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By using a multipole-conformal mapping expansion for the wire charges we examine the accuracy of approximations for the transfer elastance (elastance is the inverse of capacitance) of a one dimensional array of wires (wire grid). A simple uniform fit is constructed by introduction of the decay factor from bipolar coordinates into existing formulas for this elastance.
Recent analyses of some of the test property data from the AGC-1 creep capsule are reported. Specifically the analyses of data for the effects of compressive creep strain on the Dynamic elastic modulus (by the fundamental frequency and ultrasonic velocity/tof methods) are reported. Statistical “t” testing was used to establish the statistical significance of any differences observed between the Dynamic elastic modulus of the creep (irradiated with compressive stress) and the control (irradiated without stress) specimens. Compressive creep strain does have a small effect on Dynamic elastic modulus, reducing it at the higher doses as volume turnaround is approached.
Selective laser melting (SLM) is an additive manufacturing technique commonly used in the rapid prototyping of components. The complexity of the SLM microstructure poses a unique challenge to deriving effective mechanical properties at different length scales. Representative volume elements (RVEs) are often used to homogenize the material properties of composites. Instead of RVEs, we use statistical volume elements (SVEs) to homogenize the elastic and fracture properties of the material. This relates the inherent variation of a material’s microstructure to the variation in its mechanical properties at different observation scales. The convergence to the RVE limit is examined from two perspectives: the stability of the mean value as the SVE size increases for the mean-based approach, and the tendency of the normalized variation in homogenized properties to zero as the SVE size increases for the variation-based approach. Fracture properties tend to make the RVE limit slower than do elastic properties from both perspectives. There are also differences between vertical (normal to printing plane) and horizontal (in-plane) properties. While the elastic properties tend to make the RVE limit faster for the horizontal direction, i.e., having a smaller variation and more stable mean value, the fracture properties exhibit the opposite effect. We attributed these differences to the geometry of the melt pools.
In this paper, we demonstrate a method of measuring the flexural elastic modulus of ceramics at an intermediate (~millimeter) scale at high temperatures. We used a picosecond laser to precisely cut microbeams from the location of interest in a bulk ceramic. They had a cross-section of approximately 100 μm × 300 μm and a length of ~1 cm. They were then tested in a thermal mechanical analyzer at room temperature, 500 °C, 800 °C, and 1100 °C using the four-point flexural testing method. We compared the elastic moduli of high-purity Al2O3 and AlN measured by our method with the reported values in the literature and found that the difference was less than 5% for both materials. This paper provides a new and accurate method of characterizing the high-temperature elastic modulus of miniature samples extracted from representative/selected areas of bulk materials.
In this work, we describe a physics program at the Relativistic Heavy Ion Collider (RHIC) with tagged forward protons. The program started with the proton-proton elastic scattering experiment (PP2PP), for which a set of Rosman Pot stations was built. The PP2PP experiment took data at RHIC as a dedicated experiment at the beginning of RHIC operations. To expand the physics program to include non-elastic channels with forward protons, like Central Exclusive Production (CEP), Central Production (CP) and Single Diffraction DIssociation (SD), the experiment with its equipment was merged with the STAR experiment at RHIC. Consequently the expanded program, which included both elastic and inelastic channels became part of the physics program and operations of the STAR experiment. In this paper we shall describe the physics results obtained by the PP2PP and STAR experiments to date.
Assumed-displacement versions of the finite-element method are developed to predict large-deformation elastic-plastic transient deformations of structures. Both the conventional and a new improved finite-element variational formulation are derived. These formulations are then developed in detail for straight-beam and curved-beam elements undergoing (1) Bernoulli-Euler-Kirchhoff or (2) Timoshenko deformation behavior, in one plane. For each of these categories, several types of assumed-displacement finite elements are developed, and transient response predictions are compared with available exact solutions for small-deflection, linear-elastic transient responses. The present finite-element predictions for large-deflection elastic-plastic transient responses are evaluated via several beam and ring examples for which experimental measurements of transient strains and large transient deformations and independent finite-difference predictions are available.
A computer program is presented by which the effects of nonlinear suspension-system elastic characteristics on parachute inflation loads and motions can be investigated. A mathematical elastic model of suspension-system geometry is coupled to the planar equations of motion of a general vehicle and canopy. Canopy geometry and aerodynamic drag characteristics and suspension-system elastic properties are tabular inputs. The equations of motion are numerically integrated by use of an equivalent fifth-order Runge-Kutta technique.
The contact problem of an elastic stiffener bonded to an elastic half plane with different mechanical properties is considered. The governing integral equation is reduced to an infinite system of linear algebraic equations. It is shown that, depending on the value of a parameter which is a function of the elastic constants and the thickness of the stiffener, the system is either regular or quasi-regular. A complete numerical example is given for which the strength of the stress singularity and the contact stresses are tabulated.
A two-body central-force atomic model can be used to describe accurately the elastic properties of alpha quartz if the nontetrahedral O:O forces are included. The strength of the Si:O interaction has little effect on the bulk modulus. The technique is sufficiently general to allow calculations of the elastic properties of a specified structure under arbitrary pressure from a complete description of the interatomic forces. The elastic constants for the NaCl structure and the CsCl structure are examined. Our model includes two-body, central, anion-anion, anion-cation, and electrostatic interactions.
An investigation was conducted to determine the fore-and-aft elastic response characteristics of aircraft tires of bias ply, bias-belted, and radial-belted design. The investigation consisted of: (1)static and rolling tests, (2)a statistical analysis which related the measured tire elastic characteristics to variations in the vertical load, inflation pressure, braking force and/or tire vertical deflection, and (3) a semi-empirical analysis which related the tire elastic behavior to measured wheel slippage during a steady-state braking. The results of this investigation indicate that the bias-belted tire has the largest spring constant value for most loading conditions and the radial-belted tire has the smallest spring constant value.
The problem of modal analysis of an elastic appendage on a rotating base is examined to establish the relative advantages of various mathematical models of elastic structures and to extract general inferences concerning the magnitude and character of the influence of spin on the natural frequencies and mode shapes of rotating structures. In realization of the first objective, it is concluded that except for a small class of very special cases the elastic continuum model is devoid of useful results, while for constant nominal spin rate the distributed-mass finite-element model is quite generally tractable, since in the latter case the governing equations are always linear, constant-coefficient, ordinary differential equations. Although with both of these alternatives the details of the formulation generally obscure the essence of the problem and permit very little engineering insight to be gained without extensive computation, this difficulty is not encountered when dealing with simple concentrated mass models.
Elasticity is determined by isolators physical dimensions and by type of elastomer used. Once elastomer is selected and cast between two concentric tubes of device, isolator elasticity will remain fixed. Isolators having same dimensions can be built to different elasticity requirements using same elastomer.
The elastic deformation of two ellipsoidal solids in contact and subjected to Hertzian stress distribution was evaluated numerically as part of a general study of the elastic deformation of such solids in elastohydrodynamic contacts. In the analysis the contact zone was divided into equal rectangular areas, and it was assumed that a uniform pressure is applied over each rectangular area. The influence of the size of the rectangular area upon accuracy was also studied. The results indicate the distance from the center of the contact at which elastic deformation becomes insignificant.
A general Hamiltonian for a rotating moon in the field of the earth is expanded in terms of parameters orienting the spin angular momentum relative to the principal axes of the moon and relative to coordinate axes fixed in the orbital plane. The effects of elastic distortion are included as modifications of the moment of inertia tensor, where the magnitude of the distortion is parameterized by the Love number k2. The amplitudes of the principal periodic terms in the longitude of a point on the moon due to variations of the tide caused by the earth are discussed. A detailed derivation of the free wobble of the lunar spin axis about the axis of maximum moment of inertia is given. If the moon's rigidity is close to that of the earth there is no effect of elasticity on the rotation which can be measured with the laser ranging and, therefore, no elastic properties of the moon can be determined from variations in the rotation.
Measurements of the pressure dependence of the elastic constants of spessartite-almandine garnet are given. The basis for velocity systematics among the available natural and synthetic garnet data is then examined. As for any dense oxide, the natural anion in garnet is dominant in size. The ionic sizes of the cations in the various sites are used to determine the extent to which it might be expected that garnets of different chemical formulas are analogous in elastic properties. The results are used to predict that the elastic velocities in garnet-transformed MgSiO3 are the same as those in pyrope (Mg3Al2Si3O12).
A method of determining certain characteristic flexural rigidities and elastic properties of nonlinearly elastic materials is presented. An estimation method utilizing perturbation methods and a least squares fitting technique is used to solve the nonlinear differential equation derived from the moment curvature relation, subject to boundary values representing deflections of the bar at discrete points. Deflection data from numerical simulations of a nonlinearly elastic, prismatic bar are used to demonstrate the estimation method. Numerical experiments relating the accuracy of the identification to the number and accuracy of the boundary values are presented. Conclusions based on the numerical experiments are included.
The elastic deformation of two ellipsoidal solids in contact and subjected to a Hertzian stress distribution was evaluated numerically as part of a general study of the elastic deformation of such solids in elastohydrodynamic contacts. In the analysis the contact zone is divided into equal rectangular areas and it is assumed that a uniform pressure is applied over each rectangular area. A study was made of the influence on the size of the rectangular area upon accuracy. The results also indicate how far from the center of the contact one needs to go before elastic deformation becomes insignificant.
Nozzle-type atomic beams and time-of-flight detection methods are employed in studies of the scattering of thermal-energy He-4 atoms from LiF (001) and NaCl (001) surfaces under conditions where diffraction is observed and where substantial inelastic scattering occurs. Intensity and speed-distribution measurements are obtained for the portion of the scattering within the plane of incidence. For these measurements, incident-beam orientation with respect to target (polar angle and azimuth), incident-beam de Broglie wavelength (0.38-0.60 A), and crystal temperature (300-1000 K) are varied. For LiF, the measured intensity distributions exhibit sharp peaks comprised essentially of elastically scattered atoms and corresponding to up to third-order diffraction, inelastic scattering in the form of local dispersion about each of the elastic peaks, and a component of nominally diffuse scattering distributed below and between the peaks. For NaCl, the same general types of scattering are observed, with elastic scattering less prevalent, intensity peaks not as sharp, and dispersions of inelastic scattering harder to resolve.