Showing papers on "Displacement field published in 1974"
TL;DR: In this article, a mathematical method is proposed to decompose a general displacement field on a sphere into two parts: a part due to a rigid rotation and a remaining part of random motions.
Abstract: Continental drift and true polar wander are distinguished. If any true polar wander has occurred, it would appear as a rigid rotation of the lithosphere relative to a fixed spin axis. A mathematical method is proposed to decompose a general displacement field on a sphere into two parts: a part due to a rigid rotation and a remaining part of random motions. The rigid rotation found is the one that best fits the observed displacement field in a least squares sense over the surface of the earth. The random motions, which are separated from the rigid rotation, are then ascribed to continental drift. Formulas are developed that give the Euler angles of the best-fitting rotation in terms of the observed plate displacements for the case of small displacements. These formulas for the Euler angles are also expressed in terms of the first-order spherical harmonic coefficients of the potential generating the displacement field. The proposed method is applied to three theoretical displacement fields having an analytic expression to illustrate the decomposition of specific fields. The displacement field of the plates is constructed for the time period since the early Tertiary, and the method is applied to determine the amount, if any, of true polar wander. The best-fitting rotation, or true polar wandering, was found to be only 2°, an amount less than the uncertainty (4°) of the mean paleomagnetic pole used.
59 citations
TL;DR: In this paper, the displacement field in the form of Hankel transforms leads to a set of simultaneous dual integral equations for two unknown functions, and these equations are transformed by the use of Abel operators to a similar set involving both the Fourier cosine and Fourier sine transforms of each of these unknown functions.
41 citations
TL;DR: In this article, the authors extended the theory of dislocation theory in solids to the case of smectics and showed that two mutually perpendicular line segments do not interact; they also established the displacement field of an edge loop and the Green's function of a homeotropic sample with one free boundary and one anchored boundary.
Abstract: The distortions of a smectic phase with respect to a planar state of reference are described either by a displacement u of the layers (and the conjugated stresses σij), or by a rotation ω of the director (and the conjugated torques). In principle, the choice of ω as an independent variable is justified for the study of disclinations, and the choice of u for the study of dislocations of translation. In this latter case, and restricting the theory to small distortions, one extends various results in dislocation theory in solids to the case of smectics. With the help of the stress field due to an unit point force (Green's function), one is able to express the displacement field of a line as a surface integral, the line tension and the interaction energy with other lines as line integrals. In particular, one shows as a result that two mutually perpendicular line segments do not interact; one establishes the displacement field of an edge loop ; one obtains the Green's function of a homeotropic sample with one free boundary and one anchored boundary; the force image method is also introduced.
36 citations
TL;DR: In this paper, a polynomial expansion of the displacement model is proposed to improve the stiffness of the model, e.g. by direct approximation of the strain field as opposed to its derivation from the displacement field.
29 citations
TL;DR: In this paper, two half-spaces with different elastic constants are well-led together and subjected to a longitudinal shear strain at infinity so that the whole system is in a state of anti-plane strain.
26 citations
TL;DR: It is shown that the commonly used predictions for edge‐mode radiation obtained by neglecting the influence of the fluid on the membrane displacement are valid except when the fluid loading is very high.
Abstract: Free wave motion on a fluid‐loaded semi‐infinite membrane whose plane is extended by a rigid baffle is discussed. We consider in particular the membrane displacement field and the associated acoustic radiation when a wave on the membrane is normally incident on the membrane boundary. Typical values for the reflection coefficient for the waves, and for the radiated acoustic power are given for a wide range of membrane in vacuo wavespeeds and fluid loading parameters. It is shown that the commonly used predictions for edge‐mode radiation obtained by neglecting the influence of the fluid on the membrane displacement are valid except when the fluid loading is very high.
22 citations
TL;DR: In this article, the displacement fields give rise to characteristic diffuse arcs in RHEED patterns and the arcs are represented in reciprocal space as a series of walls of intensity, and the authors used Kinematic diffuse scattering theory to analyze the intensity generated by the displacement field.
21 citations
TL;DR: In this paper, the authors present criteria that may be incorporated in a computer algorithm to obtain an automatic selection of rays which will minimize the error in the partial ray expansion below a preselected level.
Abstract: Summary Whenever synthetic seismograms are computed for layered media with the aid of ray theories only a partial ray expansion is possible. We present criteria that may be incorporated in a computer algorithm to obtain an automatic selection of rays which will minimize the error in the partial ray expansion below a preselected level. The program, results of which are presented in this paper, can also be used for the study of multiple reflected and converted phases or for media with dipping interfaces. 1. Introduction Various ray theories which decompose the total wave field in a layered medium into contributions attributed to individual rays have been used to advantage in the generation and analysis of synthetic seismograms. Among these are generalized ray theory (Spencer 1960) in which the displacement field is decomposed into contributions from an infinite set of rays, each ray being evaluated by a numerical solution of the impulse response (Bortfield 1967; Muller 1968, 1970) or by the Cagniard-de Hoop method (Helmberger 1968; Gilbert & Helmberger 1972). The solution for each ray is exact but the computations are very complex so that only a limited number of rays are used in the solution. An alternative method is asymptotic ray theory (Hron & Kanasewich 1971; Hron 1972) in which the field quantities are expressed as an infinite power series of reciprocal frequency combined with a spacedependent vector which is independent of frequency. The displacement field also becomes decomposed into an infinite set of rays but a greater number may be taken into the approximation by limiting the power series of each to the first non-zero term in the expansion. Although different techniques are used to evaluate the ray amplitudes, the final result is always a synthetic seismogram in which the kinematic and dynamic characteristics of particular rays may be studied. Ray theories are limited invariably by computational difficulties associated with the selection of the phases in the partial ray expansion. Very often the selection is based on the personal intuition or experience of the seismologist. I€ the selection is poor then the seismograms are misleading for rays with significant amplitudes will be omitted. An initial attempt at producing a computer algorithm that would generate systematically a set of rays, determine their kinematic and dynamic analogues and test for significant amplitude levels was reported by Hron & Kanasewich (1971). The algorithm for ray generation proved to be very efficient so that seismograms based on the evaluation of more than 150 000 individual rays were not exceptional (Hron 1972). However, no estimate of the accuracy of this partial ray expansion was possible because the convergence of the complete expansion had not been established. This
20 citations
TL;DR: In this article, a linear elastic body in plane strain which contains a stationary crack and which is initially at rest and stress free is considered, and it is shown that if the elastodynamic displacement field and stress intensity factor are known, as functions of crack length, for any symmetrical distribution of time-varying forces which acts on the body, subsequent to t = 0, then the stress intensity factors due to any other symmetrical load system whatsoever which act on the same body may be directly determined.
17 citations
TL;DR: In this article, a clamped, circular, orthotropic boron-epoxy plate under a uniformly applied static pressure and vibration is considered separately, and the higher order derivatives are obtained optically by holographic-moire and numerically by employing cubic-spline and discrete-quadratic differentiate functions.
Abstract: Membrane and interlaminar stresses in statically loaded and vibrating composite structures are obtained by determining optically and numerically the respective partial derivatives of the holographically recorded transverse displacement field. A clamped, circular, orthotropic boron-epoxy plate under a uniformly applied static pressure and vibration are considered separately. Under uniform static pressure, yr0 = 0, while the anisotropy of the laminated composite results in ir9 ^ 0, which is unlike the corresponding isotropic case. The vibrating plate has complicated, unsymmetrical displacements producing both in-plane shearing strains and stresses. The higher order derivatives are obtained optically by holographic-moire and numerically by employing cubic-spline and discretequadratic differentiate functions.
15 citations
01 Jan 1974
TL;DR: In the non-polar continuous media, all torques are assumed to be the moments of forces as discussed by the authors, which means that there are neither body couples nor couple stresses in the continuous media.
Abstract: In the mechanics of non-polar continuous media all torques are assumed to be the moments of forces; it means that there are neither body couples nor couple stresses.
TL;DR: In this paper, the authors apply the mean stress approach to the integration of elastostatic equations and show that boundary value problems in a multiply-connected region may lead to an incorrect (many-valued) solution if, in addition, the conditions (2b) are not satisfied identically.
TL;DR: In this paper, a consistent finite element model for a circular wheel was developed based on triangular and quasi-triangular domains and a piecewise linear displacement field, and the minimum stress-rate principle of plasticity was used to obtain the solution of this two-dimensional continuum problem with internal unloading.
TL;DR: In this paper, a consistent finite element model for a circular wheel was developed based on triangular and quasi-triangular elements and a piecewise-linear displacement field, which was used to obtain solutions of two-dimensional continuum problems with internal unloading.
Abstract: A consistent finite element model for a circular wheel is developed based on triangular and quasi-triangular elements and a piecewise-linear displacement field. The minimum stress-rate principles of plasticity are used to obtain solutions of two-dimensional continuum problems with internal unloading. A piecewise-linear approximation of the Tresca yield condition is used. Elastic-plastic solution of a wheel with a hub load rolling on a rigid track is obtained for the first few revolutions until a steady-state condition is reached. A shakedown condition for the wheel is demonstrated.
TL;DR: In this article, the higher harmonics of prescribed edge displacements are handled without an explicit calculation of the displacement field, which is particularly well suited to the calculation of thermal stresses in a shell with constrained edges.
Abstract: Several problems in the analysis of shells of revolution are examined for which only the membrane solutions are needed. The significant displacement of truncated shells and domes under snow, wind, and end loads can be obtained for realistic conditions of edge constraint. With a variational method the higher harmonics of prescribed edge displacements are handled without an explicit calculation of the displacement field. The calculation of edge bending stress is trivial. The procedure is particularly well-suited to the calculation of thermal stresses in a shell with constrained edges.
01 Jan 1974
TL;DR: In this article, the authors describe results of some field performance applications of the 3-dimensional numerical steam displacement model described in an earlie paper, ''Three-dimensional Simulation of Steamflooding,'' by Coats, et al.
Abstract: This paper describes results of some field performance applications of the 3-dimensional numerical steam displacement model described in an earlie paper, ''Three-Dimensional Simulation of Steamflooding,'' by Coats, et al. The first part describes the main results of a history matching attempt of actual field data from a representative 5-spot steam displacement pattern in Kern River Field, California. Results are shown of caluclated and measured oil and water production representing 5-1/2 yr of field performance. A second model application gives results of a study related to optimization of steam injection rate for a homogeneous 5-spot displacement pattern of fixed size and specified initial oil saturation. The effect of rate on recovery was calculated for different reservoir thicknesses.
TL;DR: In this paper, the radial vibration of a non-homogeneous and isotropic elastic spherical shell under an internal harmonic pressure distribution was studied using the theory of Laplace transform.
Abstract: The paper is a study of radial vibration of a non-homogeneous and isotropic elastic spherical shell under only an internal harmonic pressure distribution. The problem is exactly solved by using the theory of Laplace transform. Some characteristic features of the displacement field are pointed out.