Showing papers on "Elasticity (economics) published in 1986"

Homogenization and optimal bounds in linear elasticity

Abstract: In their celebrated paper of 1963, HASHIN & SHTRIKMAN [1] addressed the problem of determining optimal bounds for the bulk and shear moduli of a statistically isotropic elastic composite material with arbitrary isotropic phase geometry. They derived a set of bounds for these moduli in the physically meaningful case of three-dimensional elasticity. In the case of a two phase composite, let K 1,/.1 and K 2,/*2 respectively denote the bulk and shear moduli for the first and the second phase, let K,/* denote their analogues for the composite and let 0 stand for the volume fraction of the first phase in the composite. Under the ordering restriction that both

Elasticity of uvarovite and andradite garnets

Abstract: The adiabatic single-crystal elastic properties of synthetic end-member uvarovite garnet (Ca3Cr2Si3O12) and a natural sample of 96% andradite garnet (Ca3Fe2Si3O12) have been measured at ambient conditions by Brillouin spectroscopy. The bulk modulus (Ks) and shear modulus (μ) of andradite (And) are Ks = 158 ± 2 GPa, μ = 90 ± 1 GPa, and those of uvarovite (Uv) are Ks = 165 ± 2 GPa and μ = 94 ± 1 GPa. Observed trends of the single-crystal elastic moduli (Cij) as a function of composition, and specifically the deviation from the Cauchy relation c12 = C44 are analogous between the Ca-bearing garnets grossular (Gr = Ca3Al2Si3O12)-And-Uv and other chemical systems such as the rock salt and corundum structure oxides, whereas other silicate garnets exhibit distinctly different behavior. Ks of andradite is substantially higher than previously estimated from data on garnet solid solutions. Garnets on the Gr-And join show a pronounced minimum in the Ks-composition relationship at a composition of approximately Gr24And76, indicating that ideal linear mixing of end-member elastic properties is inadequate to explain the elasticity of garnet solid solutions. The elastic properties of Gr-And and Al2O3-Cr2O3 solid solutions can be explained by incorporating a composition-dependent volume of mixing term into the expression for solid-solution elasticity. An evaluation of elasticity systematics relating the bulk sound speed and mean atomic weight, or Ks and molar volume, indicates that these relationships yield closer estimates of garnet elastic properties than does the seismic equation of state of Anderson (1967).

Optimal design in elasticity and plasticity

Abstract: A direct weight minimization subject to compliance constraints or plastic yielding constraints leads to a non-convex variational problem. Both the theoretical and the numerical analysis are unsatisfactory: the minimum weight is not achieved by any design, and the approximate designs oscillate as the element mesh is refined. We look for equivalent ‘relaxed problems’ with the same minima. They come from allowing composite materials constructed in an optimal way from the original materials. The constructions are different for elasticity and plasticity, but surprisingly the final relaxed problems are in some cases the same.

Stresses and deformations in cross-ply composite tubes subjected to a uniform temperature change

Abstract: This study investigates the effects of a uniform temperature change on the stresses and deformations of composite tubes and determines the accuracy of an approximate solution based on the principle of complementary virtual work. Interest centers on tube response away from the ends and so a planar elasticity approach is used. For the approximate solution a piecewise linear variation of stresses with the radial coordinate is assumed. The results from the approximate solution are compared with the elasticity solution. The stress predictions agree well, particularly peak interlaminar stresses. Surprisingly, the axial deformations also agree well, despite the fact that the deformations predicted by the approximate solution do not satisfy the interface displacement continuity conditions required by the elasticity solution. The study shows that the axial thermal expansion coefficient of tubes with a specific number of axial and circumferential layers depends on the stacking sequence. This is in contrast to classical lamination theory, which predicts that the expansion will be independent of the stacking arrangement. As expected, the sign and magnitude of the peak interlaminar stresses depend on stacking sequence. For tubes with a specific number of axial and circumferential layers, thermally induced interlaminar stresses can be controlled by altering stacking arrangement.

A justification of the one‐dimensional linear model of elastic beam

Abstract: In this paper we prove that the one-dimensional model of elastic beam is an approximation to the three-dimensional linear theory of elasticity.

On the effective thermal conductivity of multiphase composites

Abstract: While several micromechanical models have been developed today in the literature for two-phase media, the extent of their applicability to multiphase materials need yet to be investigated. The present paper studies the effective thermal conductivity of multicomponent composites, and concentrates on two methods: (a) the Mori-Tanaka model, (b) The “generalized self-consistent scheme”. The Mori-Tanaka method of “back-stress” previously developed in the context of elasticity of composites is applied here to the conduction problem. The “generalized self-consistent scheme”, based on a particle-matrix embedding in the effective medium, is studied in this paper in the context of multicomponent media and two variations of this method distinctly different in their imbedding procedure are proposed.

The Structure of Constant Elasticity Demand Models

Abstract: The demand model with constant price and income elasticities has been used extensively in applied agricultural economics. This paper analyzes the structure of incomplete systems of constant elasticity demand functions. It is demonstrated that there is a duality theory for incomplete demand systems that is analogous to the duality theory for complete systems. This theory permits the recovery of that portion of the direct and indirect preferences pertaining to the goods of interest, and we can calculate exact welfare measures for changes in income and in the prices of these goods. For an incomplete system of constant elasticity demands, the Slutsky symmetry restrictions for integrability are presented and the implied structure of the direct and indirect preferences with respect to the prices and goods of interest is derived.

Modulus of elasticity in bending of composites and amalgams.

Abstract: In this study, the modulus of elasticity in bending (a measure of rigidity) and transverse strength (a measure of edge strength) were determined for composites and amalgams. the results were as follows. The modulus of elasticity of microfilled composites is approximately one-third that of the macrofiller-containing composites. Composites containing a relatively coarse-sized macrofiller have a higher elastic modulus than those containing a finer macrofiller. The transverse strength of microfilled composites is approximately one half that of the macrofiller-containing composite, which, in turn, is close in value to the transverse strength of amalgam. High-copper amalgams are substantially more rigid than the traditional low-copper amalgams, but do not show large differences among themselves. The transverse strength among various amalgams does not appear to be related to amalgam type but does correlate to final Hg content. The modulus of elasticity of composites most likely to be used in posterior teeth is approximately one third of the modulus of elasticity of amalgam; that is, amalgams are three times more rigid.

Elastic properties of the feet of deer (Cervidae)

Abstract: Dynamic tests have been performed on the feet of deer, and on tendons removed from the feet, to determine their elastic properties. The results have been used to calculate the strain energy stored in each foot while it is on the ground in a fast galloping stride. This is compared with an estimate of the work done by the leg, and the energy-saving role of tendon elasticity is assessed.

Elasticities of Demand for Recreation Site and for Recreation Experience

Abstract: Substitution makes demand for recreation sites more elastic than that for recreation experiences. Assessment of site elasticity by direct and Clawson methods yielded elastic estimates empirically, whereas response to hypothetical increased costs of travel yielded inelastic demand for recreation experiences. It is important to use the appropriate figure in recreation evaluations.

Garment with gathered elastic regions and method of manufacture thereof

Abstract: As an example of a garment with gathered opening edges, in a disposable nappy (1) which can be shaped to form panties having a non-permeable outer layer (2) and an absorbent filling (3), the leg and waist regions are gathered by glued-on elastic material (7). In the gathered regions, the elastic material (7) is of different construction due to the different material concentration and due to the varying course of the material at the level of the elasticity. As a result, the gatherings can be adapted in an ideal manner to desired functions on the parts of the body to be covered by the gathered regions. The different shapes and courses of the elastic material (7) specified can best be achieved by using extrudable, self-adhesive, elastic material.