Showing papers on "Orthotropic material published in 1972"
TL;DR: In this paper, the authors considered the plane problem of a central crack in a rectangular sheet of orthotropic material and found the solution by an extension of the modified mapping-collocation technique, originally formulated for plane isotropic analysis.
Abstract: The plane problem of a central crack in a rectangular sheet of orthotropic material is considered. The solution is found by an extension of the modified mapping-collocation technique, originally formulated for plane isotropic analysis. Application of the technique outlined in this paper for plane orthotropic problems to a wider class of geometries and loading is evident. The numerical results indicate a dependence of the orthotropic stress intensity factors on both geometric and elastic constants over a certain parameter range.
206 citations
192 citations
TL;DR: A nonlinear theory of large elastic deformations of the aortic tissue has been developed and the third-degree expression for the strain energy density function with seven constitutive constants is particularly recommended for general use.
154 citations
122 citations
TL;DR: In this paper, an analytical form of stress-strain relationship for plain concrete in biaxial compression is proposed, which accounts for the influence of microcrack confinement as well as Poison's ratio.
Abstract: On the basis of an extensive experimental investigation reported more fully elsewhere, an analytical form of stress-strain relationship for plain concrete in biaxial compression is proposed. This plane-stress orthotropic constitutive relationship accounts for the influence of microcrack confinement as well as Poison's ratio. Other equations found in the literature are shown to be special cases of the one proposed. Also based on experimental results, a simple equation is offered which accounts for the increase in compressive strength of plain concrete when biaxial compressive stress is introduced. Both the biaxial stress-strain equation and the strength equation are shown to give good agreement with the experimental results obtained by the writers as well as by others. Finally, a constitutive law, stated in matrix terms, is given for concrete in biaxial plane stress. This relation is suitable for use in the finite element analysis of reinforced or presstressed concrete.
96 citations
TL;DR: In this article, the principal components of the creep compliance tensor in the radial longitudinal and the tangential longitudinal planes of Douglas-fir at 10 percent moisture content were measured.
Abstract: Measurements were made of the principal components of the creep compliance tensor in the radial-longitudinal and the tangential-longitudinal planes of Douglas-fir at 10 percent moisture content. Extensional creep compliance measurements at angles to the grain were also made. The results show that creep parallel to grain occurs at an increase in volume, and that creep at angles to the grain can be predicted from standard transformation equations. It is concluded that wood can be regarded as a linear orthotropic viscoelastic material.
89 citations
TL;DR: In this article, the problem of placing an inclined crack centrally placed in a generally orthotropic rectangular plate under tension was investigated and the modified mapping-collocation technique introduced by Bowie was used.
Abstract: The problem of an inclined crack centrally placed in a generally orthotropic rectangular plate under tension is investigated. The modified mapping-collocation technique introduced by Bowie ...
63 citations
01 Jan 1972
55 citations
TL;DR: In this paper, a method to analyze the three-dimensional vibrations of orthotropic cylinders is presented, where the field equations are in the form of three coupled, second-order differential equations with nine elastic constants.
Abstract: A method to analyze the three-dimensional vibrations of orthotropic cylinders is presented. The field equations are in the form of three coupled, second-order differential equations with nine elastic constants. The vibration problem is solved by means of the Frobenius method, using power series expansion in the radial coordinate, and assuming sinusoidal dependence on the longitudinal and circumferential coordinates and on time. Frequency equation for the free vibration of solid circular cylinders is derived and a numerical example is given. An extensive study of the dynamic behavior of orthotropic cylinders can be made by this analysis.
52 citations
TL;DR: In this article, the effect of orthotropic material properties on computed values of the stress intensity factor was investigated for sufficiently long notched specimens in tension, bending, and shear.
51 citations
TL;DR: In this paper, a criterion for failure prediction of anisotropic materials under combined loading is presented, which is represented in a matrix form for ease of visualization, and is applicable to general three-dimensional materials.
Abstract: A criterion is presented for the prediction of failure of anisotropic materials under combined loading. Although tensorial in nature, the criterion is represented in a matrix form for ease of visualization. The approach is developed in detail for orthotropic materials under plane stress, but is applicable to general three-dimensional anisotropic materials. Two concepts are introduced: the interaction factor, which is a measure of strength anisotropy; and the principal strength axes, which are related to the directionality of the material strength properties. The criterion provides description of strength phenomena peculiar to fiber composite materials, but it is also applicable to homogeneous anisotropic metals.
TL;DR: In this article, a finite layer method of solution for free vibrations of thick laminated finite cylinders with various end conditions is presented for the case where the cylinders are bounded by traction-free surfaces.
TL;DR: In this article, two approaches for solving orthotropic elasticity problems are outlined, both of which are characterized by embedding the real body in a "fictitious" body for which the appropriate influence functions are known.
Abstract: The present paper is concerned with the application of integral equation techniques to problems in plane orthotropic elasticity. Two approaches for solving such problems are outlined, both of which are characterized by embedding the real body in a “fictitious” body for which the appropriate influence functions are known. Fictitious tractions are then introduced such that the boundary conditions on the real body are satisfied. This results in a coupled set of integral equations in the fictitious traction components. Once these are found the unknowns, i.e., stresses, etc., are found in a straightforward manner. The difficulty is in introducing the fictitious traction field such that the resulting integral equations are useful computationally, i.e., are Fredholm equations of the second rather than the first kind. A sufficient condition for this is that the fictitious traction field is applied to the boundary of the real body. The two approaches just mentioned differ in the choice of influence function used, in one case the influence function being singular in the field and the other singular on the boundary. A solution method already exists in the isotropic case using the boundary influence function [3]. An alternate formulation is presented using an internal influence function which is shown to have computational advantages in the anisotropic (orthotropic) case. To illustrate the methods, the stress field is found in a “truncated” orthotropic quarter space, under the condition of a given traction on the truncated surface, traction-free elsewhere. This problem is of interest in certain Rock Mechanics calculations, e.g., to a first approximation the stress field is that due to a rigid wedge penetrating a brittle, orthotropic elastic solid (prior to chip formation).
TL;DR: In this article, a coordinate transformation in the radial direction has been used to obtain effective solutions by the classical Rayleigh-Ritz method, particularly for large hole sizes, over direct analysis.
TL;DR: In this article, a theoretical analysis for the large deflection elastic behavior of clamped, uniformly loaded, rectangular, orthotropic plates is presented, where the governing differential equations including the nonlinear terms in the sense of von Karman are solved by the method of perturbation.
Abstract: A theoretical analysis is presented for the large deflection elastic behavior of clamped, uniformly loaded, rectangular, orthotropic plates. The governing differential equations including the nonlinear terms in the sense of von Karman are solved by the method of perturbation. This results in the predictions of the load deflection relations, and bending stresses are presented in the graphical form for glass-epoxy, boron-epoxy and graphite-epoxy plates having various aspect ratios. In the case of isotropic plates, the present solution reduces to two of the existing solutions.
TL;DR: In this article, the effects of curvilinear material anisotropy on the temperature distribution of thin walled bodies of revolution were studied and a solution procedure was developed by means of successive integral transforms and subsequent numerical integration.
Abstract: The present paper studies the effects of curvilinear material anisotropy on the temperature distributions of thin walled bodies of revolution. To facilitate the analysis, the thinness property of shells is used to develop an approximate three-dimensional anisotropic heat conduction equation and associated boundary conditions for thin walled bodies of revolution. Based on these equations, a solution procedure is developed by means of successive integral transforms and subsequent numerical integration. Using the integral transforms, a solution is obtained for temperature distributions in cylindrical thin walled bodies. In terms of this solution, the effects of cylindrical anisotropy on the temperature distribution is discussed at length.
TL;DR: In this article, the deformation of an orthotropic glass-reinforced plastic is considered with the failure of the resin in the transverse layers, and the failure is considered in terms of the failure probability.
Abstract: The deformation of an orthotropic glass-reinforced plastic is considered with allowance for the failure of the resin in the transverse layers.
01 Feb 1972
TL;DR: In this article, the effect of interlaminar shear deformation at the free edges of solid laminates and Laminates containing a cutout was studied. And a composite element, constructed of orthotropic membranes separated by shear-resistant media, was developed and utilized.
Abstract: : Elastic and plastic interlaminar shear deformation in a laminated fibrous composite was studied by means of a finite-element method. A composite element, constructed of orthotropic membranes separated by shear- resisting media, is developed and utilized. The effect of interlaminar shear deformation at the free edges of solid laminates and laminates containing a cutout is presented. (Author-PL)
01 Jul 1972
TL;DR: In this paper, an analysis of the minimum mass-strength curve for an orthotropic cylinder subjected to axial compressive loading is presented, which includes the effects of ring and stringer eccentricities.
Abstract: An analysis was developed to calculate the minimum mass-strength curve for an orthotropic cylinder subjected to axial compressive loading. The analysis, which includes the effects of ring and stringer eccentricities, is in a general form so that various cylinder wall and stiffener geometries can be considered. Several different ring-stiffened orthotropic configurations were studied. The minimum mass-strength curves and the dimensions associated with these curves are presented for (in order of decreasing efficiency) a tubular double bead, a nonsymmetric double bead, a Z-stiffened skin, and a trapezoidal corrugation. A comparison of efficiencies of the configurations shows a tubular element cylinder to be more efficient than a 3-percent core-density honeycomb-sandwich cylinder. It was found that for an optimized Z-stiffened skin, the location of the Z-stiffeners (internal or external) made a negligible difference in efficiency.
TL;DR: In this article, a review of the recent developments in photo-orthotropic elasticity which covers methods of producing transparent, birefringent orthotropic model materials from glass fibres and plastics is presented.
Abstract: A brief review of the recent developments in photo-orthotropic elasticity which covers methods of producing transparent, birefringent orthotropic model materials from glass fibres and plastics is presented. A classical form of the stress-optic law applicable in uniaxial-stress fields is given in which the orthotropic characteristics of the model material are treated by considering the material fringe value fu to be dependent upon fibre orientation.Limitations of the orthotropic model materials are identified and the effects of material non-linearities, fibre debonding and fibre distribution are described. The methods established were used to obtain a solution of the stresses in an orthotropic half-plane loaded with a concentrated force. The experimental results obtained were compared with theoretical results due to Green, and while the agreement was good, errors were considerably larger than those encountered in photo-isotropic elasticity.Finally the methods were applied to the solution of boundar...
TL;DR: In this paper, a linear analysis is presented for determining the shear buckling load of a rectangular, sandwich panel with constant cylindrical curvature and having specially orthotropic facings and core.
Abstract: A linear analysis is presented for determining the shear buckling load of a rectangular, sandwich panel with constant cylindrical curvature and having specially orthotropic facings and core. Solution for classical simplesupport boundary conditions was carried out by the Galerkin method, taking precautions not to "escalate" the equations by differentiati on. This resulted in two doubly infinite sets of eigenvalue equations, representing buckling in the symmetric and unsymmetric modes. Numerical solutions were obtained on a digital computer and the results were compared with those of previous analyses for special cases and with limited test data available for the general case. Finally parametric design curves are presented for a range of parameters.
TL;DR: In this article, the large amplitude (non-linear) free flexural vibration of thin, elastic, orthotropic skew plates clamped along all four edges was analyzed using the Galerkin's method.
TL;DR: In this paper, the authors considered the large deflection behavior of a rectangular anisotropic plate with clamped edges and applied the classical nonlinear theory of elastic plates to the present problem, where the classical assumptions for displacements, the straindisplacement relations associated with the von Karman assumptions, and the equations of equilibrium are the same as in the theory.
Abstract: HE elastic behavior of a rectangular orthotropic plate has been studied by a few authors making use of the von Karmantype large deflection theory. Yusuff1 has considered the postbuckling of the plate under edge compression using Fourier series for both deflection and stress function. The large deflection of the plate under lateral load has been treated by Basu and Chapman.2 Aalami and Chapman3 have also looked at the problem of the plate under transverse and in-plane loads. In the last two studies the finite-difference technique has been used and the solutions have been restricted to a special class of orthotropic materials. The present investigation is concerned with the large deflection behavior of a rectangular anisotropic plate with clamped edges. The classical nonlinear theory of elastic plates is applied to the present problem. Hence the classical assumptions for displacements, the strain-displacement relations associated with the von Karman assumptions, and the equations of equilibrium are the same as in the theory. The material properties or Hooke's law can be introduced at the final stage of the formulation of the governing differential equations. These equations are then solved by the method of perturbation. 4 Because of lack of available solutions for large deflections of anisotropic plates in literature, the present solution is specified for certain special cases and then compared with existing solutions. Contents Let us consider a rectangular plate of length 2a in the x direction, width 2b in the y direction, and thickness h in the z direction under a uniformly distributed load q per unit area. The origin of the coordinate system is chosen to coincide with the center of the midplane of the undeformed plate. The stressstrain relations for a thin homogeneous anisotropic plate may be written as
TL;DR: Tangential edge stress distributions for orthotropic plates containing holes were computed for various orientations of the principal material axes with respect to load as mentioned in this paper, and the results were compared with material strength distributions to predict failure in various GRP laminates.
Abstract: Tangential edge stress distributions for orthotropic plates containing holes were computed for various orientations of the principal material axes with respect to load. The results were compared with material strength distributions to predict failure in various GRP laminates. Elastic stress distributions can be used to predict the position and remote stress level for the onset of debonding between matrix and fibres with reasonable accuracy. The stress concentrator is almost fully effective at this stage but becomes less effective at more advanced states of damage. An examination of large specimens revealed a substantial adverse size effect. It is suggested that the onset of debonding forms a suitable basis for design and that a further examination of size effects is required.
TL;DR: In this article, the transient plane thermal stress problem of a circular disc of orthotropic material with instantaneous point heat source was analyzed graphically and compared with that of the isotropic case.
Abstract: In this paper, we have analysed the transient plane thermal stress problem of a circular disc of orthotropic material with instantaneous point heat source. The variation of σθθ with time along different radius vectors is exhibited graphically and compared with that of the isotropic case.
TL;DR: In this paper, an improved theory for orthotropic plates with thickness-shear flexibility and subjected to in-plane loading is presented, which is a generalization of the work of Haringx from columns to inplane-loaded plates.
Abstract: A new, improved theory is presented for orthotropic plates with thickness-shear flexibility and subjected to in-plane loading. The improvement introduced herein is the modification of the slopes at which the in-plane stress resultants are assumed to act. This is a generalization of the work of Haringx from columns to inplane-loaded plates. Comparison with the classical (Reissner) shear-flexible plate theory shows that the improved theory imposes loading anisotropy on the governing differential equations and tends to predict higher buckling loads than the overly conservative Reissner theory. Comparison with experimental results for uniaxially-compressed, simply supported sandwich plates with glass-fiber-reinforced facings and hexagonal-cell honeycomb cores indicates that the improved-theory results agree slightly better than do the Reissner-theory results.