Showing papers on "Displacement field published in 1975"
TL;DR: In this article, a strain gradient theory of thermoelasticity is formulated employing a method due to Mindlin, and the basic equations for linear dynamical thermo-elasticities for infinitesimal motion are obtained and discussed.
42 citations
TL;DR: In this article, an assumed displacement hybrid finite-element procedure was developed for treating a general class of problems involving mixed-mode behavior of cracks is used to solve some two-dimensional, fracture mechanics problems involving rectilinear-anisotropic materials.
Abstract: An assumed displacement hybrid finite-element procedure developed for treating a general class of problems involving mixed-mode behavior of cracks is used to solve some two-dimensional, fracture mechanics problems involving rectilinear-anisotropic materials. This finite-element program uses four "singular" elements which surround the crack tip and "regular" elements which occupy the remaining region. The singular element has a built-in displacement field of the r type with the two modes of stress intensity factors, K 1 and K I I , as unknowns. Displacement compatibility between singular and regular elements is also maintained. Isoparametric transformations are used to derive the stiffness matrix of quadrilateral curved elements. Rectilinear anisotropic, nonhomogeneous, but linear elastic, material properties are considered. The program was checked out by analyzing a bimaterial tension plate with an eccentric crack and a centrally-cracked orthotropic tension plate. The results thus obtained agreed well with those by Erdogan and Biricikoglu, and Bowie and Freese, respectively. The program was then used to analyze two fracture test specimens for which analytical solutions do not exist. The first specimen was the doubly edge-notched tension plate with material principal directions oriented 0°-90° or ′45° to the geometric axes of symmetry and with varying crack length. The second specimen was the three-point bend specimen with material principal directions oriented 0°-90° to the geometric axes of symmetry. Finally, an orthotropic tension plate with an oblique center crack was analyzed. Finite-element solutions of most of these problems do not seem to have appeared in prior literature.
40 citations
01 May 1975
TL;DR: In this paper, a principle of stationary complementary energy for the finite deformation of elastic materials is discussed, but the complementary energy functional depends only on the components of the nominal stress, and not on the displacement field.
Abstract: In a recent paper Koiter (5) discussed a principle of stationary complementary energy for the finite deformation of elastic materials. The complementary energy functional he uses depends only on the components of the nominal stress, and not on the displacement field. He, incorrectly, attributes the principle to Zubov (14).
31 citations
TL;DR: In this paper, the authors studied the propagation of harmonic waves of plane strain in elastic composite materials, where the composite structure is idealized as an assembly of identical subregions, each with the displacement field represented by a finite number of generalized displacements.
Abstract: This paper presents a study of the propagation of harmonic waves of plane strain in elastic composite materials. The composite structure is idealized as an assembly of identical subregions, each with the displacement field represented by a finite number of generalized displacements. The resulting model possesses a periodic lattice‐type structure and its response to harmonic waves can be investigated as a problem in lattice dynamics. A set of generalized coordinates, applicable for the case of harmonic wave propagation in the discrete periodic structure, is employed to generate an algebraic eigenvalue problem, the solution of which gives the frequency spectrum for the medium. To show the accuracy of this method, examples of harmonic wave propagation in infinite isotropic and orthotropic homogeneous plates are presented, and cases of harmonic wave propagation in infinite isotropic and orthotropic media. The method is used to generate the frequency spectra for both a fiber‐reinforced composite plate and an i...
22 citations
TL;DR: In this article, the displacement field of a homogeneous, isotropic elastic disk that is free from body forces is analyzed by a method of equivalence and an approach based on finite elements.
17 citations
TL;DR: In this article, a solution for the steady-state thermal stress and displacement field in an infinite elastic solid containing an insulated penny-shaped crack is given, which is reduced to a mixed-boundary-value problem for the half-space.
Abstract: A solution is given for the steady-state thermal stress and displacement field in an infinite elastic solid containing an insulated penny-shaped crack. The problem is reduced to a mixed-boundary-value problem for the half-space, making use of Green's isothermal solution for the thick elastic plate in complex harmonic potentials and a particular thermoelastic solution due to Williams. In the axisymmetric case, the complex potential reduces to the real harmonic function used by Shail in his solution for the external crack.To illustrate the use of the method in both axisymmetric and non-axisymmetric problems, complete solutionsare given for (1) a uniform heat flow and (2) a linearly varying heat flow disturbed by an insulated penny-shaped crack.
14 citations
TL;DR: In this paper, 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.
13 citations
TL;DR: In this article, an elastic model of a crosslink between adjacent molecules in a polyethylene crystal is formulated and the elastic displacements arising from these forces are obtained by using the elastic Green displacement tensor, and the displacements near the crosslink are calculated by means of a simplified discrete atomic model.
Abstract: An elastic model of a cross-link between adjacent molecules in a polyethylene crystal is formulated. The model consists of two point forces and two pairs of dipole forces acting on the axes of the cross-linked molecules. The elastic displacements arising from these forces are obtained by using the elastic Green displacement tensor, and the displacements near the cross-link are calculated by means of a simplified discrete atomic model. The actual values of the forces and dipole forces generating the elastic displacements are found by matching the discrete and elastic solutions, and the complete displacement field is thus obtained for a cross-link in a crystal of infinite dimensions. It is shown that the cross-link acts as a centre of elastic distortion with principal strains ϵ 11 = - 0.5, ϵ 22 = 0.054 and ϵ 33 = - 0.055. The limitations of the calculation are discussed and it is concluded that the results are applicable with little error to cross-links lying beyond seven interatomic distances below the surface of thin lamellar crystals. Possible useful applications of the results are also indicated.
9 citations
TL;DR: In this article, the Cagniard De-Hoop technique was used to generate a pulse in an elastic half space by impulsive normal pressure over a circular area on the surface.
9 citations
TL;DR: In this article, a discrete-continuum theory for periodically layered composite materials is presented based on a two-term truncated power series expansion of the displacement field about the middle plane of each layer.
Abstract: A discrete−continuum theory for periodically layered composite materials is presented. Based on a two−term truncated power series expansion of the displacement field about the middle plane of each layer, two−dimensional equations of motion are obtained for the individual layers. After introducing appropriate continuity conditions at the interfaces between neighboring layers, the governing field equations for periodically layered media are derived in the form of a system of differential−difference equations. The accuracy of the theory is examined by applying it to the propagation of plane harmonic waves in an unbounded layered medium and comparing the results with those obtained from theory of elasticity. To illustrate the application of the theory, thickness−twist vibrations of laminated plates are studied. Numerical examples are included and comparison is made with exact solutions.Subject Classification :40.24.
7 citations
TL;DR: In this article, a theory of small deformations superposed upon large ones suitable to study the seismological effects of the existence of a state of pre-stress within the Earth is given.
Abstract: A theory of small deformations superposed upon large ones suitable to study the seismological effects of the existence of a state of pre-stress within the Earth is given. The field equations are obtained by postulating an energy balance and imposing invariance under rigid-body motions. The symmetry properties of the involved elasticity tensor allow the derivation of a general reciprocity theorem in the space of the original field functions. This theorem is then used to derive a variational formulation of the problem and a representation of the displacement field in terms of the appropriate Green tensor. The latter leads to the determination of the explicit expressions of the body force equivalent for seismic dislocations and the dislocation momentum tensor.
TL;DR: In this paper, the displacement field of a linear singularity in an anisotropic medium is developed by superimposing the displacement of a distribution of simple singularities and the result can be expressed in terms of the moments of the distribution.
Abstract: The displacement field of a linear singularity in an anisotropic medium is developed by superimposing the displacement of a distribution of simple singularities. The result can be expressed in terms of the moments of the distribution. This approach provides a means of comparing atomic displacements obtained by computer simulations of dislocations with analytical results to obtain numerical values for the moments of the effective distribution. Distributions of linear force dipoles can also be used to construct models of solute segregation to dislocations.
TL;DR: In this paper, it is shown that the displacements of a dislocation in an anisotropic crystal lying normal to a twofold axis and whose Burgers vector has components normal or parallel to it are even or odd functions in polar coordinates.
Abstract: It is shown that the displacements of a dislocation in an anisotropic crystal lying normal to a twofold axis and whose Burgers vector has components normal or parallel to it are even or odd functions in polar coordinates.
Es wird gezeigt, das die Verschiebungskomponenten einer Versetzung in einem anisotropen Kristall, die normal zu einer zweizahligen Deckachse liegt und Burgersvektorkomponenten normal oder parallel dazu hat, gerade oder ungerade Funktionen in Polarkoordinaten sind.
TL;DR: In this paper, exact solutions were obtained for the displacement field in an elastic half-space composed of two quarter spaces welded together, where the configuration is excited by a plane SH wave impinging upon the discontinuity at an arbitrary angle.
Abstract: Exact solutions are obtained for the displacement field in an elastic half-space composed of two quarter spaces welded together. The configuration is excited by a plane SH wave impinging upon the discontinuity at an arbitrary angle. The application of the Kontorovich-Lebedev transform to this boundary value problem leads to two simultaneous integral equations which are solved exactly. It is shown that the discontinuity may enhance the spectral displacements up to a factor of two. The results could be applied to propagation of seismic shear waves past fault zones in the earth's crust.
TL;DR: In this paper, it was shown that if the displacement gradient is pointwise sufficiently small, then, in any subcylinder of length 1/4a, it is possible to add a rigid body motion such that the L2 norm of the resulting displacement gradient can be bounded by a constant times the L 2 norm of strain in a subcyclinder centered at the same point.
Abstract: Consider a long thin isotropic elastic cylinder with a self-equilibrated loading on each end face, but which is stress-free on the sides and which has no internal body forces. It is shown that if the displacement gradient is pointwise sufficiently small, then, in any subcylinder of length 1/4a, it is possible to add a rigid body motion such that the L2 norm of the resulting displacement gradient can be bounded by a constant times the L2 norm of the strain in a subcyclinder of length 2a centered at the same point. The parameter a depends upon the pointwise bound for the displacement gradient (the smaller the bound, the larger a can be) and the constant is independent of the length thickness ratio of the subcylinder.
01 Jan 1975
TL;DR: In this article, the authors discuss the decomposition of the displacement vector and present a completeness theorem for scalar and vector potentials for the displacement field governed by the classical wave equations.
Abstract: Publisher Summary
This chapter discusses several formal aspects of the theory of dynamic elasticity and general methods of solution of elastodynamic problems. The chapter discusses the decomposition of the displacement vector and presents a completeness theorem for scalar and vector potentials. The scalar and vector potentials for the displacement field are governed by the classical wave equations. With the purpose of determining the elastic wave motion generated by body forces in an unbounded medium, the chapter further reviews the general integral representations to problems of elastic wave propagation for the solution of the classical wave equation. The chapter also presents a determination of the displacement and stress fields due to a time-dependent point load. The relevance of integral representations to problems of elastic wave propagation is also reviewed in the chapter.
Journal Article•
TL;DR: In this article, a three-dimensional, static problem of linear elasticity of a transversally isotropic medium is reduced to the solution of a system of three-second order differential equations for three displacement functions.
Abstract: Three-dimensional, static problem of linear elasticity of a transversally isotropic medium is reduced to the solution of a system of three-second order differential equations for three displacement functions. Components of the displacement vector and stress tensor are expressed in terms of the displacement functions. Similar equations are also obtained for two displacement functions governing the plane problem of elasticity of orthotropic bodies. The corresponding equations are also shown in the cases of three functions (spatial problem) or two functions (plane problem) describing the displacement field in isotropic media.
01 Jan 1975
TL;DR: In this paper, the authors reviewed recent computer simulation of dislocation models in α-Fe and KC1 and discussed the implications of these effects in terms of interactions of point defects with the core field.
Abstract: The highly nonlinear elastic state in the vicinity of a dislocation core is the source of a linear elastic displacement field (core field) outside the core. Recent computer simulation of dislocation models in α-Fe and KC1 have shed considerable light on the nature of the core field and these results are reviewed. An important feature of the core field is a net dilatation. A decrease in the elastic constants near the dislocation is also noted and results from the lattice expansion. The implications of these effects in terms of interactions of point defects with the core field is discussed.