Anisotropic Elastic Body Research Articles

General solution to the hygrothermoelastic interface problem with discontinuity between dissimilar anisotropic media

A general solution to the hygrothermoelastic problem associated with an interface discontinuity between dissimilar anisotropic media is presented. The complex variable representation of Lekhnitskii [Theory of Elasticity of an Anisotropic Elastic Body (Holden-Day, San Francisco, CA, 1963)] is extended into the hygrothermoelastic problem by means of five complex functions including three stress functions, one temperature function, and one moisture function. A special technique of analytical continuation is used to deal with the continuous conditions of dissimilar media. Based on the Hilbert problem formulation, the linear relation between the boundaries of discontinuity can be derived into a type of Cauchy integral, which makes the solution in a compact version. The result shows that the heat or moisture flux exhibits an inverse square-root singularity at the tips of discontinuity while the nature of singularity of the hygrothermal stresses possess the same trig-log character as those obtained for the elastic problem.

THERMAL STRESSES IN ANISOTROPIC BODIES WITH A HOLE OR A RIGID INCLUSION

The Lekhnitskii complex potential approach of anisotropic elasticity is extended to include the thermal effect. A concise formulation of the thermal stress problem of an anisotropic elastic body with a hole or a rigid inclusion in generalized plane deformation or generalized plane stress condition is presented. Special attention is paid to the systematic determination of the general forms of the complex potentials for the thermoelastic field that satisfies the prescribed boundary conditions at the interior contour. Both the Dirichlet and the Neumann type of boundary conditions arc considered. Using these general forms of solution, thermal stresses for the generalized plane problems of anisotropic body with a hole or a rigid inclusion can be determined in a simple and systematic manner. Applications of the solution method to several illustrative examples are given.

An attempt to simulate the bowing phenomenon in tenter with simple models

AbstractThe bowing phenomenon throughout a tenter was experimentally observed with a pilot plant of successive biaxial stretching. The observed results were compared with simulated ones, by which the deformation behaviors of film in a tenter were predicted, with the assumption that the film was homogeneous isotropic, homogeneous anisotropic, heterogeneous isotropic, or heterogeneous anisotropic for a two‐dimensional elastic body with an FEM. Comparatively good agreement between the simulated and observed results was obtained for a heterogeneous anisotropic elastic body with an initial mesh, involving in advance a plastic deformation part. © 1993 John Wiley & Sons, Inc.

Approximate three-dimensional analysis of rectangular thick laminated plates: Bending, vibration and buckling

A global-local approach is proposed to analyse thick laminated plates. This approach treats a thick laminated plate as a three-dimensional inhomogeneous anisotropic elastic body. The cross-section of a laminated plate is first discretized into conventional eight-node elements. The interpolation function along the span of the plate is defined by the cubic B 3-spline function. The displacement functions can be expressed as the product of the usual isoparametric shape functions and the spline function. A set of global polynomials of an appropriate order is selected to transform the nodal variables of the cross-section to a much smaller set of generalized parameters associated with the polynomials. These parameters can be obtained by means of the standard Rayleigh-Ritz technique. The total number of unknowns involved is drastically reduced with a minor sacrifice of accuracy. The six components of stresses, the fundamental natural frequencies and the critical buckling loads can be determined with acceptable accuracy. Numerical examples are given to demonstrate the accuracy and effectiveness of the global-local procedures.

The stress concentration ratio of the interface crack between dissimilar anisotropic composite materials

The relations are discussed of stress concentration value around a crack tip at the interface between an anisotropic elastic body (for example rock) and concrete, and the elastic parameters of anisotropy. The numerical modeling is based on the concept of finite stress concentration proposed by Nakagawa, Anma and Duan [ Engng Fracture Mech. 36, 439–449 (1990)], and a uniform shear force parallel to the crack faces is taken as the external load. Figures and tables are used to show the maximum shear stress variation for different anisotropic principal axis directions and the elastic properties. From these results, it is possible to conjecture the maximum shear stress concentration ratio of the interface crack between rock and concrete with a process zone, if their elastic parameters are determined.

Interlaminar stresses in a centrally notched composite laminate

A plane stress solution for an anisotropic plate with a circular hole, developed by Savin, is extended to derive the interlaminar stresses in a centrally notched composite laminate under uniform tension. Based upon Lekhnitskii's stress potentials, theory of anisotropic elastic body and boundary layer effect, stress shapes are chosen such that the zeroth order equilibrium equations, interface continuity and boundary conditions are satisfied. The unknown parameters in the stress expressions are then determined by the requirement of stress integral equilibrium. The merit of our model is highlighted by obtaining the interlaminar stresses and the order of boundary layer stress singularity simultaneously. Several examples of [0/90]s, [±45]s and [0/90/±45]s graphite/epoxy composite laminates containing centrally circular holes are analysed.

A tensorial classification of elastic waves

Pure stress equations of motion of linear homogeneous anisotropic elastodynamics are used to present a classification of the plane stress progressive waves in an infinite body. A plane stress wave is decomposed into ‘‘normal’’ and ‘‘tangential’’ parts with respect to the wave front in such a way that: (i) both parts can propagate with the same velocity, (ii) the total stress energy of the wave is represented by the positive difference between ‘‘normal’’ and ‘‘tangential’’ stress energies, and (iii) pure ‘‘tangential’’ stress wave cannot propagate. The classification is consistent with and complementary to that of the displacement progressive waves, at least for homogeneous isotropic and transversely isotropic elastic media, and provides a number of new properties of the plane progressive waves in a general anisotropic elastic body.

Wave Propagation on the Boundary Plane of an Anisotropic Body with Inclined Anisotropic Principle Axis.

In this paper, SH (horizontally polarized shear) wave propagation in an inclined anisotropic elastic body is investigated. It is analyzed as a basic boundary value problem as the interface between an inclined anisotropic half space and an isotropic half space. Direction of wave propagation is determined by the use of power flow density. It is shown that power flow density determines the direction of the principle axis of an inclined anisotropic body. Reflection and transmission coefficients in the interface are also discussed. The reflection coefficient in the interface is large when inclined angle in large.

A generalized theory of thermoelasticity for an anisotropic medium

In this paper a generalized theory of thermoelasticity for an anisotropic medium is formulated using a form of the heat transport equation which includes the time needed for acceleration of the heat flow. A uniqueness theorem is presented for the equations of generalized thermoelasticity in the case of an anisotropic elastic body. The variational principle corresponding to basic equations of generalized thermoelasticity for an anisotropic medium is derived.

Analytical Solutions for Semi-Infinite Problems under Several Boundaries Including Sliding Conditions. 2nd Report, Case of In-Plane Problems for Anisotropic Elastic Body.

This paper presents an analysis of in-plane problems for anisotropic semi-infinite body due to single force, single dislocation, dipole-force, dipole-dislocation, and so forth, with various surface boundaries such as free, fixed and two sliding conditions. Distributions of stresses and displacements under applied singular forces for the above four boundaries are illustrated by some graphical representations as numerical examples.

Internal strain analysis in a winding paper roll and its measurement.

In this paper, stress and strain distributions in the internal part of a winding paper roll are derived theoretically. In this theory, it is assumed that the winding roll paper is cylindrically anisotropic continuum elastic body. For the cases with various anisotropic parameters and various winding ratios, stress and strain distributions are calculated and buckling :conditions are considered. In the experimental model, the strains in the internal part of the winding paper roll are measured during winding. The results are in good agreement with the theoretical results.

Limit of the rate of convergence of difference schemes for the first boundary-value problem of elasticity theory in the anisotropic case

Exact difference scheme operators for a system of equilibrium equations of a non-homogeneous anisotropic elastic body rigidly clamped in the rectangle Ω are used to construct difference schemes which have O( h 2) accuracy in the grid norm of W 2 1( ω) if the solution of the original problem belongs to the space W 2 3(Ω) .

Boundary element analysis of three dimensional anisotropic elastic body with a crack.

Boundary element analysis of three dimensional anisotropic elastic body with a crack.

Stress intensity factors due to non-elastic strains and body forces for steady dynamic crack extension in an anisotropic elastic material

Explicit solutions of the stress intensity factors due to non-elastic strains and body forces are obtained for a crack extending dynamically at steady state through an anisotropic elastic body. The examples of non-elastic strains include thermal expansion, phase transformation, initial strains, plastic strains, etc. Specific results are given for creeping materials, a uniform distribution of transformation strains and discrete dislocations. It is shown that the stress intensity factors of tractions applied on the crack faces are independent of the crack velocity and the elastic constants.

On the structure and invariance of the Barnett-Lothe tensors

The three real tensors introduced by Barnett and Lothe into the theory of steady plane motions of an anisotropic elastic body are shown to have algebraic representations the structure of which is largely independent of material symmetry. The allied form of the complex impedance tensor central to the analyses of surface and interfacial waves in anisotropic elastodynamics is also obtained. A detailed study of the representations yields alternative routes to known results and a variety of new relations. The paper concludes with a discussion of the invariance properties of quantities appearing in the representations under rotations of the reference frame about the direction in which the deformation is uniform.

A Cylindrical Interface Crack in a Nonhomogeneous Anisotropic Elastic Body

This paper considers a cylindrical interface crack problem, from micro-mechanics-points of view, using a two phase material model consisting of a transversely isotropic circular cylinder embedded in a transversely isotropic infinite body which takes account of the anisotropy of a carbon fiber and the mechanical interaction between fibers. The problem relates to the stress state near a crack-like defect with curved surfaces at the interface between fiber and matrix in a unidirectional carbon fiber reinforced plastics. Mathematical formulations are made in terms of a Cauchy-type singular integral equation of the second kind and the results are compared with those of the macromechanics model in our previous paper.

A general analysis of transonic states in an anisotropic elastic body

The basic characteristics of surface-wave propagation in an anisotropic elastic body depend crucially on the transonic states, defined by the sets of parallel tangents to a centred section of the slowness surface. The number of tangents parallel to a given direction in the plane of the section is at least 3 and at most 15 and, according to the number of points of contact and the number of branches of the slowness section to which they belong, there are 6 types of transonic states. The homogeneous plane wave represented by a point of contact is called a limiting wave and a transonic state is said to be exceptional when each of its limiting waves leaves free of traction the planes orthogonal to the tangent. For an elastic material of general anisotropy with positive definite linear elasticity tensor it is shown that at most 2 transonic states can be exceptional and that precisely 4 combinations of exceptional transonic states can occur, involving only 3 of the 6 types. Necessary and sufficient conditions for the existence of each of the possible combinations are given. As an application of the general results a complete characterization of exceptional transonic states in elastic materials with hexagonal symmetry is obtained.

A potential representation of the differential equations of C∞ anisotropic elastic bodies

We give a potential representation to the differential equations of elastic waves propagating along the symmetric direction of C∞ anisotropic elastic bodies. The potential representation is a generalization of Lamb’s potential representation of the differential equations of isotropic elastic bodies. The generalized Lamb’s potential representation reduces the equations of motion to some two-dimensional Helmholtz equations and constraint equations. Moreover, using the potential representation, we briefly prove the completeness of Mirsky’s solutions of C∞ anisotropic solid and hollow circular cylinders.

An extension of the superposition method for plane anisotropic elastic bodies

The determination of the elastic field in anisotropic bodies subjected to mixed and nonhomogeneous boundary conditions has not been developed to the extent of its isotropic counterpart. This is mainly due to the complexity of the anisotropic fundamental solution. In this paper, the superposition method (SUP) is extended to allow for anisotropy. In particular, the method is developed for the plane orthotropic case. Using some examples, it is shown that the method is both efficient and very accurate. A general FORTRAN computer program based on the formulation presented here is included.

On the similarity and dissimilarity between crack problems and rigid flat inclusion problems for an anisotropic elastic body under longitudinal shear For the periodic cracks and the periodic rigid flat inclusions near the interfaceof bonded anisotropic bodies.

き裂問題と剛体偏平介在物問題の類似性と相異生を明かにする目的で,弾性定数の異なる二つの異方性半無限体が互いに接合された複合異方弾性体が接合境界近傍に周期き裂群および剛体偏平介在物群を有する場合の縦せん断問題を解析した.数値計算を行い,欠陥先端の応力の特異性の強さに及ぼす種々の影響を調べ両問題の類似性と相異生を明らかにした.