Showing papers on "Elasticity (economics) published in 1973"

Existence Theorems in Elasticity

Abstract: The subject to be developed in this article covers a very large field of existence theory for linear and nonlinear partial differential equations. Indeed, problems of static elasticity, of the propagation of waves in elastic media, and of the thermodynamics of continua require existence theorems for elliptic, hyperbolic and parabolic equations both linear and nonlinear. Even if one restricts oneself to linear elasticity, there are several kinds of partial differential equations to be considered. In static problems we encounter second order systems, either with constant or with variable coefficients (homogeneous and non-homogeneous bodies), scalar second order equations (for instance either in the St. Venant torsion problems or in the membrane theory), fourth order equations (equilibrium of thin plates), eighth order equations (equilibrium of shells). Each case must be considered with several kinds of boundary conditions, corresponding to different physical situations. On the other hand, to every problem of static elasticity corresponds a dynamical one, connected with the study of vibrations in the elastic system under consideration. Moreover, problems of thermodynamics require the study of certain diffusion problems of parabolic type. In addition to that, the study of materials with memory requires existence theorems for certain integro-differential equations, first considered by Volterra.

Interpreting the Effect of Distance on Migration

Abstract: In this paper I discuss the economic (and other) determinants of the adverse effect of distance on migration, which is demonstrated by the negative distance elasticity of migration flows. These determinants are sorted and classified into two groups: (1) increasing (with distance) psychic cost and (2) diminishing (with distance) information. I further discuss how aging and education respectively influence the relative importance of these two groups. Using data on flows of migrants cross-classified by age and by education, I estimate the effect of age and education on the distance elasticity of migration. The statistical hypothesis that aging does not affect the distance elasticity whereas increasing education strongly diminishes the absolute value of the distance elasticity is accepted. The acceptance of this hypothesis, coupled with my theoretical consideration, implies that the adverse effect of distance on migration is basically a diminishing-information phenomena.

Elastic Constants of Polycrystals

Abstract: The elastic constants of polycrystals and similar disordered materials are calculated. Exact formal solutions for the effective tensors of the elastic constants and of the compliances are given. Analytical approximations are derived by an expansion in powers of the anisotropy. Using the t-matrixmethod of scattering theory better approximations are obtained for highly anisotropic materials. Especially two new approximations are given, representing upper and lower bounds for the effective constants.

The thickness of the epidermis

Abstract: SUMMARY Epidermal thickness has been accurately measured on 214 samples of skin from 188 volunteers. Variations with the individual, body site, sex and age are described and discussed. An original technique of measurement has been developed which has several advantages over conventional methods. In particular, quick straight-forward measurements are possible on volunteer skin rather than post mortem material, and the method eliminates errors arising from the skin's elasticity. These improvements in accuracy have confirmed that much information in the literature on epidermal thickness, is misleading as the results are based on inaccurate techniques of measurement.

Boundary Value Problems of Elasticity with Unilateral Constraints

Abstract: In the preceding article “Existence Theorems in Elasticity”, which henceforth will be cited as E.T.E.1, I have treated boundary value problems of Elasticity in the case when the side conditions to be associated with the differential equations of equilibrium correspond to bilateral constraints imposed upon the elastic body. In this article I will treat the analytical problems which arise when unilateral constraints are imposed.

Torsional elasticity of human skin in vivo

Abstract: Measurements of physical properties of the intact human skin are described. An analysis of the measurements yields parameters that characterize elastic, visco-elastic and plastic properties. Between 6 and 61 years the elastic component of the extensibility of the skin under torsional conditions increases with age. The visco-elastic and plastic components are constant up to an age of fourty; at higher ages they show a small tendency to increase. Moduli of elasticity of the intact human skin derived from the torsion measurements yield values between about 2×104 N/m2 and 105 N/m2, the highest values corresponding to the youngest age. From these values the moduli of elasticity of the elastic fibres in the living skin are estimated between about 2×106 N/m2 and 107 N/m2.

Income Elasticity of Housing Demand

Abstract: This paper estimates a housing demand function from a four year panel study. The findings indicate that the income elasticity of housing demand is around .6 or .7 for owners and around .5 for renters. This means that the percentage of income spent on housing declines as income rises, and that the property tax falls more heavily on the poor than on the rich. This finding differs from earlier studies which were based on city averages rather than panel studies, and is therefore more reliable. The study also found that, other things equal, the old demand more housing than the young, whites more than nonwhites, and female headed households more than male headed households. INCOME ELASTICITY OF HOUSING DEMAND

The linearized theory of elasticity

Abstract: This chapter presents a summarization of three-dimensional equations governing isothermal linearized elasticity of a homogeneous isotropic medium. The general system of equations governing the three-dimensional motion of an elastic body in the material description is strongly nonlinear. Many wave propagation effects in elastic solids are described by a linearized theory. The chapter further presents a summarization of the basic equations of the linearized theory of elasticity and the linearized equations in rectangular, spherical, and cylindrical coordinates. The governing equations for an ideal fluid are also discussed in the chapter. A fluid at rest or in uniform flow cannot sustain shear stresses. Hence, the state of stress is purely hydrostatic. An ideal—nonviscous—fluid is a fluid that cannot sustain shear stresses even when it is in motion.

Price elasticity of demand for municipal water: A case study of Tucson, Arizona

Abstract: Estimates of the price elasticity of demand (the proportional response of consumption to price change) for municipal water in Tucson, Arizona, were derived by statistical regression procedures. A significant shift in demand was found to have occurred subsequent to 1964. The price elasticity was estimated at about −0.63 during 1946–1964 and −0.41 during 1965–1971. These results are consistent with those obtained in other studies of urban water demand in the arid parts of the western United States. The data subjected to statistical analysis were annual observations of consumption, price, and other factors for one community in contrast to the more typical approach using cross-sectional observations of a number of communities during a specific time period.

On the Principle of Stationary Complementary Energy in the Nonlinear Theory of Elasticity

Abstract: Until recently the famous principle of minimum complementary energy of the classical linear theory of elasticity has defied all attempts at an effective generalization to the nonlinear case where t...

Rayleigh‐type surface wave on a linear viscoelastic half‐space

Abstract: The analytic solution for a Rayleigh‐type surface wave on a linear viscoelastic half‐space is obtained. The general viscoelastic solution predicts several properties of the surface wave distinct from those predicted by elasticity. The velocity, absorption coefficient, and displacement field are described theoretically.

The Governing Equations and Extremum Principles of Elasticity and Plasticity Generated from a Single Functional*—Part I

Abstract: A new theoretical framework is described which generates, in a characteristic or canonical form, the governing equations and (if appropriate) inequalities of a wide class of problems in applied mathematics from a single generating functional. Variational and dual extremum principles are expressed in terms of that functional. The theory is first illustrated, here in Part I, by applying it to the familiar contexts of classical elasticity and the rigid/plastic yield-point problem. Precise identification of certain linear operators and inner product spaces is entailed. The unifying effect of the theory is emphasized by working out, in a sub-sequent Part II, further applications in finite elasticity and in incremental plasticity from a stressed state with allowance for geometry changes. New results are obtained, and the connection indicated between certain approximate methods of structural mechanics, in particular the finite-element method.

Elastic constants in singlet ground-state systems: PrSb and Pr

Abstract: The effect of crystal-field levels on the elastic constants has been measured for the singlet ground-state system PrSb. The results can be accounted for quantitatively. Elastic-constant measurements in double-hexagonal close-packed Pr reveal also strong crystal-field effects.

Elasticity of some mantle crystal structures. II.

Abstract: The single-crystal elastic constants are determined as a function of pressure and temperature for rutile structure germanium dioxide (GeO2). The data are qualitatively similar to those of rutile TiO2 measured by Manghnani (1969). The compressibility in the c direction is less than one-half that in the a direction, the pressure derivative of the shear constant is negative, and the pressure derivative of the bulk modulus has a relatively high value of about 6.2. According to an elastic strain energy theory, the negative shear modulus derivative implies that the kinetic barrier to diffusion decreases with increasing pressure.