Showing papers on "Elasticity (economics) published in 1981"

Description of Anisotropic Damage Application to Elasticity

Abstract: A general approach to anisotropic damage is presented starting from the concept of effective stress tensor. Some existing possibilities are discussed and the special case of uncoupled anisotropic damage is presented. The influence of damage on the elastic response is then investigated and it is shown that direct substitution of the effective stress tensor in the constitutive equation usually is not admissible. Some possibilities are presented to overcome this difficulty.

Ultrasonic Measurement of Orthotropic Elastic Constants of Bovine Femoral Bone

Abstract: Using a pulse transmission ultrasound method, we have determined the elastic properties of bone samples taken from along the length and around the periphery of a bovine femur. Twenty specimens, in the form of 5-mm cubes, were tested. All nine of the orthotropic elastic constants were determined for each specimen. Analysis of our data indicate that there are statistically significant variations from the usual assumption of transverse isotropy.

Elastic constants and molecular association of cyano‐substituted nematic liquid crystals

Abstract: The dielectric and elastic properties of cyano‐substituted nematic liquid crystals are investigated. The results are discussed in terms of molecular properties and molecular association.

Topics in finite elasticity

Abstract: Kinematics: Stress Elastic materials, Change of observer Material symmetry Simple shear The Piola-Kirchhoff Stress Hyperelasticity The elasticity tensor The boundary-value problem Variational formulational stability and uniqueness Incompressible materials Deformations of a cube Anti-Plane Shear.

Foam seat and back cushions

Abstract: Disclosed is a seat cushion constructed of cellular elastic material wherein its design provides more uniform distribution of supportive forces exerted by the cushion over a larger area of the anatomical portions of a person seated thereon for minimizing squeezing and restriction of arteries and nerves located in the anatomical portions of a person seated on the cushion. The cellular elastic material of the seat cushion is divided into segments having different moduli of elasticity. The modulus of elasticity of each segment is inversely proportional to the pressure exerted on such segment by the anatomical portion of a person seated on the cushion. Also disclosed is a back cushion of similar design.

Exterior Penalty Methods for Contact Problems in Elasticity

Abstract: This paper reviews recent results of Oden, Kikuchi, and Song [4] on the use of exterior penalty methods as a basis for finite element approximations of contact problems in linear elasticity.

On some numerical methods for the solution of the plane elasticity problem for bodies with cracks by means of singular integral equations

Abstract: Comparison is given of the accuracy of calculation of stress intensity factors at the crack tips by various methods when solving plane elasticity problems for bodies with cruciform and edge cracks. It is shown that, within the range of quadrature formulas for singular integrals discussed, the type of the formula chosen for the solution of an equation, if used correctly, affects negligibly the accuracy of the stress intensity factor evaluation at the crack tip, and in view of this a method is proposed based on simple relationships.

[Material properties and strength behaviour of spongy bone tissue at the coxal human femur. (author's transl)].

Abstract: Schlüsselwörter: Gebietsfestlegung im Knochenschnitt, Definition der Orthotropierichtungen, Elastizitäts-, Schubmoduli, Querkontraktionszahlen, Dehnungskoeffizientenmatrizen, Altersabhängigkeit der Materialkennwerte. Für sechs typische Strukturgebiete der Spongiosa im Schenkelkopf des proximalen Femur-Teils wurde unter Anwendung statistischer Auswertungsmethoden auf die experimentell gewonnenen Resultate und unter Annahme topographisch orthotropen Festigkeitsverhaltens des Knochenwerkstoffes die entsprechenden Dehnungskoeffizientenmatrizen [S] berechnet. In der Auswertung werden Zusammenhänge zwischen Strukturdichte und Strukturaufbau der Spongiosa aufgezeigt, sowie die Abhängigkeits des Elastizitätsmoduls, des Schubmoduls und der Querkontraktionszahl von der Strukturdichte, vom Strukturaufbau des Knochenmaterials, vom Geschlecht und vom Lebensalter des Menschen auf der Basis statistischer Methoden.

Determination of elasticity and viscosity coefficients in a ferroelectric smectic c liquid crystal

Abstract: Experimental methods of determination of the twist elasticity and rotational viscosity coefficient in ferroelectric smectics C are described. Temperature dependences of the coefficients obtained for a typical smectic C liquid crystal are presented.

A finite element computer model of the hole pressure problem

Abstract: This paper extends some earlier work in which consideration was given to the flow of a second-order visco-elastic liquid through a channel composed of two parallel plates, one plate having a rectangular slot cut into it perpendicular to the flow direction. In the present work the problem is re-solved for the case of an implicit Oldroyd-type model and solutions obtained using a numerical finite element technique. Severe numerical convergence difficulties are encountered when the elasticitiy of the liquid is increased. The relationship between the ratio of the hole pressure to first normal-stress difference and the Reynolds number is investigated for both Newtonian and elastic liquids and the results compared with a simple analytical analysis of Tanner and Pipkin and with the second-order fluid results of the previous paper. It is found that the value of this ratio falls as the Reynolds number is increased from zero up to 10 but that the rate of decay is less than for the second-order liquid. However in the present work elasticity is found to have a significant effect even at small Reynolds numbers, so that the ratio can deviate quite considerably from the Tanner-Pipkin theoretical value of 0.25. Streamline patterns plotted for various flow conditions indicate that both inertia and elasticity bring about an asymmetry in the streamlines which dip into the hole, and in the vortex contained within the hole, but that the two factors work against one another so that it is possible for an elastic liquid to see a symmetric pattern for Reynolds numbers considerably beyond the range of the Tanner-Pipkin theory.

Existence of Solutions in Finite Elasticity

Abstract: Very few exact solutions are known to static and dynamic problems of finite elasticity, particularly in the case when the material is compressible. General theorems on existence of solutions provide reassurance that the theory is mathematically sound; for example it is important to understand whether or not solutions of the basic equations have singularities consistent with assumptions used in deriving the equations. But there are several other, equally important, reasons for studying questions of existence of solutions. One such is the establishment of convergence properties for numerical methods in elasticity (in this connection it should be noted that finite-difference schemes for certain partial differential equations may converge to solutions of different equations). Experience with other partial differential equations has also taught us that existence theorems are an essential prerequisite for the study of various qualitative properties of solutions (for example, bifurcation, stability and asymptotic behaviour). In a broader context, we today face problems in elasticity similar to unsolved questions in other branches of mechanics and physics, and the unifying nature of the theory of partial differential equations can thus lead us to hope, as has been the case in the past, that advances in elasticity will lead to corresponding progress in other fields. Here, however, we concentrate on a more specific reason for proving, or attempting to prove, existence theorems in elasticity, namely that it leads to information concerning the relationship between constitutive hypotheses (i.e. assumptions on the stored-energy function, or stress-strain law of the material) and smoothness properties of solutions.

A new method for the numerical solution of singular integral equations appearing in crack and other elasticity problems

Abstract: The solution of many elasticity problems and particularly crack problems can be reduced to the solution of a singular integral equation with a Cauchy type kernel (or a system of such equations). In this paper a new method of numerical solution of singular integral equations with Cauchy type kernels is proposed, based on the replacement of the unknown function by another function. This method presents some advantages over the previous methods under appropriate conditions. An application of the method to a crack problem in plane elasticity is also made.

Flexure Modulus of Orthodontic Stainless Steel Wires

Abstract: The flexure modulus of elasticity of standard stainless steel orthodontic wires was determined by the use of an iterative finite element technique to be 25.4 x 10(6) psi (175 x 10(3) MN/m2). This technique accounts for the configurational changes in the test specimens due to the relatively large deflection during the cantilever test. Under these conditions, the elementary strength of materials relationships does not accurately describe the flexure characteristics of the wires.

Fracture Mechanics and the Design of Wood Structures

Abstract: Applications of linear-elastic fracture mechanics concepts for treating brittle fracture of wood and wood products are discussed. The influence of orthotropic elasticity and heterogeneity of wood structure on the computational and experimental aspects of wood fracture are introduced. Several applications of fracture mechanics for the development of design criteria in timber engineering are discussed to illustrate the potential benefits of application of fracture mechanics in design codes.

Theory of elasticity of coherent inclusions by means of non-metric geometry

Abstract: The concept of extra or quasiplastic deformation is applied to the non-linear theory of elasticity of coherent inclusions in a matrix of different crystal structure. K.-H. Anthony's treatment of extra-deformation by means of non-metric differential geometry is reviewed. We replace his definition of the elastic connexion by a more obvious but equivalent one. The elastic effect of the inclusion can be represented by extra-dislocations whereas the extra-disclination density vanishes, even in the non-linear theory. It is shown that the elastic stress of an inclusion can be cancelled approximately by an arrangement of lattice dislocations. Extra-deformation and extra-dislocation density are specified for a simple model of an inclusion having suffered a martensitic transformation.

Non linear pattern selection in a problem of elasticity

Abstract: 2014 The buckling of long rectangular elastic plates offers the possibility of testing a recent proposal. The wavenumber of cellular structures in slightly supercritical conditions is determined by the boundary conditions. In the present case a supercritical decrease of the wavelength is predicted. Tome 42 ? 1 ler JANVIER 1981 LE JOURNAL DE PHYSIQUE LETTRES J. Physique LETTRES 42 (1981) LI L-4 1 er JANVIER 1981, Classification Physics Abstracts 03.40D Having in mind the wavelength selection in cellular flows, as in Rayleigh-Benard convection in large horizontal layers, S. Zaleski and the author [1] solved the question of non linear pattern selection in slightly supercritical conditions for one dimensional models. This sort of problem is formulated as follows : space dependent fluctuations with a (horizontal) fixed wavenumber, say qo, become linearly unstable around a homogeneous rest state whenever a control parameter, say 8, exceeds some critical value, which can be taken at s = 0. The growth of these fluctuations is limited by non linear effects and a new steady state is reached via a supercritical (or normal) bifurcation. In a large class of problems, for slightly positive values of 8 linearly unstable fluctuations grow from the homogeneous state whenever their wavenumber belongs to a band of width of order 81/2 near the threshold value qo. However, owing to the boundary conditions limiting the lateral extent of the structure, the supercritical steady pattern has its wavenumber in a much narrower band of width of order 8 near qo. The applicability of this sort of consideration to the Rayleigh-Benard problem is not obvious, since long rolls, when parallel to a lateral boundary, are unstable against a cross roll instability localized near this boundary [1]. One should account for the structure of these boundary rolls parallel to their axis. This structure is due either to the cross roll modulation or to lateral boundaries inhibiting their growth. A realistic treatment of this problem is not an easy task. Therefore it is of interest to look at a physical situation involving a non linear selection of the wavelength, but nevertheless permitting quantitative predictions from simple ab initio calculations. That is why I have considered the following version of the von Karman problem in elasticity of thin plates [2]. This is the buckling of long rectangular elastic plates [3] submitted to a load along their long axis (see Fig. 1). According to the general considerations of reference [1], whenever the length of the long axis, say L, is much larger than a quantity of order E-1, one may limit oneself to the consideration of a half infinite problem. The possible buckling patterns for a large (but finite) L are obtained by gluing together two half infinite solutions in a convenient way. We shall not consider this specific problem here ; it is treated in reference [1]. Fig. 1. At the centre of the figure the plate is represented from above; its cuts along the short (A) and long (B) are represented on the left and right. A similar figure is in reference [4]. Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyslet:019810042010100 L-2 JOURNAL DE PHYSIQUE LETTRES The von Karman [2] equations for the static buckling are [4, 5] :

Elasticity analysis of lung deformation problems.

Abstract: In the characterization of stress-strain relationships for the lung using solid continuum-mechanics analysis, the lung parenchyma is assumed to be in a state of uniform expansion and nonhomogeneous deformations are considered from the uniform state. If the nonhomogeneous deformations are small, nonhomogeneous lung deformation problems are reduced to those solvable using infinitesimal elasticity, since only the small superimposed deformations are considered. Using this incremental approach, the relevant elastic constants of lung parechyma have been measured and their applicability has been verified by comparing the results of the theoretical analysis of several nonhomogeneous deformation problems with experimental data.

The Elasticity of Derived Net Supply and a Generalized Le Chatelier Principle

Abstract: The Marshall (1920)-Hicks (1963) rules for the elasticity of derived demand for an input, which demonstrate how the price elasticity of demand for the input changes as the price elasticity of demand for the product, the price elasticity of supply of a competing factor, the first factor's cost share and the elasticity of substitution between the two factors change, have been generalized to the case where there are N inputs and one output by Sato and Koizumi (1970), (1973). Andrieu (1974) and Razin (1974) have also generalized the Marshall-Hicks rules to the case where there is one output and three inputs, but one of the inputs is fixed.' However, since most real life firms or industries produce a wide variety of products, it would appear to be useful to obtain rules for the price elasticity of derived supply for an output, where other output and input markets are allowed to adjust to the change in the price of the first output. The recent increases in energy prices have perhaps provided a reason for renewed interest in the microeconomic determinants of industry supply. In Section 5 below, we derive analogues to the Marshall-Hicks-Sato-Koizumi Rules in a multiple output framework. In Section 2, we list our assumptions on the technology and note some preliminary results from duality theory. In Section 3, we define the elasticity of derived (net) supply and we show that it will always be nonnegative in our model. We also compare the elasticity of derived supply, which takes into account adjustments induced by an increase in the price of the output in other input and output markets, with an ordinary price elasticity of supply, which holds the prices of the other inputs and outputs fixed. We also compare the above two elasticities with intermediate elasticities of derived supply that are obtained by assuming that some input and output prices are fixed but others are not. We find that the more markets that adjust to the price increase in the first market, the smaller the elasticity of derived supply becomes in the first market. We could term this an inverse Le Chatelier principle, since it acts in a manner which is seemingly opposite to the usual Le Chatelier principle (cf. Samuelson (1947), pp. 36-39), which says that the more markets that we allow to adjust to the effects of a price increase in the first market, the larger is the elasticity of supply in the first market. However, the two Le Chatelier principles are not really opposed. As we shall see later, our inverse Le Chatelier principle formally contains Samuelson's Le Chatelier principle as a special case. In Section 4, we consider the comparative statics effects of an exogenous increase in the price of the first good on a weighted average of other prices as well as on a weighted average of changes in the industry supply of other outputs and changes in the industry demand for other inputs, taking into account the "general equilibrium" repercussions on other markets of the increase in the price of the first good.