Effects Of Material Anisotropy Research Articles

Heat Conduction in an Anisotropic Medium Homogeneous in Cylindrical Regions—Unsteady State

A number of problems of heat conduction in an anisotropic medium of a monoclinic system which is homogeneous in circular cylinder coordinates are solved through the use of Green’s functions. Regions of solid and hollow cylinders, and an infinite region bounded internally by a cylindrical surface with boundary conditions of Dirichlet, Neumann, and mixed types are considered. Calculated results for two examples are shown, and the effects of material anisotropy on the temperature field are discussed. This paper is the first of a series to be reported in the open literature concerning the analytical solution for heat conduction in anisotropic media which are homogeneous in circular cylinder and rectangular coordinate systems.

Effect of fabric anisotropy on compressional-wave propagation in various metamorphic rocks for the range 20–700°C at 2 kbars

In all rocks investigated (peridotite, amphibolite, serpentinite, marble) the observed seismic anisotropy is primarily a consequence of preferred orientation of minerals and of the elastic anisotropy of the constituent minerals of the rocks. Generally the compressional-wave velocity decreases with temperature. The amount of velocity decrease, however, is different in the various rock types and even for different directions in the same anisotropic media. Fabric-induced seismic anisotropy is not drastically reduced with temperature. In the amphibolite, and especially in the serpentinite seismic anisotropy even increases with temperature. It is expected that the preferred orientation of minerals may have an effect on wave propagation even at great depths in the earth's crust and in the upper mantle.

Thermoelasticity of Anisotropic Generally Laminated Slabs Subject to Spatially Periodic Thermal Loads

Based on 3-D thermoelasticity theory, the effects of mechanical and thermal material anisotropy on the local stationary fields of generally laminated plates are investigated. In particular, to model the stated problem, each individual lamina of the slab is considered to be composed of mechanically and thermally possibly fully anisotropic materials whose fields satisfy 3-D elasticity and conduction theory. Using complex series expansions, together with the properties of complex adjoint differential forms, a 3-D solution of the given model is obtained. Its generality is such that plates consisting of any number of distinct fully anisotropic lamina subject to arbitrary spatially periodic external and internal mechanical and thermal loads can be handled. In terms of the model and its solution, the results of several numerical experiments which emphasize the effects of material anisotropy on the governing fields of symmetric, alternating, and shingle-type laminates are reported.

Boundary-integral equation analysis of cracked anisotropic plates

A numerical procedure based on the boundary-integral equation method, is formulated using the fundamental solution (Green's function) for an infinite anisotropic plate containing an exact crack. The boundary-integral equation developed can be solved numerically for the mode 1 and mode 2 stress intensity factors by approximating boundary data on the surface of an arbitrary body, excluding the crack surface. Thus the efficiency and generality of the boundary-integral equation method and the precision of exact crack model analyses are combined in a direct manner. The numerical results reported herein are as accurate as previously published isotropic results. The effects of material anisotropy are reported for center and double-edge cracked geometries. A path independent integral for obtaining mode 1 and mode 2 stress intensity factors directly for arbitrary loading is reported.

Thermoelasticity of an Anisotropic Half Space

The thermoelasticity of an anisotropic Hookean half space is studied herein. A solution based on successive integral transforms is developed. The solution can handle arbitrary thermal and mechanical boundary conditions together with distributed body forces and heat sinks or sources. To illustrate the substantial effects of material anisotropy, a specific boundary-value problem is solved. Numerical results based on the solution are presented. These illustrate the significant effects of both thermal and mechanical material anisotropy.

Quasi-analytical finite element procedures for axisymmetric anisotropic shells and solids

Using complex series representations, a quasi-analytical finite element procedure is developed which can analyze the static and dynamic mechanical fields of anisotropic axisymmetric shells and bodies. Due to its generality the procedure can handle arbitrary laminate construction with possible meridional and radial variations in locally or globally mechanically anisotropic materials. In this respect, in contrast to traditional quasi-analytical procedures which are limited to the ‘specially’ orthotropic case, the present treatment reveals several important effects of material and/or structural anisotropy. To illustrate the procedure as well as the significant effects of material anisotropy, several numerical examples are given along with comparisons with known analytical treatments.

Natural frequencies of monoclinic circular plates

The present paper studies the effects of material anisotropy on the frequency eigenvalues of fiber reinforced circular plates. A general solution is developed by means of an integral transformation of the plate equations together with the subsequent use of power series expansions to solve the resultant transformed equation. In terms of this solution, the effects of fiber orientation on the frequency eigenvalues are discussed at length.

Semi‐analytical finite element procedure for conduction in anisotropic axisymmetric solids

AbstractThrough the use of complex series representations and the properties of adjoint differential operators, a semi‐analytical finite element procedure is developed which can analyse the steady state and transient temperature fields of thermally anisotropic axisymmetric bodies with complete circumferential properties. Due to its generality, the procedure can handle arbitrary laminate construction with possible meridional and radial variations in locally or globally thermally anisotropic materials. In this respect, the procedure developed herein supercedes the classical semi‐analytical treatment which is limited to specially orthotropic materials. Furthermore, in contrast with the classical procedure, the present treatment reveals several important effects of material anisotropy which are entirely missed by the specially orthotropic assumption.

Numerical analysis of anisotropic rotational shells subjected to nonsymmetric loads

Through the use of an integral transform, the present paper extends the applicability of the multisegment numerical integration technique to include the solution of general macroscopically anisotropic multilayered shells of revolution. It is found that compared with orthotropic shells, material anisotropy induces a doubling in the number of transformed fundamental equations characterizing the static response. Employing the transform together with the multisegment integration technique and several concepts from the direct stiffness method of structural analysis, procedures are developed which can handle branched anisotropic multilayered shells of revolution in a more effective manner than was previously possible. Based on the procedures outlined in the paper, numerical studies are presented which show the effect of segment size on the solution accuracy and the effects of material anisotropy on selected shell configurations.

Thermal Contact Resistance of Anisotropic Materials

This work presents an extension of the understanding of thermal contact resistance to include anisotropic materials. The extension involves a mathematical geometric transformation which leaves the thermal currents unchanged while making the temperature distribution in the anisotropic materials soluble by previously published methods. The development of this transformation technique is presented, and the effect of material anisotropy is calculated for a set of interface orientations and material conductivities which characterize typical contact situations. The degree of material anisotropy and the orientation of the contact interface are shown to be important factors affecting the contact resistance in addition to surface roughness, material hardness, and contact load.