Showing papers on "Orthotropic material published in 1979"
TL;DR: In this paper, an effective stress law is derived to describe the effect of pore fluid pressure on the linearly elastic response of saturated porous rocks which exhibit anisotropy.
Abstract: An effective stress law is derived analytically to describe the effect of pore fluid pressure on the linearly elastic response of saturated porous rocks which exhibit anisotropy. For general anisotropy the difference between the effective stress and the applied stress is not hydrostatic. The effective stress law involves two constants for transversely isotropic response and three constants for orthotropic response; these constants can be expressed in terms of the moduli of the porous material and of the solid material. These expressions simplify considerably when the anisotropy is structural rather than intrinsic, i.e., in the case of an isotropic solid material with an anisotropic pore structure. In this case the effective stress law involves the solid or grain bulk modulus and two or three moduli of the porous material, for transverse isotropy and orthotropy, respectively. The law reduces, in the case of isotropic response, to that suggested by Geertsma (1957) and by Skempton (1961) and derived analytically by Nur and Byerlee (1971).
132 citations
TL;DR: In this article, a method for designing laminated plates with orthotropic layers under uniaxial and biaaxial compression is presented. The objective is to find the fiber direction of all the layers that give the highest buckling stress; therefore, it is necessary to solve an unconstrained maximization problem.
Abstract: The paper presents a method for designing laminated plates with orthotropic layers under uniaxial and biaxial compression. The objective is to find the fiber direction of all the layers that give the highest buckling stress; therefore, it is necessary to solve an unconstrained maximization problem. The optimization technique used is Powell's conjugate direction method. Numerical calculations were made for plates with three, four, and six layers.
112 citations
01 Apr 1979
97 citations
TL;DR: In this article, a theoretical and experimental study of ultrasonic plate waves in machine-made paper is described, where the paper is assumed to behave as a homogeneous orthotropic plate.
93 citations
TL;DR: In this paper, a mathematical model was presented for the transmission of airborne noise through the walls of an orthotropic cylindrical shell, and parameters were varied to see how orthotropicity affected noise transmission.
64 citations
TL;DR: In this article, the four independent material parameters of plane orthotropic elasti city are introduced as the effective stiffness, the effective Poisson ratio, the stiffness ratio and the shear parameter.
Abstract: The four independent material parameters of plane orthotropic elasti city are introduced as the effective stiffness, the effective Poisson ratio, the stiffness ratio and the shear parameter. It is proved that stress boundary value problems with zero resulting force on internal contours lead to stress fields that are independent of the effective stiffness and the effective Poisson ratio, and a general transformation is described which is equivalent to a change of the stiffness ratio. These properties suggest the importance of the remaining shear parameter, that has the interesting property of being invariant with respect to a 90 degree rotation of the principal axes of the material.
58 citations
TL;DR: In this article, the optimal design of plates with orthotropic layers under shear was studied. But the authors considered the laminates of N orthotropic layer whose principal material axes coincide with the plate axes and the fiber directions which gave the highest shear buckling stress were found by utilizing a mathematical optimization technique.
Abstract: This paper is concerned with the optimum design of plates with orthotropic layers under shear. The plates considered are the laminates of N orthotropic layers whose principal material axes coincide with the plate axes. Each layer is assumed to have the same thickness and an equal number of fibers in the direction of + alpha sub i and - alpha sub i with respect to the plate axis. The fiber directions which give the highest shear buckling stress are found by utilizing a mathematical optimization technique.
53 citations
TL;DR: In this article, the singular behavior of the stresses for two special crack geometries is studied in some detail, and numerical examples are worked out in order to separate the primary material parameters influencing the stress intensity factors and the powers of stress singularity.
Abstract: In this paper the elastostatic problem for a nonhomogeneous plane which consists of two sets of periodically arranged dissimilar orthotropic strips is considered. It is assumed that the plane contains a series of collinear cracks perpendicular to the interfaces and is loaded in tension away from and perpendicular to the cracks. First the problem of cracks fully imbedded into the homogeneous strips is considered. Then the singular behavior of the stresses for two special crack geometries is studied in some detail. The first is the case of a broken laminate in which the crack tips touch the interfaces. The second is the case of cracks crossing the interfaces. An interesting result found from the analysis of the latter which may have an important bearing on a possible delamination fracture initiation at stress-free boundaries in bonded orthotropic materials is that for certain orthotropic material combinations the stress state at the point of intersection of a crack and an interface may be bounded whereas in isotropic materials at this point stresses are always singular. A number of numerical examples are worked out in order to separate the primary material parameters influencing the stress intensity factors and the powers of stress singularity, and to determine the trends regarding the influence of the secondary parameters. Finally, some numerical results are given for the stress intensity factors in certain basic crack geometries and for typical material combinations.
53 citations
TL;DR: In this article, the authors considered the elastostatic problem for a relatively thin-walled spherical cap containing a through crack and derived the numerical solution of the problem for an isotropic shell and for two specially orthotropic shells.
52 citations
TL;DR: A survey of the literature concerning plate-type structural elements of composite material or sandwich construction is given in this article, with special attention given to rectangularly orthotropic, cylindrically orthotropic and anisotropic plates.
Abstract: This paper surveys literature concerning dynamics of plate-type structural elements of either composite material or sandwich construction. Papers from 1976 through early 1979 are reviewed. Special attention is given to rectangularly orthotropic, cylindrically orthotropic, and anisotropic plates; laminated plates; thick and sandwich plates; and nonlinearities. Free vibration, harmonic and random forced vibration, thermally and flow induced vibration (flutter) and impact are also treated.
47 citations
TL;DR: In this article, the buckling of cylindrical shells under the simultaneous action of torsion, external pressure, and axial compression was investigated, taking into account the exact form of the boundary conditions and nonlinear prebuckling deformations.
Abstract: This study consisted of a theoretical and experimental investigation of the buckling of circular cylindrical shells under the simultaneous action of torsion, external pressure, and axial compression. Laminated anisotropic behavior was considered, as was the effect of small axisymmetric shape imperfections. The theoretical analysis took into account the exact form of the boundary conditions and nonlinear prebuckling deformations. Interactive stability surfaces were computed for a variety of laminate configurations together with approximate formulas for buckling under these three loading conditions. Comparisons with experimental data obtained from buckling tests on glass/epoxy cylinders were also made.
TL;DR: In this article, a simplified method of predicting the nonlinear stress-strain curves upt to the tensile and compressive failures for an unidi rectionally orthotropic lamina, symmetric biaxial and triaxial laminates is presented.
Abstract: This paper presents a simplified method of predicting the nonlinear stress-strain curves upt to the tensile and compressive failures for an unidi rectionally orthotropic lamina, symmetric biaxial and triaxial laminates. The analytical procedure is based on the classical Laminated Plate Theory (L.P.T.). With applying L.P.T. to the small sress or strain increments of the stress-strain curve, nonlinear stress-strain curve is continuously predicted for various laminates. Comparisons are made between analytical predic tions and experimental results. As the results, the nonlinear stress-strain curves for various cases could be estimated and the results have consider ably good agreement with experimental ones.
TL;DR: In this paper, the authors considered the problem of a cylindrical shell with transverse shear and obtained the stress intensity factors for the bending moment as well as the membrane force as the external load.
Abstract: The objectives of the paper are to solve the problem of a circumferentially-cracked cylindrical shell by taking into account the effect of transverse shear, and to obtain the stress intensity factors for the bending moment as well as the membrane force as the external load. The formulation of the problem is given for a specially orthotropic material within the framework of a linearized shallow shell theory. The particular theory used permits the consideration of all five boundary conditions as to moment and stress resultants on the crack surface. The effect of Poisson's ratio on the stress intensity factors and the nature of the out-of-plane displacement along the edges of the crack, i.e., bulging, are also studied.
TL;DR: In this paper, the axisymmetric dynamic behavior of clamped isotropic and orthotropic spherical cap with central circular hole under a uniform step pressure of infinite duration is investigated, and critical loads are determined by using the rapidly converging Chebyshev series in a space domain and a Houbolt numerical integration scheme in time domain.
TL;DR: In this article, the free vibration of ring-shaped polar-orthotropic sector plates is analyzed by the Ritz method using a spline function as an admissible function for the deflection of the plates.
TL;DR: In this article, the authors considered the elastostatic problem for an infinite orthotropic strip containing crack, where the crack was located along an axis of orthotropy, hence at an arbitrary angle with respect to the sides of the strip.
Abstract: The elastostatic problem for an infinite orthotropic strip containing crack was considered. It was assumed that the orthogonal axes of material orthotropy may have an arbitrary angular orientation with respect to the orthogonal axes of geometric symmetry of the uncracked strip. The crack was located along an axis of orthotropy, hence, at an arbitrary angle with respect to the sides of the strip. The general problem was formulated in terms of a system of singular integral equations for arbitrary crack surface tractions. As examples Modes 1 and 2 stress intensity factors were calculated for the strip having an internal or an edge crack with various lengths and angular orientations.
01 May 1979
TL;DR: In this article, a finite-width orthotropic laminates with a circular hole and remote uniaxial loading using a two-dimensional finite element analysis with both uniform stress and uniform displacement boundary conditions were analyzed.
Abstract: Stresses were calculated for finite-width orthotropic laminates with a circular hole and remote uniaxial loading using a two-dimensional finite element analysis with both uniform stress and uniform displacement boundary conditions. Five different laminates were analyzed. Computed results are presented for selected combinations of hole diameter/sheet-width ratio d/w and length-to-width ratio L/w. For small L/w values, the stress-concentration factors K sub tn were significantly different for the uniform stress and uniform displacement boundary conditions. Typically, for the uniform stress condition, the K sub tn values were much larger than for the infinite strip reference condition; however, for the uniform displacement condition, they were only slightly smaller than for this reference. The results for long strips are also presented as width correction factors. For d/w less or = 0.33, these width correction factors are nearly equal for all five laminates.
TL;DR: In this article, a hardening model for an orthotropic material is proposed and the corresponding anisotropic parameters are the components of a fourth order tensor function of the plastic strain, entering a quadratic equation for the yield surface.
Abstract: A hardening model for an orthotropic material is proposed. The corresponding anisotropic parameters are the components of a fourth order tensor function of the plastic strain, entering a quadratic equation for the yield surface. Assuming polynomial dependence on the plastic strain, the most general form of a polynomial fourth order orthotropic tensor function of a second order symmetric tensor is constructed. This is obtained by imposing on the anisotropic parameters form-invariance conditions under the orthogonal group of coordinate transformations associated with orthotropic symmetries. This yields the appropriate form of polynomial dependence of these parameters on the corresponding integrity basis. An interesting conclusion is that in addition to the initial orthotropic parameters, new anisotropic parameters appear with plastic strain. Kinematic hardening is also considered. The form-invariance of the rate constitutive equations is discussed.
Es wird ein Verfestigungsmodell fur ein orthotropes Material vorgeschlagen. Die entsprechenden anisotropen Parameter sind die Komponenten einer Tensorfunktion vierter Ordnung der plastischen Dehnungen, die in eine quadratische Gleichung fur die Fliesflache eingehen. Indem eine Polynomabhangigkeit von den plastischen Dehnungen angenommen wird, gelingt es, die allgemeinste Form einer orthotropen Tensorfunktion eines symmetrischen Tensors zweiter Stufe zu konstruieren. Dies wird erreicht durch Auferlegung von Invarianzbedingungen fur die orthogonale Gruppe von Koordinatentransformationen, die mit orthotropen Symmetrien verbunden sind. Ein interessantes Ergebnis besteht darin, das zusatzlich zu den orthotropen Anfangsparametern neue anisotrope Parameter mit plastischen Dehnungen erscheinen. Kinematische Verfestigung wird auch betrachtet. Die Invarianz der Konstitutivgleichungen wird diskutiert.
TL;DR: In this article, the vibrating modes of an annular orthotropic disc were analyzed using a finite element program, while the experimental analysis was based on real time and time average holographic interferometry.
TL;DR: In this paper, the governing equations applicable for the large amplitude free, flexural vibration of orthotropic rectangular plates are formulated in terms of the displacement components u, v and w.
TL;DR: In this paper, the uncoupled equation of motion for the flexural displacement of an orthotropic composite circular plate having symmetric lamination is presented, and a numerical method is employed to calculate the symmetric and nonsymmetric vibrational frequencies of full and annular composite plates subjected to a variety of boundary conditions.
Abstract: The uncoupled equation of motion for the flexural displacement of an orthotropic composite circular plate having symmetric lamination is presented. A numerical method is employed to calculate the symmetric and nonsymmetric vibrational frequencies of full and annular composite plates subjected to a variety of boundary conditions. Effects produced by lamination interchange and fiber reversal are discussed; in particular, certain laminations are capable of producing a higher fundamental frequency than either of the constituent materials alone can attain. For annular plates it is found that for certain lay‐ups the fundamental frequency derives from a nonsymmetric mode. Finally, pinhole‐center annuli are examined and, for a free inner edge, a comparison is made with corresponding full‐plate frequencies.
TL;DR: In this article, the problem of an elastic plate containing a through crack and subjected to twisting moments or transverse shear loads is considered, and it is found that the resulting asymptotic stress field around the crack tip becomes identical to that given by the elasticity solutions of the plane strain and antiplane shear problems.
Abstract: The problem of an elastic plate containing a through crack and subjected to twisting moments or transverse shear loads is considered. By using a bending theory which allows the satisfaction of the boundary conditions on the crack surface regarding the normal and the twisting moments and the transverse shear load separately, it is found that the resulting asymptotic stress field around the crack tip becomes identical to that given by the elasticity solutions of the plane strain and antiplane shear problems. The problem is solved for uniformly distributed or concentrated twisting moment or transverse shear load and the normalized Mode II and Mode III stress-intensity factors are tabulated. The results also include the effect of the Poisson's ratio and material orthotropy for specially orthotropic materials on the stress-intensity factors.
TL;DR: In this article, the non-linear partial differential equations obtained from von Karman's large deflection plate theory have been solved by using the Chebyshev series in the space domain and the Houbolt numerical integration scheme in the time domain.
Abstract: In the present paper, Chebyshev series are employed to obtain the non-linear static and dynamic response of isotropic and orthotropic annular plates. The non-linear partial differential equations obtained from von Karman's large deflection plate theory have been solved by using the Chebyshev series in the space domain and the Houbolt numerical integration scheme in the time domain. Two different sets of boundary conditions of the annulus are investigated and detailed numerical results have been obtained for different cases of orthotropy and geometry.
TL;DR: In this article, the effect of transient (non-steady) creep and orthotropic material on stress and strain distributions in rotating disks of orthotropic materials has been discussed and depicted graphically.
TL;DR: In this article, a finite-difference formulation that gives accurate bending moments for thin elastic plates is presented, where the biharmonic equation is replaced with two deflection-normal bending moment relations and the equilibrium equation in terms of the moments.
TL;DR: In this article, a computational analysis of the non-linear oscillations of elastic orthotropic annular plates of variable thickness is presented, where the boundary value problem is converted into a corresponding eigenvalue problem by using a Kantorovich time-averaging method.
TL;DR: In this paper, non-linear transverse vibrations of elastic, orthotropic cylindrical shells of linearly varying thickness and embedded in an incompressible fluid are analyzed by using the Rayleigh-Ritz procedure.
TL;DR: In this paper, it was shown that a number of heat conduction problems in layered-composite cylinders and plane laminates of anisotropic materials with boundary conditions of the first (Dirichlet), second (Neumann), third (mixed or convective) and fourth kind can be transformed into the corresponding orthotropic ones.