Nonhomogeneous Material Properties Research Articles

Analysis of rail track structures (ARTS)

The computer program ARTS for the static non-linear analysis (with or without allowing any element to take tension) of track structures is presented. The finite element method is used and a choice of hexahedronal, pentahedronal and beam elements is provided which can model non-homogeneous isotropic elastic material properties. The program allows the calculation of contact forces between two structures (i.e. the ground and the tie/rail system). There are two techniques for describing the material non-linearity. Triaxial test data for ballast or granular material may be processed in a cubical spline form to allow for variable Young's modulus and Poisson's ratio, or a hyperbolic model may be employed. This permits the program to take into account the ballasts' stress path dependence. Elements can be selected as permitted, or not, to take tension. If permitted to take tension then the stress-strain or Poisson's ratio-strain characteristics are identical in tension and compression. Initial elastic properties may be imposed or body and surcharge conditions may be input allowing the program to calculate initial stresses and thus properties. A sample analysis has been selected to demonstrate the general problem solving procedure and the input and output descriptions.

Transient Thermal Stress Analysis of a Nonhomogeneous Hollow Sphere due to Axisymmetric Heat Supply.

In this paper, theoretical analysis of an axisymmetric transient thermal stress problem is developed for a nonhomogeneous hollow sphere. Assuming that the hollow sphere has non-homogeneous thermal and mechanical material properties in radial direction, heat conduction problem and the associated thermoelastic behaviors for such nonhomogeneous medium are developed by introducing the theory of laminated composite as one of the theoretical approximation. The transient heat conduction problem under the condition of axisymmetric heat supply due to the inner or outer surrounding medium is evaluated with aid of the method of Laplace transform, and the associated thermoelastic field is analyzed making use of the thermoelastic displacement potential and the complementary harmonic function. Thereafter, the numerical results for the temperature change and the stress distributions are shown in figures, and the influences of the nonhomogeneous material properties are discussed briefly.

Nonlinear Behavior of Nonhomogeneous Beam due to Unsteady Heat Supply.

In this paper, nonlinear behaviors such as large deflection, prebuckling and postbuckling are developed for a nonhomogeneous beam. Assuming that the beam is composed of a medium with nonhomogeneous thermal and mechanical material properties in the transverse direction, the one-dimensional transient heat conduction problem for such a nonhomogeneous beam is solved under the condition that the upper and lower surfaces of the beam are kept at constant temperature by the surrounding media. Thereafter, the associated nonlinear thermal deformation fields are analyzed theoretically making use of von Karman's deformation theory under the assumption of Bernoulli-Euler's hypothesis. As for the nonlinear response of the beam, the stationary principle of total potential energy is employed, and the numerical calculations are carried out for the thermal buckling behavior of a simply supported beam, making use of the calculating program for the nonlinear search procedure. The results for the thermal pre- and postbuckling behaviors are shown in the figures, and the influences of the nonhomogeneous material properties are discussed briefly.

TRANSIENT THERMAL STRESS AND DEFORMATION OF A LAMINATED COMPOSITE BEAM DUE TO PARTIALLY DISTRIBUTED HEAT SUPPLY

Abstract This paper is concerned with a two-dimensional transient thermal stress analysis of a laminated beam due to a partially distributed heat supply. The beam is composed of different materials in multilayers. For the laminated composite beam we use the finite cosine transform and the Laplace transform for the temperature field and we adapt the elementary beam theory to the thermoelastic field. We then evaluate the temperature change, thermal stress distribution, and thermal deformation in a transient state. We apply the proposed theoretical method to the analysis of a beam with nonhomogeneous material properties, and examine the distributions of thermal stress and thermal deformation and the effect of relaxation of the stress distributions in a nonhomogeneous beam.

Transient thermal stress analysis of a multilayered composite laminate cylinder with a uniformly distributed heat suply and [its analytical development to nonhomogeneous materials

As one of the analytical models of the thermal stress problem for composite materials, we consider a hollow circular cylinder composed of multilayered composite laminate and discuss the transient thermal stress problems of a hollow cylinder with a uniform heat supply from the outer or inner surface. In studying the analytical developments for a multilayered composite cylinder, we introduce the method of Laplace transform for the temperature field and Airy's stress function method for the thermoelastic field. and then evaluate the temperature and thermal stress distributions in a transient state. Extending the theoretical developments proposed in the present paper to the analysis of a hollow cylinder with nonhomogeneous material properties, we examine the thermal stress distributions and the effect of relaxation of stresss values in nonhomogeneous cylinders made of functionally gradient material.

Predicted dynamic response of a composite beam with history-dependent damage

The transverse vibration solution for both uniform and non-uniform (variable cross-section) beams, with homogeneous or non-homogeneous (such as composites) linear elastic material properties has been widely discussed and is well documented. However, spatial variations in material properties due to history-dependent damage have not been previously considered. In this paper, the internal state variable concept is introduced to account for the cumulative stress-induced damage in a simple composite beam structure resulting from a fatigue-type loading of several hundred thousand cycles. Furthermore, the transverse vibration solution based on the history-dependent material is presented for a simple beam.

Yarn Tensile Property for Analysis

Along with the woven structure, the material property of the yarn that is intensified or weakened under the woven deformation will be a primary factor to govern the mechanical characteristics of fabrics. Out of these diversity the attempt to grasp the material non-linearity of the yarn, that is the three dimensional assemblies of filaments has been made actively. However, the experimental research to evaluate the heterogeneous characteristics of the yarn has not carried out popularly.In the first part of this paper, the non-linear and non-homogeneous material properties of the yarn under the tensile and compressive deformation are cleared up by experiment. Secondly, for the purpose of introducing the optimum yarn property to designing system on woven fabrics, the effect of tensile and compressive properties of the yarn on the uniform biaxial tensile characteristics of plain weaves is cleared up by an analytical research.It is made clear that the material property of the yarn against tensil deformation shows an essentially nonhomogeneous and non-linear characteristics influenced by the specimen length. Subsequently, the unsymmetric shape deformation and heterogeneous distribution of filaments in the yarn cross section subjected to compressive displacement can be observed by a microscope. Also the non-linearity of compression ratio α, indicated in the previous paper can be measured. The influence of heterogeneous property of the yarn upon tensile deformation of plain weaves is cleared up by analyzing the uniform biaxial extension of plain weaves, especially in its large deformation area. And it is considered that the available guideline for the practical woven design can be given by taking into account of the average filament length of the yarn for the tensile rigidity of the consituent rahmen element and using 1/4 to 1/2value as compression ratio α.

Macroscopic isotropy of lung expansion

The presence of geometrical irreversibility in excised human lungs has been invoked by Hills (1971) as a major source of pressure-volume hysteresis. We have repeated similar experiments on the smaller fresh rabbit lung supported by saline such that distortion due to its own weight was minor. In the air-filled state dimensional changes between orthogonally-placed pleural markers were nearly equal on inflation and deflation paths (excluding the first cycle after degassing), while at the same time pressure-volume (P-V) hysteresis was large. With saline in the lungs, expansion was slightly more irregular although surface strain in one axis was typically within 10% of that on an axis at right angles. Since P-V hysteresis in the saline preparation was small, but large in the air-filled lung, geometrical irreversibility did not correlate with the presence of P-V hysteresis. It is further demonstrated that the equations proposed to relate geometrical irreversibility to open P-V loops must be corrected to conform with energy conservation. We conclude that both nonelastic and nonhomogeneous material properties are required in order for geometrical irreversibility to be manifested, but conversely that the presence of this irreversibility cannot be used to quantitatively predict or explain P-V hysteresis.

Monte Carlo solution of structural dynamics

The recent advent of high speed digital computers has made it not only possible but also highly practical to apply the Monte Carlo techniques to a large variety of engineering problems. In this paper a technique of digital simulation of multivariate and/or multidimensional Gaussian random processes (homogeneous or nonhomogeneous) which can represent physical processes germane to structural engineering is presented. The paper also describes a method of digital simulation of envelope functions. Such simulations are accomplished in terms of a sum of cosine functions with random phase angles and used as the basic tool in a general Monte Carlo method of solution of a wide class of problems in structural engineering. Most important problems for which the method is found extremely useful includes (a) numerical analysis of dynamic response of nonlinear structures to random excitations, (b) time domain analysis of linear structures under random excitations performed for the purpose of obtaining a kind of information, such as first excursion probability and time history of a sample function, that is not obtainable from the standard frequency domain analysis, (c) numerical solution of structural problems involving randomly nonhomogeneous material property such as wave propagation through random medium, and (d) dynamic analysis of extremely complex systems such as those involving structure-fluid interaction. Numerical examples of some of these problems are presented.

Stress-wave propagation in a class of nonhomogeneous elastic media.

A scheme for changing one of the independent variables is used to transform the curvilinear characteristics associated with continuously nonhomogeneous material properties into straight lines of equal slope. By using this scheme, some of the practical difficulties caused by curvilinear characteristics are alleviated. The characteristic relations and appropriate jump conditions in the transformed space-time plane are derived for a hyperbolic system of quasi-linear partial differential equations of first order for two functions of two independent variables. The resulting equations are solved numerically. Accurate results are obtained for several cases in which previous investigators had encountered difficulties. In addition to checking against existing solutions, the authors also applied the method to problems for which solutions had not previously been obtained.