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Showing papers on "Displacement field published in 1987"


Journal ArticleDOI
TL;DR: In this paper, a displacement-pressure (up) finite element formulation for the geometrically and materially nonlinear analysis of compressible and almost incompressible solids is proposed.

439 citations


Journal ArticleDOI
TL;DR: In this paper, an approximate method to derive the crack opening displacement field from the stress intensity factor was proposed by Petroski and Achenbach [Engng Fracture Mech. 10, 257].

161 citations


Journal ArticleDOI
TL;DR: In this article, the displacement field is evaluated throughout the elastic medium so that the continuity of the displacement and the traction fields along the interfaces between the layers is satisfied in a least-squares sense.
Abstract: Diffraction of plane harmonic P, SV , and Rayleigh waves by dipping layers of arbitrary shape is investigated by using an indirect boundary integral equation approach. The layers are of finite length perfectly bonded together. The material of the layers is assumed to be homogeneous, weakly anelastic, and isotropic. The displacement field is evaluated throughout the elastic medium so that the continuity of the displacement and the traction fields along the interfaces between the layers is satisfied in a least-squares sense. Presented numerical results show that the surface strong ground motion amplification effects depend upon a number of parameters present in the problem, such as, type, frequency, and angle of the incident wave, the impedance contrast between the layers, the component of the displacement field being observed, and the location of the observation point at the surface of the half-space. The results demonstrate that the presence of soft alluvial deposits in form of dipping layers may cause locally very large amplification or reduction of the surface ground motion when compared with corresponding free-field motion.

134 citations


Journal ArticleDOI
TL;DR: In this article, a two-dimensional elastoplastic model of a long cylindrical cavity in an infinite rock mass subject to non-hydrostatic far-field stress loading is presented.

113 citations


Journal ArticleDOI
TL;DR: In this article, a hybrid stress model based on the modified complementary energy principle and taking into account the transverse shear deformation effects is developed for the analysis of laminated composite plates.

112 citations


Journal ArticleDOI
TL;DR: In this paper, the authors prove the existence of a displacement field and a stress field that satisfy the dynamical equation for continuous media and the Prandtl-Reuss constitutive law of elasto-perfect plasticity.
Abstract: We prove the existence of a displacement field and of a stress field that satisfy the dynamical equation for continuous media and the Prandtl-Reuss constitutive law of elasto-perfect plasticity. First we obtain the existence of a displacement rate in a space of functions of bounded deformation, where the constitutive law is satisfied in an integral form, then we show that one can choose a good representative for the stress in such a way that the Prandtl-Reuss law is satisfied almost everywhere with respect to the deformation measure.

58 citations


Journal ArticleDOI
TL;DR: In this paper, a Bueckner singular displacement field is incorporated into the boundary element method in order to calculate weight functions for mixed mode stress intensity factor in a two-dimensional cracked body.
Abstract: A Bueckner singular displacement field is incorporated into the boundary element method in order to calculate weight functions for mixed mode stress intensity factor in a two-dimensional cracked body. Weight functions for modes I and II can be calculated independently and hence the factors KI and KII can be obtained for any arbitrary loading on any boundary. Results are obtained for some slant crack problems in finite sheets and compared with known results where available.

58 citations


Journal ArticleDOI
TL;DR: In this article, the displacement field u and the vector Airy stress function O for a dislocation with Burgers vector b and a line force of strength f acting along the central axis of a rotationally inhomogeneous medium are derived in terms of the integral theory of elasticity.
Abstract: In a rotationally inhomogeneous medium the elastic constants show an angular dependence Cijkl (ω) around an axis. Grain boundaries, bicrystals, wedges and wedge cracks are special cases of a rotationally inhomogeneous medium. The displacement field u and the vector Airy stress function O for a dislocation with Burgers vector b and a line force of strength f acting along the central axis of such a medium are derived in terms of the integral theory of elasticity.

42 citations


Journal ArticleDOI
TL;DR: In this article, a high-order plate bending displacement field is developed for the analysis of layered composite plates, where the parabolic distribution of the transverse shear strains is considered and a mixed finite element model is introduced from the equation.

40 citations


Journal ArticleDOI
TL;DR: In this paper, the authors used laser holographic interferometry to measure the out-of-plane displacement field in the uniaxial compression testing of a marble plate with an inclined crack.

34 citations


Journal ArticleDOI
TL;DR: In this article, stress intensity factors are calculated in weighted average at the surface and the deepest point of a circular-fronted surface crack in a cylindrical bar by use of the weight function method.
Abstract: Stress intensity factors are calculated in weighted average at the surface and the deepest point of a circular-fronted surface crack in a cylindrical bar by use of the weight function method. A wide range of various crack shapes are studied, from a nearly straight-fronted edge crack to a semi-circular crack front. Use of the weight function method requires that the crack opening displacement field of a reference load has to be known. It was obtained by 3-D finite element analysis. Results are presented for the cracked cylinder subjected to a constant stress (tension) and a linear stress distribution acting perpendicular to the crack faces and they are compared with values found by other investigators.

Journal ArticleDOI
TL;DR: In this paper, the longitudinal elastic modulus of a composite possessing dilute concentrations of aligned cylindrical fibers is calculated using a boundary value problem, referred to as the auxiliary problem, which yields the perturbed displacement field directly.

Journal ArticleDOI
TL;DR: In this paper, a new numerical method for calculating the properties of waves on surfaces of inhomogeneous elastic materials of any anisotropy is presented. But the method uses the wave equation with the elastic moduli and mass density assumed to be functions of position and the displacement field is expanded in a series of Laguerre functions.

Journal ArticleDOI
01 Aug 1987-Wear
TL;DR: In this paper, the effect of bearing deformation on the static and dynamic performance characteristics of an elliptical bearing is presented, where the finite element method has been used to solve the three-dimensional Navier-Stokes and the continuity equations governing the lubricant flow in the clearance space of the journal bearing and the threedimensional elasticity equations governing displacement field in the bearing shell.

Journal ArticleDOI
TL;DR: In this article, the weight function method is applied to solving three-dimensional linear elastic fracture mechanics (LEFM) problems, and the fundamental equations of LEFM are satisfied and the minimum of additional assumptions are used.
Abstract: The weight function method is applied to solving three-dimensional linear elastic fracture mechanics (LEFM) problems. Within the framework of the present approach the fundamental equations of LEFM are satisfied and the minimum of additional assumptions are used.

Journal ArticleDOI
TL;DR: In this paper, the problem of finding an optimal design of the midsurface of an elastic shell with respect to a given load (self-weight or wind, for instance), has to resist as well as possible towards given criteria.
Abstract: We suppose that a shell submitted to a given load (self-weight or wind, for instance), has to resist as well as possible towards given criteria. We aim at the following problem: Is it possible to find an optimal design of the midsurface of the shell with respect to this criteria? This problem can be worked using gradient-type algorithms. In this paper we work on the differentiability proof and numerical computation of the gradient. For a given shape of the midsurface, we consider that the shell works in linear elastic conditions. We use the Budiansky-Sanders model for elastic shells, from which we get the displacement field in the shell. The criteria to be minimized are supposed to depend on the shape directly, and also through the displacement field. In this paper, we prove that the displacement field depends on the shape in a Frechet-differentiable manner (for an appropriate topology on the set of admissible shapes). Then we give a way to compute the gradient of a given criteria from a theoretical point of view and from a numerical point of view. This allows us to use descent-type methods of optimization. They will lead to shapes which react better and better. Notice that we know nothing about convergence of these methods, the existence and unicity of a theoretical optimal solution. But from a practical point of view, it is quite interesting to be able to modify a given shape to obtain a better one.

Journal ArticleDOI
TL;DR: Real-time methods for differentiation of in-plane displacement fields produced by the moire interferometry technique are introduced and the issue of carrier patterns and extraneous fractional fringe order is clarified.
Abstract: Real-time methods for differentiation of in-plane displacement fields produced by the moire interferometry technique are introduced. Two approaches are developed: (1) optical shearing of displacement patterns and (2) superposition of two lateral shear interferograms of wavefronts from 2 diffraction orders of the specimen grating. Coherence problems are circumvented by polarization effects. In both cases additive-type moire fringes give the map of displacement derivatives of the object under load. The issue of carrier patterns and extraneous fractional fringe order is clarified. Experimental verification of the principle is presented.

Journal ArticleDOI
TL;DR: In this article, the fundamental frequency of vibration (antisymmetric mode) of a frame elastically restrained against translation and rotation at the ends, carrying concentrated masses, was determined by means of the Rayleigh-Ritz method and simple polynomial coordinate functions in order to represent the displacement field.

Journal ArticleDOI
TL;DR: Heterodyne holographic interferometry provides automated interference phase measurement with high resolution and allows the quantitative evaluation of 3-D displacement and strain on solid objects and its possibilities and limitations are discussed in detail.
Abstract: Heterodyne holographic interferometry provides automated interference phase measurement with high resolution and allows the quantitative evaluation of 3-D displacement and strain on solid objects. The fundamentals of heterodyning in double-exposure holography are reviewed and its possibilities and limitations are discussed in detail. Experimental results of strain measurement on a curved object surface are reported. Three double-exposure hologram recordings with different illuminations are used to get the vector displacement. Based on locally calculated derivatives of the displacement field, a sensitivity for the strain components of 1 μm/m with a spatial resolution of a few millimeters has been achieved. The features of heterodyne holographic interferometry are compared with those of quasiheterodyne (phase stepping) fringe interpolation.

Journal ArticleDOI
TL;DR: In this paper, a three-dimensional eight-node hybrid stress finite element method is developed for the analysis of laminated plates, which is based on the modified complementary energy principle and takes into account the transverse shear deformation effects.

Proceedings ArticleDOI
TL;DR: In this article, the elastic Kirchhoff migration is implemented for the VSP recording geometry, where the pressure data are replaced by the magnitudes of the elastic data as reconstructed from the vertical components, and the acoustic Green's functions are replaced with either the P or S wave elastic Green's function.
Abstract: Elastic Kirchhoff migration is implemented for the VSP recording geometry. The resulting migration formula requires measurement of the stress as well as the displacement. Since stress is not measured in a VSP, and in many cases the horizontal component of displacement is not measured, approximate migration formulas are given for these cases. The elastic migration formula for the case where only the vertical components are available, is the same as the acoustic migration formula, where the pressure data are replaced by the magnitudes of the elastic data as reconstructed from the vertical components, and the acoustic Green’s functions are replaced with either the P or S wave elastic Green’s functions. Two expressions for migration of two component displacement data are presented. In the first, the terms involving traction data are simply ignored. In the second, an improved backpropagation operator for the displacement field is obtained by replacing the traction data in the Kirchhoff integral by displacement data using Hooke’s law. The migration expressions for the cases where two component data are available produce images which are less contaminated by artifacts than the migration images of one component data.

Journal ArticleDOI
TL;DR: In this paper, a displacement finite element method for analyzing a beam on continuous elastic foundation is presented, which accounts for the effects of both the Filonenko-Borodich and Pasternak foundation models in a consistent and complete way.

Patent
08 Sep 1987
TL;DR: In this article, a fine positioning device is formed of a rigid support member, a first set of radial flexible-beam displacement mechanisms provided symmetrically to each other on the support member to produce angular displacements about a first axis, a second set of flexible-beam displacement mechanisms connected to either one of the sets of radial flexibly-beam displacements for producing angular displacement about a third axis which is perpendicular to both the first and second axes.
Abstract: A fine positioning device is formed of a rigid support member; a first set of radial flexible-beam displacement mechanisms provided symmetrically to each other on the support member to produce angular displacements about a first axis; a second set of radial flexible-beam displacement mechanisms provided symmetrically to each other on the support member to produce angular displacements about a second axis which is perpendicular to the first axis; a third set of radial flexible-beam displacement mechanisms connected to either one of the sets of radial flexible-beam displacement mechanisms to produce angular diaplacements about a third axis which is perpendicular to both the first and second axes; and a fine motion table fixed on the radial flexible-beam displacement mechanisms which are other than those connected to the radial flexible-beam displacement mechanisms for producing angular displacements about the third axis.

Journal ArticleDOI
TL;DR: In this paper, the effect of the flexibility of bearing linings on the static and dynamic performance of a three-lobe journal bearing was studied, where the authors used the finite element method and an iteration scheme to solve the three-dimensional Navier-Stokes and the continuity equations governing the lubricant flow in the clearance space of the bearing.

Journal ArticleDOI
TL;DR: In this article, a non-shallow shell made of an isotropic homogeneous material, working in linear elastic conditions, subjected to a given load, was considered and the shape of the shell was modified to fit better towards a given criterion.
Abstract: We consider a non-shallow shell made of an isotropic homogeneous material, working in linear elastic conditions, subjected to a given load. Our aim is to change the shape of the shell so that it resists better towards a given criterion. By shape, we mean essentially the midsurface of the shell. The thickness could be added without any difficulty. The important aspect that we study here is the midsurface. This problem is worked by gradient type methods. We prove that if the criterion depends on the displacement field through a differentiable function, then it depends on the shape in a differentiable manner, because the displacement field is a differentiable function of the shape. Then we present an analytical formula giving the exact gradient of the criteria before any discretization. After that, we explain how to compute numerically an approximation to this exact gradient. Then we give numerical results.

Journal ArticleDOI
TL;DR: In this paper, a moving Dugdale model for modes I, II and III is proposed and a fully dynamic analysis of the problem with the help of complex function theory is given.
Abstract: This study proposes a moving Dugdale model for modes I, II and III, presents a fully dynamic analysis of the problem with the help of complex function theory and gives an exact analytical solution. From this solution, the stress and displacement fields and the dynamic crack opening displacement for mode I, II and III are determined. Based on this, the author proposes a criterion to describe dynamic behaviour of a moving defect in solids.

Journal ArticleDOI
TL;DR: In this paper, a method for determining for determining the elastodynamic (P and SV waves) radiation characteristics of finite-size sources buried in horizontally layered media, having periodically corrugated interfaces, is described.
Abstract: A method for determining for determining the elastodynamic ( P and SV waves) radiation characteristics of finite-size sources buried in horizontally layered media, having periodically corrugated interfaces, is described. In particular, the example problem chosen to illustrate the procedure is as follows: a solid plate lies on top of a solid half-space; the solid-solid interface has been taken to be planar, but traction-free conditions prevail on the other boundary of the elastic plate, which surface is also periodically corrugated; and the source has been taken to be an isotropic, P -wave line source located inside the elastic plate. The technique presented utilizes the plane wave spectral decomposition of the relevant fields within the framework of the extended boundary condition method or the T matrix method. Since the T -matrix method is a matrix approach, it is very attractive computationally and is certainly more tractable than a method based on the direct solution of the integral equations involved in the scattering problem. Numerical results are given to delineate the various features of the field diffracted into the elastic half-space, as well as the displacement field induced on the traction-free boundary of the elastic plate. The specific example examined is directly related to regional wave propagation in a continental crustal wave guide.

Journal ArticleDOI
TL;DR: In this paper, many-beam computer image simulations are described for model line defects within a crystal and for the same defects lying on a crystal boundary, with the aim of determining the degree to which a simple mapping approach might be used to provide a quantitative, if preliminary, measure of the range, form and magnitude of the displacement field of an unknown boundary defect.

Patent
22 Oct 1987
TL;DR: An apparatus for measuring linear displacement having three slides movable along orthogonal axes is described in this paper, where the linear displacement along all three axes can be viewed and read on all three scales from the same position and in subtantially the same sighting direction.
Abstract: An apparatus for measuring linear displacement having three slides movable along orthogonal axes. Two slides each having a scale for measuring linear displacement which extends substantially parallel to the path of movement of its associated slide. The third slide has a movable scale for measuring linear displacement, with a portion extending at substantially a right angle to the path of movement of the third slide, so that the linear displacement along all three axes can be viewed and read on all three scales from the same position and in subtantially the same sighting direction.

Journal ArticleDOI
TL;DR: In this article, the authors developed a solution scheme for the analysis of the transfer of an axially symmetric torque from a non-uniform elastic bar into a layered elastic halfspace.
Abstract: This paper develops a novel solution scheme for the analysis of the transfer of an axially symmetric torque from a nonuniform elastic bar into a layered elastic halfspace. The torsional deformation of the bar is specified by a set of kinematically admissible functions that are indeterminate to within a set of arbitrary constants. The embedded bar‐elastic halfspace system is represented by extended halfspace and a fictitious bar. The fictitious traction distribution on the extended half‐space due to a specified displacement field is determined by a discretization procedure. The results of the analysis is used to develop the total potential energy functional for the bar‐elastic halfspace loading system. The minimization of the functional determines explicitly the torsional deformation field. The numerical results presented in the paper illustrate the manner in which the torsional stiffness of the bar is influenced by its nonuniformity and its relative rigidity.