Showing papers on "Orthotropic material published in 1977"

Stresses Around Pin-Loaded Holes in Elastically Orthotropic or Isotropic Plates

Abstract: The stress distribution round a pin-loaded hole in an elastically ortho tropic or isotropic plate is investigated. The hole is loaded frictionless on only a part of its edge by an infinitely rigid pin of the same diameter. The loading force is carried over on the edge by normal stresses, represented by a sine series. It is shown that these stresses depend strongly on the material properties. Infinite plate results are used to estimate the stresses in plates nite width. Numerical results are shown graphically for three laminates n fibre reinforced plastic and for three ratios of width of plate to mole diameter.

Stress-strain relations for materials with different moduli in tension and compression

Abstract: Models in the form of stress-strain, or constitutive, relations are discussed for materials with moduli under tensile loading which are different from those under compressive loading. Criteria for consistent material models are given which are based on the principles of anisotropic elasticity and on the known behavior of such materials. The Ambartsumyan material model is compared with the criteria and found to violate the requirement of symmetric compliances. An improved model, called the weighted compliance matrix (WCM) material model, is shown to satisfy the criteria for isotropic and orthotropic bodies under plane stress. The new model can be extended by deduction to more complicated situations such as anisotropic bodies under general stress states.

Elastic modulus of single wood pulp fibers

Abstract: Careful measurements have been made of the elastic modulus of softwood fibers over a range of fibril angle 0-50°. For fibers of similar fibril angle, the modulus varies appreciably and this is shown to be caused by microcompressions, dislocations, and other inhomogeneities in the structure. For fibers that are free from such defects, the plot of modulus against fibril angle follows a smooth curve. Using orthotropic elasticity theory, an explicit equation for modulus in terms of fibril angle and the orthotropic elastic constants of the cell wall has been derived. The experimental data fit theory excellently. The elastic constants of the cell wall derived from the fit show the wall to be highly anisotropic.

The problem of internal and edge cracks in an orthotropic strip

Abstract: The plane elastostatic problem of internal and edge cracks in an infinite orthotropic strip is considered. The problems for the material types I and II are formulated in terms of singular integral equations. For the symmetric case the stress intensity factors are calculated and are compared with the isotropic results. The results show that because of the dependence of the Fredholm kernels on the elastic constants, unlike the crack problem for an infinite plane, in the strip the stress intensity factors are dependent on the elastic constants and are generally different from the corresponding isotropic results.

Flutter and Buckling of General Laminated Plates

Abstract: An anisotropic buckling and flutter analysis is developed with allowance for both bending-extensional coupling and bending-twisting coupling within the framework of linear small deflection theory for simply supported general laminated plates. The extended Galerkin method is used to obtain approximate solutions to the coupled governing equations. The effects of various anisotropic stiffness parameters on the static and dynamic stability of laminated plates are evaluated, with particular emphasis on assessing the range of applicability of classical orthotropic plate theory. It is shown that bending-extensional coupling and bending-twisting stiffness terms have a destabilizing effect on buckling and flutter, the effect being more pronounced for a small number of layers. For symmetric plates, the number of layers required for orthotropic plate theory to be applicable is generally less for the buckling problem than for flutter. For square plates, aligning the fibers with the direction of airflow over the plate surface results in the highest flutter dynamic pressure.

Analysis of Nonlinear Stress-Strain Behavior of Fiber-Reinf orced Composite Materials

Abstract: Fiber-reinforced composite materials generally exhibit nonlinear stress-strain behavior in at least one of the principal material directions. For example, boron/epoxy and graphite/epoxy have highly nonlinear shear behavior. Moreover, boron/aluminum has nonlinear behavior transverse to the fibers as well as a shear nonlinearity, and carbon/carbon has nonlinearities in all principal material directions. The Jones-Nelson strain energy based nonlinear mechanical property model is extended to treat all nonlinearities of fiber-reinfor ced composites. The basic model will converge only up to a specific strain energy value. That limitation is eased by using new extrapolations of the stress-strain curve and mechanical property - energy curve for strain energies above available stress-strain data. These extrapolations are necessary because the strain energies of biaxial loading exceed the strain energies of uniaxial loading under which the properties are defined and because the maximum strain energies under uniaxial loading are different in the various principal directions due to orthotropy. Strains predicted with the new material model correlate well with strains measured by Cole and Pipes in uniaxial off-axis loading of boron/epoxy and graphite/epoxy. The predicted strains are also close to strains predicted by Hahn and Tsai, who use a material model with a single (shear) nonlinearity. Our model can be used for the several nonlinearities of boron/aluminu m and carbon/carbon; therefore, it is more widely applicable than the Hahn and Tsai model.

Interlaminar Stresses around Circular Cutouts in Composite Plates under Tension

Abstract: 1~5 From these results, the static failure strengths are obtained with good quantitative prediction compared to experiments. Delamination at free edges is another failure mode of laminated composites, especially under fatigue loadings. Extensive delamination at free edges is reported on static strength as well as fatigue strength, with and without notches.6"10 Hence, the determination of interlaminar shear stresses and the normal or "peel" stress is a current research topic. However, all the previous studies are restricted to straight boundaries11"27 except for finite element solutions in Refs. 14 and 28-30. There is no analytical closed-form solution available to predict interlaminar stresses for curvilinear boundaries. Therefore, the present paper attempts to study the interlaminar stresses at a circular cutout in an "infinite" composite laminate under uniform tensile load. The boundary-layer theory for composite laminates in Ref. 20 is extended here to the formulation of polar coordinates, and the title problem is investigated for the case of orthotropic composite plates. The laminate considered here is under inplane loading symmetric about the midplane. The construction of the laminate is also midplane symmetric so that there is no stretching/bending coupling of the plate due to external load. The force resultants around the hole of an orthotropic or anisotropic plate are given by Refs. 31 and 32. The radial and shear force resultants at the edge of the hole are zero. From the plane stress solution, the strains at the edge of the hole can be calculated by the force resultant-strain relation. Due to the compatibility of deformation, the strains of individual layers are the same as the laminate. Therefore, the stresses of each layer may then be computed from the layer stress-strain law. However, the computed radial and shear stresses of each layer along the contour of the hole are in general not zero. Because there exists a three-dimensio nal state of stresses at the free edge of each layer where the plane stress solution cannot predict. The region of the plate adjacent to and including the edge, where the plane stress solution may not be adequate, is called the boundary layer. To obtain the governing equations in this

On the use of special crack tip elements in cracked elastic sheets

Abstract: This paper presents a finite element method for determining the stress intensity factor in a cracked elastic sheet. Special cracked elements are placed around each crack tip; in each special element the stresses and displacements are derived from the exact stress function while the continuity of the displacements at the nodes is satisfied in a least square sense. A general procedure for evaluating the stiffness matrix of a cracked isotropic, or orthotropic, element is presented, and the numerical results obtained are compared with exact analytical results.

Measurements of anisotropic elastic constants of type 308 stainless-steel electroslag welds

Abstract: In austenitic-stainless-steel weld metal, mechanical anisotropy is caused by preferred local orientation of elongated subgrains and preferred crystallographic orientation. Ultrasonic and static tensile-test methods used to determine elastic stiffness and compliance matrices, respectively, demonstrated that orthotropic symmetry exists. Inversion of this compliance matrix gave a stiffness matrix which showed general agreement between the two methods. It is suggested that the data can be used directly in finite-element analyses of weldments containing Type 308 stainless steel.

Impact Damage in Graphite-Fiber-Reinforced Composites

Abstract: Theoretical and experimental studies are presented on the failure modes in graphite-fiber-reinforced composite plates subjected to low-velocity impact. Influence of the following parameters is studied theoretically or experimentally or both: fiber and matrix properties, fiber orientation, stacking sequence, and laminate thickness. A quasi-dynamic approach is used to predict theoretically the influence of the noted parameters on the impact response of composite plates. A previously developed approach is used and extended to predict the time-dependent surface pressure and its distribution in a generally orthotropic target impacted by a body of revolution. The triaxial stress state in the composite target (assumed to be generally orthotropic) is determined using a finite-element computer program. These stresses are used with failure criteria for generally orthotropic solids to determine the extent of impact damage. To verify predictions of the impact-induced failure modes, ball-drop tests are conducted on circular composite plates incorporating different fiber-resin combinations, fiber layups, and stacking sequences. Types of graphite fibers used in the experimental program include Thornel 300, Modmor II, and Celion GY-70. Fiber layups investigated include unidirectional, 2:1 bidirectional, 1:1 bidirectional, and tridirectional (pseudo-isotropic).

The Nonlinear Behaviour of Thin, Orthotropic, Curved Panels under Lateral Loading

Abstract: A theoretical analysis is presented for the snap-buckling behaviour of thin, orthotropic, spherically curved panels subject to central point and uniform pressure loading on the convex face. Clamped and simply supported edges are considered. The results are presented graphically for a range of panel aspect ratios and comparison is made with experimental studies.

Frequency analysis of coupled shear wall assemblies

Abstract: The finite strip procedure is used to predict the free vibration response of both planar and non-planar coupled shear wall assemblies. The solid walls are considered as vertical cantilever strips and a comparison is made between modelling the spandrel beams as discrete beams and as an equivalent continuum with orthotropic plate properties. It is shown that both approaches lead to essentially the same frequencies. The effects of vertical inertial forces and shear deflection are included, and structures considered may have properties that vary with height. The method presented appears to be more versatile than previously published techniques and numerical comparisons with existing methods indicate the predicted results to be accurate.

Buckling of Rotationally Restrained Orthotropic Plates Under Uniaxial Compression

Abstract: A solution methodology is developed to predict critical conditions for rotationally restrained orthotropic plates loaded by a uniform axial com pression. In addition, parametric studies are performed to find the effect, on the critical load, of various elastic constants for a practical range of aspect ratio values and the entire range of rotational restraint, including the extreme cases of simply supported and clamped plates. The generated data are based on the assumption of symmetric boundary conditions (the amount of rotational restraint is equal for opposite sides) although the methodology is not limited by this assumption. Among the conclusions one may list that the most significant effect is that of the ratio of Young's moduli and amount of rotational restraint.

Random vibrations of orthotropic plates clamped or simply supported all round

Abstract: An approximate method is presented for determining the probabilistic response of rectangular orthotropic plates clamped all round. For solving the stochastic boundary value problem, the probabilistically given and sought functions are expressed in terms of series of approximate modes of vibration, which satisfy the boundary conditions but not the field equation. Galerkin's procedure then yields a set of linear equations for the cross-spectral densities of the displacements. The cross-spectral density of the external pressure is taken to be a product of longitudinal and transverse correlation coefficients which depend on frequency and separation distance. When the approximate method presented here is applied to cases capable of closed solutions (i.e. plates having a pair of opposite edges simply supported), the result coincides with that obtained by the classical normal-mode approach.

Plates and shells with cracks : a collection of stress intensity factor solutions for cracks in plates and shells

Abstract: 1 Interaction of arbitrary array of cracks in wide plates under classical bending.- 1.1 Introduction.- 1.2 Basic relations.- 1.3 Complex potentials for traction free cracks.- 1.4 Arbitrary array of cracks in wide plate.- 1.5 Numerical results.- 1.6 Discussions.- References.- 2 Improved approximate theories of the bending and extension of flat plates.- 2.1 Introduction.- 2.2 Approximate theories by variational methods.- 2.3 Applications to crack problems.- 2.4 Guidelines for practical applications.- References.- 3 Through cracks in multilayered plates.- 3.1 Introduction.- 3.2 Minimum complementary energy applied to a layered plate.- 3.3 An approximate three-dimensional theory of multi-layered plates.- 3.4 Through crack in a layered plate.- 3.5 Stress distribution across the plate thickness.- 3.6 Discussion of numerical results.- 3.7 Appendix: Definition of constants.- References.- 4 Asymptotic approximations to crack problems in shells.- 4.1 Introduction.- 4.2 General theory - classical.- 4.3 The stress field in a cracked spherical shell.- 4.4 The stress field in a cracked plate.- 4.5 The stress field in a cracked cylindrical shell.- 4.6 Approximate stress intensity factors for other shell geometries.- 4.7 Plates on elastic foundations.- 4.8 Particular solutions.- 4.9 Discussion.- References.- 5 Crack problems in cylindrical and spherical shells.- 5.1 Introduction.- 5.2 Formulation of the specially orthotropic cylindrical shell problem.- 5.3 The skew-symmetric problem.- 5.4 The symmetric problem.- 5.5 Results for a specially orthotropic cylindrical shell.- 5.6 The effect of Poisson's ratio.- 5.7 Interaction of two cracks.- 5.8 Further results for isotropic shells.- References.- 6 On cracks in shells with shear deformation.- 6.1 Introduction.- 6.2 Shell theory with shear deformation.- 6.3 Symmetric loading.- Appendix: Integrand and Kernel functions.- References.- 7 Dynamic analysis of cracked plates in bending and extension.- 7.1 Introduction.- 7.2 Classical plate bending theory.- 7.3 Mindlin's theory of plate bending.- 7.4 Kane-Mindlin's equation in plate extension.- 7.5 Plates subjected to sudden loading.- References.- 8 A specialized finite element approach for three-dimensional crack problems.- 8.1 Introduction.- 8.2 Three-dimensional elastic calculations.- 8.3 Finite element method - background.- 8.4 Specialized elements for the crack edge.- 8.5 Applications to crack problems.- 8.6 Details of the analysis.- 8.7 Results of the finite element analysis.- 8.8 Summary.- References.- Author's Index.

A Nonsymmetric Compliance Matrix Approach to Nonlinear Multimodulus Orthotropic Materials

Abstract: Multimodulus materials have moduli or stiffnesses under tension loading which are different from those under compression loading. Several approaches to their analysis have been suggested recently. Most of these approaches are based on the hypothesis that the compliance matrix in the strain-stress relations must be symmetric. Jones makes the matrix symmetric by weighting the tension compliances and the compression compliances on the basis of the proportion of tensile and compressive stresses. Isabekyan and Khachatryan determine very severe restrictions under which a multimodulus material has a symmetric compliance matrix in all coordinate systems. However, the Jones weighted compliance matrix approach cannot be derived from basic principles. Moreover, the Isabekyan and Khachatryan restricted compliance matrix approach is not realistic because the properties of known multimodulus materials do not satisfy their restrictions. The purpose of this paper is to relax the previously held requirement of compliance matrix symmetry to see whether suitable agreement can be obtained between predicted and measured strain response of ATJ-S graphite to mixed tension and compression loading under plane stress conditions.

Shrinkage stresses in wood logs considered as layered, cylindrically orthotropic materials

Abstract: The deformation and stresses in a circular wood log resulting from an arbitrary radial moisture distribution are examined. In this paper the log is modeled as a layered cylinder, with each layer assumed to be linearly elastic, cylindrically orthotropic, and homogeneous. The general solution to the equations of elasticity for a representative layer is given; constants of integration in the solution are determined through application of appropriate continuity conditions at the layer interfaces. Numerical examples are presented for logs of Scots pine which illustrate the effect of nonuniform moisture content upon the displacement and stress distributions.