Showing papers on "Displacement field published in 1984"

High-temperature failure of polycrystalline alumina: II, creep crack growth and blunting

Abstract: Creep crack growth in fine-grain alumina is measured by using surface cracks. A narrow power-law crack growth regime occurs at both 1300° and 1400°C, wherein the power-law exponent and activation energy are comparable to steady-state creep values. Asymptotic crack velocity behavior is exhibited near both the critical stress intensity factor, KC, and the crack growth threshold, Kth. The threshold occurs near 0.4 K1C at both 1300° and 1400°C and is associated with a transition in the size and distribution of damage. Displacement measurements indicate that crack tip damage exerts a strong influence on the displacement field, as predicted by recent theories. Furthermore, use of the stress intensity factor as a loading parameter does not produce adequate correlation with displacement measurements and is, therefore, not strictly suitable for nonlinear creeping ceramic poly crystals.

Control system having variably biased manipulatable unit

Abstract: In a control system with a manually actuatable unit (1) by means of which a controlled instrumentality (29) is controlled, the position of displacement (δ) of the unit and change in displacement position are determined. A moment motor (5) is coupled to the manipulatable unit for imposing upon it a moment (F) that opposes the displacement. From information about the displacement position (8) and the change in displacement position the moment (F) is determined in dependence upon first and second charcteristics (y 1 , y 2 ), for increasing and decreasing displacement positions (8), respectively. When a turning point in the displacement of the manipulatable unit occurs, corresponding to a change in displacement position from increasing to decreasing displacement positions or vice versa, the moment (F) is determined in dependence upon a third characteristic (y 3 ) that goes through the turning point and has a larger moment gradient than the first and second characteristics (y 1 , y 2 ).

Theory of the surface acoustic soliton. I. Insulating solid

Abstract: Starting from the equation of motion for anharmonically interacting surface phonons, a theory of the surface acoustic soliton in an insulating solid is developed, based on the coherent-state representation. The two-dimensional nonlinear integro-differential equation for the classical displacement field is obtained. By using the reductive perturbation method, the equation can be reduced to the nonlinear Schr\"odinger equation, which allows the existence of the surface acoustic soliton of the envelope type. The possibility of observing the surface acoustic soliton is also discussed.

A Study of EHD Lubrication in a Journal Bearing with Piezoviscous Lubricants

Abstract: The deformation of a bearing, which can be of the order of the fluid film thickness when the bearing operates at large eccentricities, may affect the performance appreciably, and all the more so if the viscosity of the lubricant changes with pressure. In this paper, matched solutions for pressure distribution and the bearing displacement field, taking into account the combined effects of bearing liner deformation as well as change in viscosity of the lubricant, are obtained by solving the respective governing equations using a suitable iteration scheme for eccentricity ratios up to unity. The performance characteristics of the journal bearing and their variations with bearing flexibility, are studied with reference to eccentricity ratio and a deformation coefficient which is a measure of the flexibility of bearing shell.

A linear programming upper bound approach to the shakedown limit of thin shells subjected to variable thermal loading

Abstract: This paper describes an upper bound technique for the evaluation of the shakedown limit of thin cyclindrical shells subject to thermal loading. The method is based upon the upper bound kinematic shakedown theorem of Koiter. By suitable choice of displacement field, in a finite element form, and yield surface, the problem is reduced to a linear programming problem. A number of solutions are presented involving a tube subjected to a moving temperature front which indicates that the technique provides, in an efficient way, a complete description of the load levels at which ratchetting would occur and the corresponding modes of deformation. The technique seems therefore, to provide a useful intermediary between the use of the simple rules incorporated in design codes and full inelastic analysis.

Dynamic stresses and displacements around cylindrical cavities of arbitrary shape

Abstract: Etude des deplacements et des contraintes dynamiques autour de cavites circulaires, triangulaires et carrees. Estimation des effets des coins et de la diffusion multiple

An invariant eight‐node hybrid‐stress element for thin and thick multilayer laminated plates

Abstract: A hybrid-stress eight-node isoparametric element is developed for the analysis of thin or thick multilayer fiber-reinforced composite plates. Transverse shear deformation effects are included by allowing for individual layer cross-section warping for thick laminates, or alternatively, laminate non-normal cross-section rotations for thin to moderately thick laminates. All stress components are included and are interpolated independently within each layer. Interlayer surface traction continuity and appropriate upper/lower surface traction-free conditions are exactly satisfied. The layer stress field is selected on the basis of earlier single-layer element studies so that the resulting element is naturally invariant with respect to co-ordinate translation or rotations, is non-locking in the thin-plate limit, and the element stiffness is of correct rank. An example for which an elasticity solution is available is used to demonstrate the element performance. Schemes for reduction of element stiffness computation time are also presented.

Diffuse X-ray scattering from interstitial nitrogen in niobium. I. Huang diffuse scattering

Abstract: The symmetry and strength of the displacement field around N atoms interstitially dissolved in Nb single crystals is determined from Huang diffuse scattering of X-rays. The measurements were performed at various temperatures from -180 to 150 degrees C. The force dipole tensor describing the long-range displacement field has tetragonal symmetry. It shows no temperature dependence within the present accuracy.

Theory of Acoustic Emission From Phase Transformations.

Abstract: A theoretical framework is developed within which it is possible to predict the dynamic elastic displacement field (acoustic emission) for a phase transformation in which there is a change of both crystal structure (elastic constants) and shape (density). An integral equation is presented for the acoustic emission displacement field due to formation of inhomogeneous inclusions. This integral equation is solved by . expressing the source in multipolar form and using the Eshelby equivalent inclusion method to estimate the dynamic multipolar coefficients. Expressions for the source of elastic radiation are explicitly calculated for small isotropic spherical and ellipsoidal inclusions embedded in an isotropic matrix. These expressions are used for qualitative interpretation of recent experiments on martensitic transformations in steels and for identifying the information that may be deduced about transformation dynamics from quantitative measurements of acoustic emission.

Mechanical properties of pleural membrane

Abstract: The pleural membrane is modeled as a planar collection of interconnected randomly oriented line elements. By assuming that the line elements follow the strain field of a continuum, a strain-energy function is formulated. From the strain-energy function, an explicit stress-strain equation for large deformations is derived. In the linear approximation of the stress-strain equation the shear modulus and the area modulus of the membrane are respectively found to be 2.4 and 2.8 times the tension at the reference state. The stress-strain equation for large deformations is used to predict the displacement field around a circular hole in pleura. Good agreement is found between these predictions and measurements made on ablated pleura from dog lungs. From these theoretical and experimental results the conclusion is drawn that the pleura has a significant role in carrying shear forces and maintaining the lung's shape.

Elastic radiation from a point force in an anisotropic medium

Abstract: An expression for the displacement field due to a point force in an unbounded, anisotropic elastic medium is derived using a radon-transform method. The field is thus a Green's function for the anisotropic elastic whole space. A relatively simple algebraic expression for the asymptotic field is then found by means of the principle of stationary phase together with certain aspects of the differential geometry of the slowness surface. The general results are applied to the transversely isotropic medium; numerical results are presented for the hexagonal crystals of cobalt and apatite. The results of this work should be of value in the disciplines of crystal physics and seismology.

Elastic wave scattering by a surface-breaking or subsurface planar crack

Abstract: A boundary integral representation of the displacement field is developed and solved for the crack‐opening displacement by expressing the latter on the crack surface as an expansion in localized functions, whose parametrization is determined by fitting exactly‐known cross sections. Numerical results are presented for scattering of antiplane (SH) waves as a function of frequency from surface‐breaking and buried 2D cracks for a variety of crack inclinations and burial depths. The theory and the method apply to the 3D case. Its numerical implementation will be straightforward but tedious.

Kinematic Analysis of Stephenson Six-Link Mechanisms : 1st Report, Discrimination of Composition Loops

Abstract: In this paper, a simple method of displacement analysis of Stephenson six-link mechanisms of three kinds which have two closed five-link loops including the fixed and driving links is developed in the form of a solution of a sixth order equation. Moreover, their composition loops to arise from inversions of link chains for a set of kinematic constants are discriminated by means of the domains on the angular displacement curve of the component four-link chain; the domains are separated by the points which correspond to the limits of rotation of the driving link of the six -link mechanism and the positions of the longest or shortest distance between the end pairing points of the component two-link chain and are distinguished by the sign of the sine of the relative displacement angle of the latter.

Theory of the surface acoustic soliton. II. Semiconducting solid

Abstract: A theory of the surface acoustic soliton in a semiconductor is presented based on the coherent-state representation of the equation of motion for the surface phonons interacting with the conduction electrons. It is shown that the two-dimensional displacement field satisfies the nonlinear integro-differential equation with a damping term. With the aid of the reductive perturbation method, the equation can be reduced to the nonlinear Schr\"odinger equation with a damping term whose coefficient is the attenuation rate of the surface phonon. The approximate solution is derived to reveal excellent agreement with the numerical result.

Finite Deformation Analysis of Cable Networks

Abstract: A finite deformation formulation for dynamic analysis of cable nets is presented. Lagrangian coordinates and Piola‐Kirchhoff stresses are used and elasto‐plastic material behavior is considered. Under assumption of straight cable elements and a displacement field varying linearly along the element, global equations of motion are established by referring the displacements to an initial configuration. These equations are linearized for iterative computation of the equilibrium configuration and for determining the eigenfrequencies and mode shapes of the linear vibration of the net about its equilibrium configuration. This analysis is performed by means of a computer program that can analyze nets anchored in fixed points. Slackness of cable elements is allowed. Three application examples are presented for linear elastic material behavior, showing a good agreement with experimental and computed published data.

Dynamic Analysis of Impact Test Specimens

Abstract: Two methods are represented by means of which the dynamic behaviour of impact test specimens can be analysed. First such problems can be treated by use of a finite difference scheme. On the basis of the results of this technique, a second method can be developed, which founds upon a beam model of the impact test specimen. In both cases, the dynamic stress intensity factor can be calculated from the measured hammer force.

Wave Propagation in Heterogeneous Media.

Abstract: : The propagation of stress wave due to a point type excitation in the form of a sinusoidal pulse in an infinite medium with inclusions having different properties is studied. The solution is carried out using the boundary element method in the frequency domain with a Discrete Fourier transform. The inclusion-medium interfaces are discretized using a constant element which assumes a uniform stress and displacement field over the element. Studies were conducted primarily with a two-dimensional plane strain model but some were also performed in the three-dimensional case, focusing on the attenuation characteristics and the velocity of the wave in terms of the arrival time for both the free field and the case with inclusions. Results are presented in the form of a dimensionless displacement and arrival times at the target under consideration. With a point excitation, as used in this study, the free field attenuation follows the geometrical damping law for both the two and the three-dimensional cases, except at distances in the neighborhood of one wavelength or closer, where a more complex pattern of waves is developed. Originator-supplied keywords: Wave propagation, Effect of Inclusions, Soil dynamics, Propagation velocities, Attenuation.

Effective elasticity of a solid suspension of spheres. II: Effective moduli in lowest multipole approximation

Abstract: We evaluate explicitly through terms of second order in volume fraction the effective elastic moduli derived formally in a preceeding article for a random suspension of spherically symmetric inclusions in a background matrix. By interpreting the earlier formulae in terms of induced stresses on an inclusion we reduce the calculation to the treatment of a one-inclusion and a two-inclusion problem only. To treat the one-inclusion problem we derive a Faxen type theorem for the total stress induced on the inclusion by an incident displacement field. For the two-inclusion problem we use a method of reflections whereby we obtain the contribution of lowest order in the separation of inclusion centres. By introducing a point stress model of the inclusions we sum a subset of reflections to all orders in inclusion separation. We find that in the point stress model the effective moduli are given in terms of only two of the scattering coefficients introduced elsewhere for the one-inclusion problem. For the special case of uniform inclusions we give numerical results for the effective moduli which are compared with exact upper and lower bounds.

Propagation of shock waves at the surface of heterogeneous soil grounds

Abstract: The paper deals with the propagation of shock waves at the surface of soils. Heterogeneity and damping are introduced into analytical half-space solutions. The suggested model explains two phenomena, often observed with shock propagation in actual soils, that differ from the behaviour of the homogeneous half-space: the pronounced decay of the disturbances with distance and the elongation of the disturbance into a train of waves. The effects of heterogeneity and damping are discussed quantitatively. The response of footings on heterogeneous soils has been investigated by several authors. Awojobi4 considered the Gibson soil in which the shear modulus increases linearly with depth. Luco5 and Gazetas and Roesset6 investigated a multi-layered soil, the shear modulus being constant within each layer. Gazetas7, using a technique suggested by Gupta8 extended this method to layers with linearly varying shear modulus. Little work is available on the propagation of waves in heterogeneous bodies. Some results concerning the modes and the mode shapes in heterogeneous soils were reported by Ewing, Jardetzky and Press9 and Bath.10 The modes have to be superposed in an appropriate way to obtain the displacement field at the surface. This has been approximately achieved by the finite element formulations of Lysmer, 11, Lysmer and Waas12 and Waas.13 Auersch14 applied this method to a homogeneous layer on a rigid base. He found some dispersion of the Rayleigh wave within a narrow frequency range. Finite elements combined with discrete Laplace transforms, however, consume much computer time. Rao and Goda15 and Rao16 calculated surface vibrations of a half-space with exponentially varying shear modulus and density. Their method is similar to Lamb'S1 procedure for the homogeneous half-space. Only one mode–the Rayleigh wave–occurs in their heterogeneous half-space. The examples show the considerable effect of heterogeneity on wave propagation. In the present paper, more general variations of the shear modulus are considered.

Nonlinear response theory—I

Abstract: A general nonlinear response theory for the case of linear coupling of physical systems to arbitrary external fields is formulated for applications in different branches of physics This is done within the framework of non-relativistic density matrix approach of quantum mechanics Some simple properties of response functions and other related functions, which are introduced here for convenience, are studied to obtain suitable representations of the nonlinear response functions, including important sum-rules As an example, the sum rule for the second-order response function is applied to electronic dipole nonlinearity at optical frequencies which includes both the Raman nonlinearity arising from perturbation to the electronic motion from external ionic displacement field and the usual optical sum, difference and harmonic generations This immediately allows us to visualize a rigorous connection between these two types of non-linearities

New criteria for onset and subsequent crack growth in a viscoelastic strip

Abstract: Based on the analysis of displacement field around the tip of a crack in a linearly viscoelastic strip, a new criterion for onset of crack growth is proposed. Extending the above criterion to the growing crack, experimental crack growth behavior under a wide range of temperature is well predicted.

Calculation of displacement fields by means of the motion detection transform

Abstract: This paper describes a new technique for calculating the displacement field in a motion sequence of two-dimensional imagery generated by a moving sensor. It proposes a scheme wherein a simple algorithm for calculating single displacement vectors is applied over numerous subimages to create a displacement field. This algorithm is an application of the MDT (motion detection transform) [15,16], thus is based on the 1D (one-dimensional) Fourier transform.