Stresses and Displacements under a Flexible Circular Foundation in the Presence of Friction or Adhesion

Die Vorliegende Arbeit beschäftigt sich mit den Spannungen und Verschiebungen an einem elastischen Halbraum unter einem kreisförmigen biegsamen Fundament, wenn an der Kontaktfläche vollkommenes Haften besteht. Das gemischte Randwertproblem wird mit Hilfe von Hankel-Transformationen auf duale Integralgleichungen von Titchmarsh- Typ zurückgeführt. Für die Berechnung der Spannungen und Verschiebungen werden Gaußsche Quadraturformeln benutzt. Die Ergebnisse werden mit denen verglichen, die man bei glattem Fundament erhält, und der Einfluß der Poisson-Zahl auf die Spannungen und Verschiebungen wird deutlich gemacht. Schließlich werden die Ergebnisse für den praktischen Gebrauch in Diagrammen und Tabellen zusammengefaßt.

The elastic constants of isomorphous sodium bromate and sodium chlorate from 77 to 350 K

The elastic constants of NaBrO3 and NaClO3 are evaluated from ultrasonic velocity measurements using pulse superposition techniques. The values of C11, C12 and C44 for NaBrO3 at 298°K are 5.578, 1.705, 1.510 (x 1010 N/m2) and for NaClO3 the values are 4.897, 1.389, 1.174. The values at 77°K are respectively 6.35, 1.98 and 1.65 for NaBrO3 and 6.15, 2.16 and 1.32 for NaClO3.

Influence of Joint Thickness and Mortar-Block Elastic Properties on the Strength and Stresses Developed in Soil-Cement Block Masonry

Soil-cement blocks are employed for load bearing masonry buildings. This paper deals with the study on the influence of bed joint thickness and elastic properties of the soil-cement blocks, and the mortar on the strength and behavior of soil-cement block masonry prisms. Influence of joint thickness on compressive strength has been examined through an experimental program. The nature of stresses developed and their distribution, in the block and the mortar of the soil-cement block masonry prism under compression, has been analyzed by an elastic analysis using FEM. Influence of various parameters like joint thickness, ratio of block to mortar modulus, and Poisson's ratio of the block and the mortar are considered in FEM analysis. Some of the major conclusions of the study are: (1) masonry compressive strength is sensitive to the ratio of modulus of block to that of the mortar (Eb/Em) and masonry compressive strength decreases as the mortar joint thickness is increased for the case where the ratio of block to mortar modulus is more than 1; (2) the lateral tensile stresses developed in the masonry unit are sensitive to the Eb/Em ratio and the Poisson's ratio of mortar and the masonry unit; and (3) lateral stresses developed in the masonry unit are more sensitive to the Poisson's ratio of the mortar than the Poisson's ratio of the masonry unit.

Propagation characteristics in distensible tubes containing a visco-elastic fluid

The propagation characteristics of a visco-elastic fluid in a distensible tube tube are studied. The linear visco-elastic nature of the fluid is described by a complex coefficient of viscosity η*. The equation of motion of the vessel wall takes into account the pulsatile nature of the wall. Results are presented for wave propagation velocity, the resistance and the reactance of the fluid and the wall impedance. It is seen that the visco-elastic influence is significant for high values of the frequency of oscillation in various arterial vessels.

Stability of large flexible damped spacecraft modeled as elastic continua

Vibrational stability of a large flexible, structurally damped spacecraft subject to large rigid body rotations is analysed modelling the system as an elastic continuum. Using solution of rigid body attitude motion under torque free conditions and modal analysis, the vibrational equations are reduced to ordinary differential equations with time-varying coefficients. Stability analysis is carried out using Floquet theory and Sonin-Polya theorem. The cases of spinning and non-spinning spacecraft idealized as a flexible beam plate undergoing simple structural vibration are analysed in detail. The critical damping required for stabilization is shown to be a function of the spacecraft's inertia ratio and the level of disturbance.

Elastic constants of sodium chlorate from 77 K to 350 K

The elastic constantsC 11,C 12 and C 44 of sodium chlorate single crystal have been evaluated using 10 MHz ultrasonic pulse echo superposition technique. The values are C 11=4.90,C 12=1.39,C 44=1.17 (× 1010 N/m 2) at 298 K and 6.15, 2.16, 1.32 (×1010 N/m 2) at 77 K. The data agree well with the values measured earlier up to 223 K. Brief mention is also made of the low temperature bonding problems in these soft crystals.

Random vibration of a second order non-linear elastic system

A method is presented for obtaining, approximately, the response covariance and probability distribution of a non-linear oscillator under a Gaussian excitation. The method has similarities with the hierarchy closure and the equivalent linearization approaches, but is different. A Gaussianization technique is used to arrive at the output autocorrelation and the input-output cross-correlation. This along with an energy equivalence criterion is used to estimate the response distribution function. The method is applicable in both the transient and steady state response analysis under either stationary or non-stationary excitations. Good comparison has been observed between the predicted and the exact steady state probability distribution of a Duffing oscillator under a white noise input.

Free vibrations of a reservoir-foundation system

The natural frequencies of a reservoir-foundation system are calculated by treating the foundation as a system of linear springs with inertia. The reservoir is treated as consisting of compressible liquid, and the influence of waves at the free surface is included. It is shown that the natural frequencies decrease monotonically as the depth of foundation participating in the motion increases. The influence of waves at the reservoir surface is negligible for the cases normally occurring in practice. It is also shown that the wavelength of motion along the reservoir has no influence on the frequencies when the foundation depth is large compared to the reservoir depth.

Elastic modulus of Ti-6Al-4V-xB alloys with B up to 0.55 wt.%

An anomalous variation in the experimental elastic modulus, E, of Ti-6Al-4V-xB (with x up to 0.55 wt.%) is reported. Volume fractions and moduli of the constituent phases were measured using microscopy and nanoindentation,respectively. These were used in simple micromechanical models to examine if the E values could be rationalized. Experimental E values higher than the upper bound estimates suggest complex interplay between microstructural modifications, induced by the addition of B, and properties.

Elastic Properties of Boron Nitride Nanotubes and Their Comparison with Carbon Nanotubes

Boron Nitride Nanotubes (BNNTs) have alternating boron and nitrogen atoms in graphite like network and are strongly polar in nature due to a large charge on boron and nitrogen atoms. Hence electrostatic interactions are expected to play an important role in determining the elastic properties of BNNTs. In the absence of specific partial atomic charge information for boron and nitrogen, we have studied the elastic properties BNNTs varying the partial atomic charges on boron and nitrogen. We have computed Young modulus (Y) and Shear modulus (G) of BNNT as a function of the tube radius and number of walls using molecular mechanics calculation. Our calculation shows that Young modulus of BNNTs increases with increase in magnitude of the partial atomic charge on B and N and can be larger than the Young modulus of CNTs of same radius. This is in contrast to the earlier finding that CNTs has the largest tensile strength (PRL, 80, 4502, 1998). Shear modulus, on the other hand depends weakly on the magnitude of partial atomic charge and is less than the shear modulus of the CNT. The values obtained for Young modulus and Shear modulus are in excellent agreement with the available experimental results.

The partition of unity finite element method for elastic wave propagation in Reissner-Mindlin plates

This paper reports a numerical method for modelling the elastic wave propagation in plates. The method is based on the partition of unity approach, in which the approximate spectral properties of the infinite dimensional system are embedded within the space of a conventional finite element method through a consistent technique of waveform enrichment. The technique is general, such that it can be applied to the Lagrangian family of finite elements with specific waveform enrichment schemes, depending on the dominant modes of wave propagation in the physical system. A four-noded element for the Reissner-indlin plate is derived in this paper, which is free of shear locking. Such a locking-free property is achieved by removing the transverse displacement degrees of freedom from the element nodal variables and by recovering the same through a line integral and a weak constraint in the frequency domain. As a result, the frequency-dependent stiffness matrix and the mass matrix are obtained, which capture the higher frequency response with even coarse meshes, accurately. The steps involved in the numerical implementation of such element are discussed in details. Numerical studies on the performance of the proposed element are reported by considering a number of cases, which show very good accuracy and low computational cost. Copyright (C)006 John Wiley & Sons, Ltd.