"
TL;DR: The orthotropic elastic coefficients and the variation of these coefficients are presented as a function of anatomical position and the elastic properties of human and canine cortical femora are presented here.
735 citations
TL;DR: In this article, a second rank symmetric tensor which describes the degree of orientation in orthotropic materials is presented and shown to reflect accurately patterns of experimental data, and the use of this tensor to describe microstructural anisotropy is compared to currently accepted methods.
Abstract: A second rank symmetric tensor which describes the degree of orientation in orthotropic materials is presented and shown to reflect accurately patterns of experimental data. The use of this tensor to describe microstructural anisotropy is compared to currently accepted methods and is found to be more useful and accurate in experimental studies. A method for determining the anisotropy tensor in a material is given, based on measurements on any three mutually perpendicular planes, and the fundamental restriction of this method to orthotropic materials is discussed. Experimentally determined anisotropy tensors in five specimens of cancellous bone from five different human bones are given.
601 citations
206 citations
TL;DR: In this paper, the plate theory was extended to laminates and closed-form solutions of this theory, as well as those of Reissner-Mindlin plate theory with appropriate shear correction, Seide's discrete-layer plate theory, and the higher-order theory of Lo et al. were all compared with Pagano's elasticity-theory solution for the cases of cylindrical bending of a single orthotropic layer and a symmetric cross-ply (0°/90°/0°) laminate consisting of three equal-thickness layers
152 citations
TL;DR: In this paper, an orthotropic model of wave propagation was used to interpret the measurements and compute estimates of the elastic compliances of six species (pine, spruce, douglas-fir, oak, beech, tulip-tree).
Abstract: Ultrasonic measurements were carried out on cubic specimens of six species (pine, spruce, douglas-fir, oak, beech, tulip-tree). An orthotropic model of wave propagation was used to interpret these measurements and compute estimates of the elastic compliances. In order to calculate the off-diagonal stiffness terms, velocities were computed on samples with faces at an angle to the principal directions. The elastic compliance matrix was calculated by inverting the stiffness matrix.
140 citations
TL;DR: In this paper, the total potential energy for a body composed of an anisotropic micropolar linear elastic material is developed and used to formulate a displacement type finite element method of analysis.
97 citations
TL;DR: In this paper, a compact analytical solution of stresses around a pin-loaded hole in orthotropic plates is obtained by the complex stress functions which satisfy the displacement boundary conditions along the hol...
Abstract: A compact analytical solution of stresses around a pin-loaded hole in orthotropic plates is obtained by the complex stress functions which satisfy the displacement boundary conditions along the hol...
69 citations
TL;DR: In this article, the governing equations of motion for the nonaxisymmetric and axisymmetric variational of a general multilayered cylindrical shell having an arbitrary number of orthotropic material layers have been derived using variational principles.
Abstract: The governing equations of motion for the nonaxisymmetric and axisymmetric variational of a general multilayered cylindrical shell having an arbitrary number of orthotropic material layers have been derived using variational principles. The refined analysis considers bending, extension, and shear deformations in all layers of a multilayered cylindrical shell, including rotary and longitudinal translatory as well as transverse inertias. The solution for a radially simply supported shell has been obtained and the procedure for determining the damping effectiveness in terms of the system loss factor for all families of the modes of vibration in a multilayered shell with elastic and viscoelastic layers is reported. Numerical results are reported in Part II of the paper.
68 citations
TL;DR: In this paper, a general equation for the plane-stress yield condition of orthotropic sheet material that is isotropic in its plane is given, and a set of constitutive relations for planar-isotropic strain hardening is formulated on the basis of the usual normality rule for strain rates, together with the assumption of a scalar relation between an effective stress and a work-equivalent effective strain.
Abstract: A general equation is written for the plane-stress yield condition of orthotropic sheet material that is isotropic in its plane. A set of constitutive relations for planar-isotropic strain hardening is then formulated on the basis of the usual normality rule for strain rates, together with the assumption of a scalar relation between an effective stress and a work-equivalent effective strain. It is shown how particular laws proposed earlier for sheet-metal plasticity fit into the general scheme. Solutions to the problem of balanced biaxial stretching of a sheet containing a circular hole illustrate a wide range of effects produced by various realizations of the general constitutive relations.
66 citations
Metz1
TL;DR: In this article, the authors compare experimental results and finite elements computation to verify fracture mechanics concepts applied to wood by assuming that the material is orthotropic and elastic, in order to verify these assumptions.
Abstract: Since Porter (1964), some authors have applied fracture mechanics concepts to wood by assuming that the material is orthotropic and elastic. In order to verify these assumptions, the objective of this paper is to compare experimental results and finite elements computation.
60 citations
TL;DR: In this paper, a finite-element technique for solving frictional contact problems is described based on logical steps to establish the contact geometry and regions of slip and nonslip, which can be extended readily to multiple contact surfaces.
TL;DR: In this paper, the authors derived equations of motion for vibrations of a general multilayered plate consisting of an arbitrary number of alternate stiff and soft layers of orthotropic materials using variational principles.
TL;DR: In this paper, a method that determines the mutually orthogonal, effective elastic moduli in the plane perpendicular to a borehole has been developed, which relates the radial displacements in a cylindrical borehole to an elastically orthotropic material.
TL;DR: In this paper, the static and dynamic axisymmetric buckling of elastic orthotropic thin shallow spherical shells with elastically restrained edge for inplane and rotational displacements was investigated.
Abstract: This investigation deals with the static and dynamic axisymmetric buckling of elastic orthotropic thin shallow spherical shells with elastically restrained edge for inplane and rotational displacements. Governing equations in terms of normal displacementw and stress function ψ have been employed. Orthogonal point collocation method is used for spatial discretisation and Newmark-β scheme is used for time-marching. The uniformly distributed static and step function conservative loadings normal to the underformed surface are considered. The present results are in good agreement with the available results. The influence of orthotropicity parameter β and the support stiffness parameters on the static and dynamic buckling loads has been investigated.
TL;DR: In this article, the authors investigated the linear thermoelastic problem of uniform heat flow disturbed by a central crack in an orthotropic plate using the techniques of Fourier Transforms and multiple integrations.
Abstract: The linear thermoelastic problem of uniform heat flow disturbed by a central crack in an orthotropic plate is investigated using the techniques of Fourier Transforms and multiple integrations. The thermoelastic stresses and displacements in the crack plane are obtained in closed forms. The stress intensity factor is presented as a function of the material properties.
TL;DR: In this paper, a general analytical and numerical procedure for free and forced vibra tion of thin-walled shells of revolution made of arbitrarily laminated orthotropic elastic material is developed.
Abstract: A general analytical and numerical procedure is developed for free and forced vibra tion of thin-walled shells of revolution made of arbitrarily laminated orthotropic elastic material. The equations of motion are derived with the aid of Hamilton's variational principle. A numerical solution is obtained by expanding the variables in Fourier series in the circumferential direction, and using conical finite elements in the meridional direction. Several examples involving different shell geometries are considered, in cluding the effects of fiber orientation and boundary conditions.
TL;DR: In this paper, a simple Ritz method analysis is presented for dealing with vibration of completely free annular plates having polar orthotropic characteristics, and the natural frequencies of these plates are obtained for the various orthotropic parameters, and comparison is made with exact values for isotropic cases, showing excellent agreement.
TL;DR: In this article, it was shown that the components of a sixth rank anisotropy tensor are physically significant in representing the distortion observed in both the initial and subsequent yield surface for a polycrystalline material.
Abstract: It is shown that the components of a sixth rank anisotropy tensor are physically significant in representing the distortion observed in both the initial and subsequent yield surface for a polycrystalline material. This feature of anisotropy does not appear in the ellipsoidal surface given by previous theories in which second and fourth rank anisotropy tensors are employed. The number of tensor components, for a series function embodying tensor terms in ascending rank, reduces to a manageable number by the imposition of symmetry and coincidence between the axes of stress and principal orthotropic directions. The identification is made between the yield limits, as found from biaxial stress experiments and tensor components in composite sum form. A one-to-one correspondence is found from a further simplification through the assumption of incompressibility. This is confirmed experimentally for an orthotropic rolled copper and copper alloy sheet.
TL;DR: In this paper, the results of a three-dimensional, geometrically nonlinear, finite-element analysis of the bending of cross-ply laminated anisotropic composite plates are presented.
TL;DR: In this article, a solution for the bending of polar orthotropic pie and ring sector plates is presented for three cases of boundary conditions along the straight edges, the classical method of separation of variables is employed and, the basic function in the angular direction satisfies the boundary conditions of the radial edges.
Abstract: A solution for the bending of polar orthotropic pie and ring‐sector plates is presented for three cases of boundary conditions along the straight edges. The classical method of separation of variables is employed and, the basic function in the angular direction satisfies the boundary conditions of the radial edges. Satisfaction of the governing differential equation of the plate is achieved by the derivation of appropriate radial functions. The deflection expression is generated. Isotropic and Orthotropic sector plates of various end conditions have been analyzed and compared with other methods wherever comparisons have been possible.
TL;DR: In this article, the tendency of moving cracks to spread along the preferred directions of material anisotropy is treated, and the possibility of crack bifurcation is examined by application of the strain energy density criterion for several composite systems.
TL;DR: In this article, the authors used Tsai and Wu's tensor polynomial theory to derive a formula originally derived by Cowin for shear strength variation in a plane of material symmetry of orthotropic materials.
Abstract: In this study, the writers used Tsai and Wu's tensor polynomial theory to rederive a formula originally derived by Cowin for shear strength variation in a plane of material symmetry of orthotropic materials. Experimental work was then performed (based on a method by Arcan, Hashin, and Voloshin) on Sitka spruce specimens to verify the formula. The theory and experiment agreed closely. When the angle between shear force and grain on the longitudinal‐tangential plane increased from 0‐30° shear strength decreased more than 43%. Engineers should take this relationship into account when designing wood structural members.
TL;DR: In this paper, the elastic constants of a particle-reinforced-composite wrought plate produced by powder-metallurgy methods were investigated by measuring ultrasonic-wave velocities using a pulse-echo method.
TL;DR: In this paper, nonlinear axisymmetric static and dynamic buckling of clamped isotropic and cylindrically orthotropic elastic cap with central circular hole have been investigated.
TL;DR: In this article, the postbuckling behavior of cylindrically orthotropic circular plates is investigated through a finite element formulation, with the plates resting on an elastic foundation and their edges are elastically restrained against rotation.
TL;DR: In this paper, the effect of fibre orientation on the fundamental frequency of thin rectangular/square orthotropic plates was studied using a high precision triangular orthotropic finite element, which is useful in studying plates of arbitrary plan form and arbitrary fibre orientation.
TL;DR: In this article, an analysis for the vibration and stability of an orthotropic circular cylindrical shell subjected to an axial static load by use of the transfer matrix approach is presented.
Abstract: An analysis is presented for the vibration and stability of an orthotropic circular cylindrical shell subjected to an axial static load by use of the transfer matrix approach. The applicability of the thin‐shell theory is assumed, and the governing equations of free vibration of the shell are written in a matrix differential equation by using the transfer matrix of the shell. Once the matrix has been determined by a solution to the equation, the natural frequencies and the critical loads are calculated numerically in terms of the elements of the matrix for a given set of boundary conditions at the edges. This method is applied to orthotropic circular cylindrical shells simply supported at the edges, and the effects of the length ratio, orthotropy, and axial load on the vibration and stability are studied.
TL;DR: In this article, the problem of a rigid punch on an elastic half plane with orthotropic and non-homogeneous material is considered, and the Fourier Transform Technique is used to reduce the mixed boundary value problem to a singular integral equation which is solved numerically.
TL;DR: In this paper, an orthotropic half-plane subjected to a concentrated edge load is proposed as a calibration specimen for photoelastic calibration of birefringent-orthotropic model materials also.
Abstract: New experimental methods continue to be proposed for determining the in-plane elastic constants of orthotropic composite materials, as no single method has been found completely satisfactory. In particular, the in-plane shear modulus is difficult to measure. In this paper, an orthotropic half-plane subjected to a concentrated edge load is proposed as a calibration specimen. Photoelastic calibration of orthotropic-birefringent composites is also difficult due to the need to conserve the commercially unavailable, difficult-to-make model materials and the absence of many closed-form solutions. In this paper, the orthotropic half-plane specimen is proposed for photoelastic calibration of birefringent-orthotropic model materials also. For elastic and photoelastic calibration of orthotropic materials, the least-squares procedure is used for processing the experimental data.
01 Dec 1984
TL;DR: In this article, the buckling loads of a rectangular orthotropic plate with a centrally located cutout were analyzed using a computer program that implements this analysis, and the program use is demonstrated by sample problems.
Abstract: An analysis to obtain the buckling loads of a rectangular orthotropic plate with a centrally located cutout is described Cutout shapes can be elliptical, circular, rectangular, or square The boundary conditions considered in the analysis are simply supported unloaded edges and either clamped or simply supported loaded edges The plate is loaded in uniaxial compression by either uniform edge displacement or uniform edge stress A computer program that implements this analysis is described, and the program use is demonstrated by sample problems