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Showing papers on "Displacement field published in 1979"


Journal ArticleDOI
TL;DR: Load-free notch surfaces of bodies made of a linear-elastic, homogeneous, isotropic material are optimized within given variation domains by means of an interation procedure so that the occurring maximum tangential stress is reduced to a minimum as discussed by the authors.
Abstract: Load-free notch surfaces of bodies made of a linear-elastic, homogeneous, isotropic material are optimized within given variation domains by means of an interation procedure so that the occurring maximum tangential stress is reduced to a minimum. The hypothesis of a constant tangential stress distribution for obtaining minimal notch stresses proposed by R. V. Baud has been confirmed by means of the Fade-away Law of the notch stress theory. The finite element method is applied for calculating the displacement and stress field of the styructure. An increment procedure is used for determing the displacement field after every iteration step, which permits the calculation of the displacement quantities with sufficient accuracy in a single step. Numerical solutions and their comparison with analytical solutions and stress results obtained with the aid of photo-elasticity confirm the usefulness of this procedure. The known optimization methods1,2 differ from those used in the present paper.

96 citations


Journal ArticleDOI
TL;DR: In this paper, a new method of estimating effective macroscopic elastic constants for microscopically inhomogeneous materials is formulated using elastic wave scattering theory, where the self-consistent medium is determined by the condition that the scattered longwavelength displacement field must vanish on the average.
Abstract: A new method of estimating effective macroscopic elastic constants for microscopically inhomogeneous materials is formulated using elastic‐wave scattering theory. The self‐consistent medium is determined by the condition that the scattered long‐wavelength displacement field must vanish on the average. The resulting formulas are simpler to apply than previous methods due to the reduction from tensor to vector equations. Our formulas are automatically symmetric under interchange of constituent labels whereas some other ’’self‐consistent’’ formulations for needle and disk inclusions do not possess this property. For spherical inclusions, the standard self‐consistent elastic constants are reproduced.

46 citations


Patent
16 Jul 1979
TL;DR: In this article, an elastic suspension is provided to support at least one of the displacement elements for permitting elastic movement between the elements in a plane perpendicular to the axis of translatory circular movement.
Abstract: In a displacement machine operating according to the spiral principle and having two displacement elements presenting respective axially interengaging sprial-shaped walls, and drive means connected between the elements to produce a relative translatory circular movement therebetween, an elastic suspension is provided to support at least one of the displacement elements for permitting elastic movement between the elements in a plane perpendicular to the axis of translatory circular movement. In such a displacement machine, whether or not the elastic suspension is provided, the walls of the displacement elements are preferably made, at least at the surfaces contacting one another, of respectively different materials presenting a low mutual coefficient of friction.

44 citations


Journal ArticleDOI
TL;DR: In this article, a formalism due to Willis (1973) is used to obtain analytic expressions for the space derivatives, to any order, of the displacement field below a point impulsive force to the surface of a half-space.
Abstract: Expressions given previously for the dynamic elastic Green's function of a half-space have been in the form of a single integral. These expressions clearly reduce to closed analytic forms when the field (receiver) point is at the epicentre, but have not formerly been written out. Broad-band acoustic emission experiments have now provided motivation to do so. A formalism due to Willis (1973) is used to obtain analytic expressions for the space derivatives, to any order, of the displacement field below a point impulsive force to the surface of a half-space. A reciprocal theorem then yields the epicentre surface displacements due to a buried point force multipole source. A few examples are illustrated graphically.

38 citations


Journal ArticleDOI
TL;DR: In this article, the structures of several large-angle twist grain boundaries with widely different values of Σ in gold bicrystal specimens have been studied using X-ray diffraction techniques.
Abstract: The structures of several large-angle [001] twist grain boundaries with widely different values of Σ in gold bicrystal specimens have been studied using X-ray diffraction techniques (Σ is the reciprocal of the fraction of lattice sites in one crystal in good coincidence across the boundary plane). New reflections in addition to gold reflections were observed from all the boundaries studied, indicating that low-, medium- and high-Σ boundaries all have periodic structures. The positions of the reflections are consistent, with one exception, with the coincidence site-lattice unit cell corresponding to the particular Σ value of the boundary. The observed reflections can be classified into two groups depending on their indices and intensities. These structure factor rules are related to the form of the displacement field of the grain boundary. Specifically, these rules are linked with the existence of a displacement field that varies (falls off) with distance from the boundary plane. An initial attemp...

34 citations


Journal ArticleDOI
TL;DR: In this article, the generalized displacement field functions are represented by the exact solutions of the coupled homogeneous differential equations governing the static behavior, which also permits the evaluation of exact work-equivalent nodal forces due to external loadings.
Abstract: Exact solutions to the linear static behavior including warping torsion of thin-walled spatial curved beam structures are obtained by the displacement formulation through the use of minimum potential energy. The generalized displacement field functions are represented by the exact solutions of the coupled homogeneous differential equations governing the static behavior, which also permits the evaluation of exact work-equivalent nodal forces due to external loadings. The obtained total torsional moment is separated through an analytical procedure into St. Venant and warping torque. Several examples are presented and comparisons made.

31 citations


Journal ArticleDOI
TL;DR: In this paper, the modal radiation impedance of a rectangular panel simply supported in an infinite baffle in the presence of an inviscid, uniform, subsonic flow is determined.

22 citations


Journal ArticleDOI
TL;DR: In this article, the exact formulae for the strain and displacement field, which changes near the surface due to relaxation of the internal concentration stresses, can be used for determination of the distribution of the solute atoms by X-ray diffraction techniques.
Abstract: Deformation caused by a modulated distribution of solute atoms, periodic in one dimension, in a plate-like crystal is studied within the framework of the isotropic theory of elasticity. The exact formulae for the strain and displacement field, which changes near the surface due to relaxation of the internal concentration stresses, can be used for determination of the distribution of the solute atoms by X-ray diffraction techniques.

16 citations


Journal ArticleDOI
TL;DR: In this paper, the authors measured the preferred orientation of the basal planes of kaolinite crystals with an X-ray pole-figure goniometer and calculated the strain according to the theory of March.

16 citations


Journal ArticleDOI
23 Oct 1979
TL;DR: In this paper, the displacement field of a regular N -sided polygonal dislocation loop of arbitrary Burgers vector was derived for a stacking-fault tetrahedron.
Abstract: The computer simulation of electron microscope images of lattice defects requires detailed knowledge of the displacement fields of the defects. By using the method of Yoffe (1960), expressions are derived for the displacement field of a regular N -sided polygonal dislocation loop of arbitrary Burgers vector, and of a stacking-fault tetrahedron, in forms suitable for use in image simulation.

14 citations


Journal ArticleDOI
TL;DR: In this paper, a method of calculating the total force exerted on a slender rigid fiber in a homogeneous displacement field based on the analogous Stokeslet approximation in fluid mechanics is reported.

Journal ArticleDOI
TL;DR: In this paper, the stress distribution in rotating discs made with orthotropic material has been calculated by defining the displacement field by means of both an algebraic and trigonometrical series, and the approximate solutions thus obtained have been compared with known analytical solutions for the particular cases of constant thickness discs with and without a central hole.

Journal ArticleDOI
TL;DR: The theory of multidirector surfaces is shown to correspond to a theory of multi-layered shells based on the assumption of piece-wise linearity of the displacement field across the thickness.

Journal ArticleDOI
TL;DR: In this paper, an analysis of the postbuckling behavior of isotropic cylindrical and conical shells under axial compression is presented, based on Lagrange's variational principle.
Abstract: This paper presents an analysis of the post-buckling behaviour of isotropic cylindrical and conical shells under axial compression. The starting point of the paper is Lagrange's variational principle, the application of which consists in assuming a kinematically admissible strain and displacement field. The field is determined considering the geometry of quasi-isometric deformations of the shell after buckling. That permits solving the problem with no limitation on the magnitude of the displacements.

ReportDOI
01 Jul 1979
TL;DR: In this paper, the deformation theory of plasticity is used to determine the residual stress and displacement field caused by preexpanding fastener holes with an oversize mandrel.
Abstract: : Pre-expanding fastener holes with an oversize mandrel has received considerable attention for use in aircraft structures, since this process has been shown to greatly improve the fatigue life of fastener holes The deformation theory of plasticity is used here to determine the residual stress and displacement field caused by this process Employing plane stress assumptions, general results are obtained for various interference levels and are presented in a graphical form useful to the designer In addition, this analysis indicates that there is an optimum level of interference dependent primarily on the plate geometry The optimum interference levels agree well with experience values established by fatigue testing in aircraft structural alloys

Journal ArticleDOI
TL;DR: In this paper, the elastic interaction energy between a point defect and a stress field is determined for the case in which the point defect displacement field has spheroidal symmetry, called the shape interaction.
Abstract: The elastic interaction energy between a point defect and a stress field is determined for the case in which the point‐defect displacement field has spheroidal symmetry, called the shape interaction. Results are given for the stress field of an edge dislocation, including a term from excluding the elastic interaction arising from the defect and dislocation core regions. With parameters appropriate to an fcc lattice it is then shown that a vacancy will tend to migrate around the dislocation to the compressional side, but that there is an energy barrier in the radial direction between the vacancy and the dislocation on the compressional side.

Journal ArticleDOI
TL;DR: In this article, the effect of an elastic foundation on the natural frequencies of coupled frame shear wall structures was studied. But the authors focused on the finite strip method and did not consider the elasticity of the foundation.
Abstract: The finite strip method is used to study the effect of an elastic foundation on the natural frequencies of coupled frame shear wall structures. The solid wall in the structure is divided into several strip elements, the column is treated as a line element and the effect of the connecting beams is dealt with through the compatibility matrices which transfer their structural properties to the adjacent strip or line elements. The comparison functions which satisfy the boundary conditions of being free at the top and being spring supported at the bottom are used for the displacement field in the longitudinal direction. A series of numerical examples is presented to show the accuracy and applicability of the proposed method.

Journal ArticleDOI
TL;DR: In this article, the authors illustrate anti-plane shear in the setting of finite elasticity theory and with particular reference to an issue which has come to be called Ericksen' s problem.
Abstract: A solid body which in its undeformed state occupies a cylindrical region is said to undergo a deformation corresponding to anti-plane shear if each particle of the body is displaced parallel to the generators of the cylinder by an amount which is independent of the axial position of the particle. The displacement vector field thus has a nonvanishing component u only in the axial direction, and u is a function of position on a cross-section D of the cylinder. Problems involving such deformations are ordinarily simpler than those in which the displacement vector has a more elaborate character, and for this reason they often serve usefully as pilot problems for the analysis of qualitative effects, especially when nonlinearity is involved. (Examples may be found in [1] and in the references cited in [2].) The present paper is intended to illustrate anti-plane shear in its role as exemplar in the setting of finite elasticity theory and with particular reference to an issue which has come to be called Ericksen' s problem.

Patent
02 Aug 1979
TL;DR: In this article, the displacement of a linear motion body can be detected accurately without requiring any complicated mechanism such as a rack and pinion, by converting weight displacement into the body displacement in a fixed method.
Abstract: PURPOSE: To make it possible to detect the displacement of a body in nearly linear motion accurately by a simple constitution by converting weight displacement into the displacement of the body in a fixed method. CONSTITUTION: For weight measurement, weight displacement is changed into the displacement of spring 1, which is further changed into that of lever 2. The displacement of this lever 2 is transferred to lever 3 to rotate slit plate 4 on fulcrum O 2 by driving pin 4' of slit plate 4 through arms A and B and read sensor 5 counts slits 4" to read the displacement. Thus, the linear displacement of a linear motion body can be detected accurately without requiring any complicated mechanism such as a rack and pinion. COPYRIGHT: (C)1981,JPO&Japio

Journal ArticleDOI
TL;DR: In this paper, exact expressions for the displacement field in a homogeneous isotropic elastic half space whose surface is subjected to a unit normal pressure are obtained in the form of triple integrals over finite ranges.

Journal ArticleDOI
TL;DR: In this paper, the 2D problem of scattering of obliquely incident P and SV waves by an infinite rigid elliptic cylinder embedded in an infinite, isotropic and homogeneous elastic medium is solved.

Book ChapterDOI
01 Jan 1979
TL;DR: In this article, the authors consider the analysis of extended defects which are nearly always present in crystalline solids, e.g., stacking faults, dislocation loops, coherent and semicoherent precipitates, extrinsic grain boundary dislocations, etc.
Abstract: Most of the other contributions to this workshop consider the analytical use of the electron microscope in a chemical or structural/crystallographic sense. In this section, we consider the analysis of extended defects which are nearly always present in crystalline solids. These defects are those which are visible in conventional transmission electron microscopy as a result of their extended nature or their long range elastic displacement fields, e.g. dislocations, stacking faults, dislocation loops, coherent and semicoherent precipitates, extrinsic grain boundary dislocations,’etc. It is important to note at the outset that the images of such defects are not dependent only on the form of their displacement field, but also on factors such as their geometry or orientation in the crystal. For example, the image of a small dislocation loop depends, among other things, upon the shape and size of the loop, the orientation of the Burgers vector relative to the plane of the loop, and the orientation of the loop with respect to the electron beam. Even for a straight dislocation in an elastically anisotropic crystal, the image depends not only on the Burgers vector and its orientation with respect to the dislocation line, but also on the direction in the crystal of the dislocation line itself. Thus, a total analysis of a defect involves the determination of these other mainly geometric and crystallographic factors in addition to the displacement field.

Journal ArticleDOI
Jack Pelton1
TL;DR: In this paper, the authors derived an expression which relates a displacement field u defined on a continuum to the change in gravity (ΔgD) brought about by deformation, based on the principle of conservation of mass as stated in continuum mechanics.

Journal ArticleDOI
TL;DR: In this article, the displacement field in a layered medium excited by a moving source is investigated and the resonance occurring when the speeds of the source and the Rayleigh wave coincide is investigated.
Abstract: The displacement field in a layered medium excited by a moving source is investigated. The resonance occurring when the speeds of the source and of the Rayleigh wave coincide is investigated and the character of the damping in this case is clarified.