Showing papers on "Elasticity (economics) published in 1992"

Locking effects in the finite element approximation of elasticity problems

Abstract: We consider the finite element approximation of the 2D elasticity problem when the Poisson ratiov is close to 0.5. It is well-known that the performance of certain commonly used finite elements deteriorates asv?0, a phenomenon calledlocking. We analyze this phenomenon and characterize the strength of the locking androbustness of varioush-version schemes using triangular and rectangular elements. We prove that thep-andh-p versions are free of locking with respect to the error in the energy norm. A generalization of our theory to the 3D problem is also discussed.

Linear finite element methods for planar linear elasticity

Abstract: A linear nonconforming (conforming) displacement finite element method for the pure displacement (pure traction) problem in two-dimensional linear elasticity for a homogeneous isotropic elastic material is considered. In the case of a convex polygonal configuration domain, error estimates in the energy (L[sup 2]) norm are obtained. The convergence rate does not deteriorate for nearly incompressible material. Furthermore, the convergence analysis does not rely on the theory of saddle point problems. 22 refs.

Composite and Reinforced Elements of Construction

Abstract: Part 1 Mechanics of inhomogeneous deformable solids: basic relations of continuum mechanics basic equations of thermoelasticity and electroelasticity mechanical models of composite materials. Part 2 Asymptotic homogenization of regular structures: homogenization techniques for periodic structures homogenization method for regions with a wave boundary local problems and effective coefficients. Part 3 Elasticity of regular composite structures: homogenization of the linear elasticity problem laminated composites - effective properties and fracture criteria effective characteristics of unidirectional fibre composites plane elasticity problem for a periodic composite with a crack homogenization of the geometrically nonlinear elasticity problem for a periodic composite elastic stability equatiions. Part 4 Thermoelasticity of regular composite structures: homogenization of thermoelasticity problem fibre composites - local stresses and effective properties laminated composite with prescribed thermoelastic properties composite material design. Part 5 General homogenization models for composite shells and plates with rapidly varying thickness: elasticity problem for a shell of a regularly nonhomogeneous material with wavy surfaces thermal conductivity of a curved thin shell of a regularly nonhomogeneous material with corrugated surfaces thermoelasticity of a curved shell of regularly nonhomogeneous material with corrugated surfaces geometrically nonlinear problem for a thin regularly nonhomogeneous shell with corrugated faces. Part 6 Structurally nonhomogeneous periodic shells and plates: local problem formulation for structurally nonhomogeneous shells and plates of orthotropic material an approximate method for determining the effective properties of ribbed and wafer shells effective properties of a three-layered shell with a honeycomb filler elastic moduli and local stresses in wafer type plates and shells, including the interaction between cell elements stretching of shells or plates reinforced by regular system of thin surface strips shells and plates with corrugated surfaces of regular structure. Part 7 Network and framework reinforced shells and plates with regular structure effective elastic moduli of a network reinforced shell effective thermoelastic properties of network reinforced shells heat conduction of network reinforced plates and shells constitutional equations for network reinforced plates and shells of rectangular, rhombic and triangular structure composite shells with high stiffness framework type reinforcement. Part 8 The fundamental solution of the periodic elasticity problem: the derivation of a doubly periodic fundamental solution of the three-dimensional elasticity problem transformation of the doubly periodic fundamental solution of the elasticity problem singly periodic fundamental solution of the plane elasticity. Appendices.

Bending elasticity of electrically charged bilayers : coupled monolayers, neutral surfaces, and balancing stresses

Abstract: We investigate in terms of Poisson-Boltzmann theory the contribution of electrostatic double layers to the bending elasticity of charged symmetric bilayers, considering in detail three special problems: first, the coupling of the monolayers by the electric field traversing a curved bilayer; second, the dependence of the elastic moduli on the position of the monolayer's neutral surface; and third, the role of the mechanical stresses balancing the electric ones.

Peak and off‐peak residential water demand

Abstract: Residential water demand is studied with microdata and with allowance for (1) seasonal differences in price elasticity, (2) a dynamic adjustment process, (3) a marginal price specification, (4) cross-price effects between peak and off-peak demand, and (5) the inclusion of a detailed set of household demographic variables including accurate measures of age distribution and household income. The findings are that the peak (summer) price elasticity of demand is more than twice the off-peak elasticity; cross price effects are important at the 5% level of significance; variables measuring household income, property value, related property features, and age distribution are simultaneously significant; and finally, peak period adjustment rates are found to be less than off-peak rates.

Pseudomomentum and material forces in nonlinear elasticity : variational formulations and application to brittle fracture

Abstract: This work examines critically the various formulations of the balance of linear momentum innonlinear inhomogeneous elasticity. The corresponding variational formulations are presented. From the point of view of the theory of elastic inhomogeneities, the most interesting formulations are those which, being either completely material or mixed-Eulerian, exhibit explicitly the inhomogeneities in the form ofmaterial forces. They correspond to the balance ofpseudomomentum, a material covector which is seldom used but which we show to play a fundamental role in the Hamiltonian canonical formulation of nonlinear elasticity. The flux associated with pseudomomentum is none other than theEshelby material tensor. Applying this formulation to the case of an elastic body containing a crack of finite extent, the notion of suction force acting at the tip of the crack follows while afracture criterion a la Griffith can be deduced from a variational inequality. Possible extensions to higher-grade elastic materials and inelastic materials are indicated as well as the role played by pseudomomentum in the quantization of elastic vibrations.

Price Elasticity Dynamics over the Adoption Life Cycle

Abstract: Little empirical research has been conducted to test the dynamic behavior of elasticities over the product life cycle. Competing specifications of price elasticity dynamics are examined to test the...

Hybrid trefftz plane elasticity elements with p ‐method capabilities

Abstract: A family of p-method plane elasticity elements is derived based on the hybrid Trefftz formulation.1 Exact solutions of the Lame-Navier equations are used for the intra-element displacement field together with an independent displacement frame function field along the element boundary. The final unknowns are the parameters of the frame function field consisting of the usual degrees of freedom at corner nodes and an optional number of hierarchic degrees of freedom associated with the mid-side nodes. Since the element matrices do not involve integration over the element area, the elements have a polygonal contour with an optional number of curved sides. The quadrilateral element has the same external appearance as the conventional p-method plane elasticity element.2,3 But unlike in the conventional p-method approach, suitable special-purpose Trefftz functions are generally used to handle the singularity and/or stress concentration problems rather than a local mesh refinement. The practical efficiency of the new elements is assessed through a series of examples.

A Variational Approach to Three-Dimensional Elasticity Solutions of Laminated Composite Plates

Abstract: The displacements in a laminated composite are represented as products of two sets of unknown functions, one of which is only a function of the thickness coordinate and the other is a function of the in-plane coordinates (i.e., separation of variables approach), and the minimization of the total potential energy is reduced to a sequence of iterative linear problems. Analytical solutions are developed for cross-ply and angle-ply laminated composite rectangular plates. The solution for simply-supported cross-ply plates under sinusoidal transverse load reduces to that of Pagano. Numerical results for stresses and is placements for antisymmetric angle-ply laminates are presented. The three-dimensional elasticity solutions developed are important because they can be used to study the behavior of composite laminates, in addition to serving as reference for approximate solutions by numerical methods and two-dimensional theories.

New results in the theory of elasticity for two-dimensional composites

Abstract: We bring together and discuss a number of exact relationships in two-dimensional (or plane) elasticity, that are useful in studying the effective elastic constants and stress fields in two-dimensional composite materials. The first of these dates back to Michell (1899) and states that the stresses, induced by applied tractions, are independent of the elastic constants in a two-dimensional material containing holes. The second involves the use of Dundurs constants which, for a composite consisting of two isotropic elastic phases, reduce the dependence of stresses on the elastic constants from three independent dimensionless parameters to two. It is shown that these two results are closely related to a recently proven theorem by Cherkaev, Lurie and Milton, which we use to show that the effective Young's modulus of a sheet containing holes is independent of the Poisson's ratio of the matrix material. We also show that the elastic moduli of a composite can be found exactly if the shear moduli of the components are all equal; a previously known result. We illustrate these results with computer simulations, where appropriate. Finally we conjecture on generalizations to multicomponent composite materials and to situations where the bonding between the phases is not perfect.

Experimental determination of elastic constants of Oshima granite, Barre granite, and Chelmsford granite

Abstract: Employing polyhedral specimens, longitudinal and shear wave velocities were measured in various directions of propagation and polarization. Sound velocities showed orthorhombic elasticity in all of the rocks. With the assumption of orthorhombic elasticity the nine stiffness constants of all samples were determined by the sound velocities under atmospheric pressure and Kelvin-Christoffel's equation. Twenty-one stiffness constants of Oshima granite, determined without assuming any symmetry, also showed orthorhombic features. Directions of the symmetry axes agreed well with the orientation of the preexisting cracks. Akaike's Information Criterion showed that the orthorhombic model with nine nonzero elastic stiffnesses was better than the model having 21 nonzero elastic stiffnesses for Oshima granite. The polyhedrons of two granitic rocks were loaded under hydrostatic pressure. All components of the stiffness constants increased with pressure. Under pressure of more than 120 MPa, two granitic rocks were approximately isotropic. The results show that oriented microcracks are mainly responsible for the orthorhombic elasticity of the granitic rocks and also indicate that dry oriented cracks can not be a cause for the anisotropic elasticity of granites at depths of more than 6–8 km.

Hierarchic models for laminated composites

Abstract: The principles governing the formulation of hierarchic models for laminated composites are discussed. The essential features of the hierarchic models described herein are: (1) the exact solutions corresponding to the hierarchic sequence of models converge to the exact solution of the corresponding problem of elasticity for a fixed laminate thickness; and (2) the exact solution of each model converges to the same limit as the exact solution of the corresponding problem of elasticity with respect to the laminate thickness approaching zero. Hierarchic models make the computation of any engineering data possible to an arbitrary level of precision within the framework of the theory of elasticity.

Intracavity ultrasonic device for elasticity imaging

Abstract: An intracavity ultrasonic device for elasticity imaging of human tissue to obtain palpation information in a quantitative form by using a probe that has an ultrasonic transducer at one end thereof, the probe having a small diameter and being capable of being inserted inside a conduit of a body. An outer elastic sheath surrounds the probe and is sealed so that it can be filled with a fluid under pressure to create a chamber surrounding the ultrasonic transducer while the sheath is on the interior of the bodily conduit to be examined. By regulating the interior pressure, the sheath can be made to expand against the interior of the conduit and change the deformation of the tissue forming the conduit. The sheath includes a region of greater elasticity adjacent the transducer to facilitate localized deformation of a selected region of the bodily conduit wall. Obtaining images of the selected conduit region before and after compression provides data to calculate the elasticity of tissue in that region and surrounding regions. Elasticity is an informative characteristic for tumor detection as is known from the palpation technique of detecting tumors.

Interfacial stability of multilayer viscoelastic fluids in slit and converging channel die geometries

Abstract: Interfacial stability of stratified Oldroyd‐B liquids with constant and shear rate dependent viscosity in slit and converging channel die geometries has been examined by utilizing both asymptotic and numerical techniques. To elucidate the mechanisms by which shear thinning viscosity and elasticity influence interfacial stability, neutral stability contours in the parametric space of viscosity, depth, and elasticity ratio as well as interfacial tension and Reynolds number have been constructed. Our results indicate that elasticity and viscosity stratification as well as inertial forces affect the stability of the interface at all disturbance wavelengths. Moreover, it is found that neutral stability contours are substantially altered in converging channel flows. Overall, our analysis indicates that under certain physical (i.e., viscosity and elasticity ratio) and geometric conditions (i.e., depth ratio and channel convergence) stable regions at all disturbance wavelengths can be attained. Hence, based on th...

On two circular inclusions in harmonic problems

Abstract: In this paper, we derive the solution for two circular cylindrical elastic inclusions perfectly bonded to an elastic matrix of infinite extent, under anti-plane deformation. The two inclusions have different radii and possess different elastic properties. The matrix is subjected to arbitrary loading. The solution is obtained, via iterations of Mobius transformations, as a rapidly convergent series with an explicit general term involving the complex potential of the corresponding homogeneous problem, i.e., when the inclusions are absent and the matrix material occupies the entire space and is subjected to the same loading. This procedure has been termed \"heterogenization.\" The technique used can be applied to problems governed by Laplace's equation. Finally some remarks are included concerning the relation of our solution to the theory of discontinuous groups and automorphic functions and possible generalizations to multiple inclusions.

The Price Elasticity of Mass Preferences.

Abstract: I compare the price elasticity of economic and political preferences. My central hypothesis is that willingness to pay, whether expressed verbally or through cash transactions, is more price-elastic for economic consumption goods than for public goods. I find that increases in price greatly diminish the proportion of people willing to pay for consumer goods, such as housing or hardback books; whereas the proportion willing to pay more in taxes to support a public good, such as environmental protection or shelter for the homeless, is much less responsive to changes in price. I conclude by discussing the theoretical and political implications of willingness to pay for public and private goods.

Elastomeric polymer networks

Abstract: Looking at recent advances in the area of elastomers and rubber-like elasticity, this monograph reviews and evaluates existing elastomers and presents some new results.

A time integration algorithm for elasto‐viscoplastic cubic crystals applied to modelling polycrystalline deformation

Abstract: An algorithm for integrating the constitutive equations for an elasto-viscoplastic cubic crystal is presented which is shown to be easily employed in a polycrystalline analysis. Anisotropic elastic behaviour is incorporated into the standard constitutive equations for ductile single crystals. The algorithm is shown to be efficient, robust and general. The primary advantage of this algorithm is that is provides an implicit integration of the plastic deformation gradient while including the elastic response. This permits taking large time steps while maintaining accuracy and stability. Several polycrystalline examples are presented to demonstrate the effect of the time step on the solution. Examples also are presented which compare the algorithm described herein to an algorithm which neglects the elastic part of the deformation. In addition, the effect of the anisotropic component of the elasticity is investigated by comparing the results with those obtained assuming isotropic elasticity.

Droplet dynamics in water-in-oil microemulsions and macroemulsions stabilised by non-ionic surfactants. Correlation of measured rates with monolayer bending elasticity

Abstract: We have investigated the structure and inter-droplet exchange rates of water-in-oil (w/o) microemulsions, and the stabilities of w/o emulsions stabilised by three different non-ionic surfactants of the alkylpolyoxyether (CnEm) type. The surfactants investigated were C8E3, C10E4 and C12E5. The aim of the study was to test whether there is a correlation between the measured rates and the bending elasticity constant K for the different surfactant systems. Care was taken to ensure that, as far as possible, the different systems were compared in equivalent states with regard to equilibrium-phase behaviour. For the three systems studied, it was found that the energy barrier to inter-droplet exchange between microemulsion droplets increases in the order C8E3 < C10E4 < C12E5. The emulsion stability also increases in this same order. For both the microemulsion and macroemulsion systems, the effectiveness of the different monolayers in stabilisng the droplets is found to scale approximately with the bending elasticity constant K. Thus, the data suggest that K is an important determinant of kinetic stability in surfactant monolayer stabilised emulsions.

Transverse and longitudinal waves at the air-liquid interface in the presence of an adsorption barrier

Abstract: Sternling and Scriven1 showed that the Marangoni elasticity induced by the isothermal transfer of a surface active solute between two adjacent immiscible bulks could result in convective motion.