Showing papers on "Displacement field published in 1998"

Settlement and additional internal forces of grouped piles in layered soil

Abstract: This paper recognizes that soil layering may have a profound effect on the settlement of pile groups and that pile-to-pile interaction induces not only additional settlement at the head of each pile but also additional stresses along its shaft. A general analytical formulation is developed, based on the Winkler model of soil reaction, for determining the vertical interaction factors between two piles embedded in multi-layered soil. It is shown that such interaction factors depend not only on the displacement field arising from the settlement of a loaded ('source') pile but also on the interplay between the adjacent ('receiver') pile and the soil subjected to this displacement field. Such interplay, which has not been considered (at least explicitly) in currently available simple methods, is quantified here through an analytically determined factor ζ which lies between 0 and 1. The paper also develops closed-form expressions for pile stiffness and interaction factors in a two-layer stratum, and highlights ...

Displacement field for an edge dislocation in a layered half‐space

Abstract: The displacement field for an edge dislocation in an Earth model consisting of a layer welded to a half-space of different material is found in the form of a Fourier integral following the method given by Weeks et al. [1968]. There are four elementary solutions to be considered: the dislocation is either in the half-space or the layer and the Burgers vector is either parallel or perpendicular to the layer. A general two-dimensional solution for a dip-slip faulting or dike injection (arbitrary dip) can be constructed from a superposition of these elementary solutions. Surface deformations have been calculated for an edge dislocation located at the interface with Burgers vector inclined 0°, 30°, 60°, and 90° to the interface for the case where the rigidity of the layer is half of that of the half-space and the Poisson ratios are the same. Those displacement fields have been compared to the displacement fields generated by similarly situated edge dislocations in a uniform half-space. The surface displacement field produced by the edge dislocation in the layered half-space is very similar to that produced by an edge dislocation at a different depth in a uniform half-space. In general, a low-modulus (high-modulus) layer causes the half-space equivalent dislocation to appear shallower (deeper) than the actual dislocation in the layered half-space.

Vibration of a Cracked Cantilever Beam

Abstract: A continuous cracked bar vibration model is developed for the lateral vibration ofa a cracked Euler-Bernoulli cantilevered beam with an edge crack. The Hu-Washizu-Barr variational formulation was used to develop the differential equation and the boundary conditions for the cracked beam as an one-dimensional continuum. The crack was modelled as a continuous flexibility using the displacement field in the vicinity of the crack found with fracture mechanics methods. The results of three independent evaluations of the lowest natural frequency of lateral vibrations of an aluminum cantilever beam with a single-edge crack are presented: the continuous cracked beam vibration model, the lumped crack model vibration analysis, and experimental results. Experimental results fall very close to the values predicted by the continuous crack formulation. Moreover, the continuous cracked beam theory agrees better with the experimental results than the lumped crack flexibility theory.

Reflections on the mechanics of granular matter

Abstract: During recent years, a rather basic conflict has emerged between departments of mechanics/physics concerning the description of granular media. Experts from mechanics measure stress/strain relations, using the so-called triaxial tests, and then use these data to predict the behavior of a sample under given boundary conditions. Some physicists have a different view: they have claimed that it is not possible to define a proper displacement field in a heap of sand, and that the notion of strains is thus ambiguous. In the present text, we conclude that the crucial features are the following: (a) a heap is usually formed from a flowing phase of sand, (b) there is (empirically) a sharp interface between the flowing phase and the frozen heap below, (c) we may define for each grain a displacement, which is measured from the moment when it froze. (This displacement is due, for instance, to a compaction of the heap under its own weight.) We also present some aspects of the dynamics, including dune motions and surface flows of grains. Bouchaud, Cates and coworkers have constructed a very compact description for thin flows. We discuss the practical consequences of this picture, emphasizing some possible extensions for thicker flows. This suggests a number of possible experiments on avalanches.

Equivalence of the floating frame of reference approach and finite element formulations

Abstract: The floating frame of reference formulation which is widely used in flexible multibody simulations leads to a highly non-linear inertia matrix. This matrix which exhibits a strong inertia coupling between the reference motion and the elastic deformation can be expressed in terms of a unique set of inertia shape integrals that depend on the assumed displacement field. In this paper, we demonstrate that the floating frame of reference formulation leads to the same dynamic relationship obtained using large deformation finite element formulations. This result clearly demonstrates that the floating frame of reference formulation can also be used in the large deformation analysis of constrained flexible bodies provided that no infinitesimal or finite rotations are used as nodal coordinates; instead, displacements and slopes are used to describe the element configuration. The relationship between the local and the global slopes is defined and used to establish a coordinate transformation which is used to demonstrate the equivalence of the dynamic relationships and the inertia forces obtained using two different finite element formulations. Using this equivalence relationship, a simple and systematic procedure for evaluating all the inertia shape integrals that appear in the floating frame of reference formulation from the constant mass matrix that appears in linear structural dynamics is developed. In order to develop this procedure, the concepts of the local and global shape functions are introduced. The local shape function, which is used in the floating frame of reference formulation, does not have any rigid body modes and is defined using an appropriate set of reference conditions. The global shape function, on the other hand, has a complete set of rigid body modes that can describe an arbitrary rigid body displacement. The analysis presented in this paper demonstrates that the floating frame of reference formulation does not lead to a separation between the rigid body motion and the elastic deformation, and in such a formulation, the reference motion cannot be considered as the rigid body motion of the deformable body.

Submicron deformation field measurements: Part 1. Developing a digital scanning tunneling microscope

Abstract: A new experimental method has been developed for studying deformations of micromechanical material systems at the submicron scale. To that end, a special digital scanning tunneling microscope (STM) was designed to be coupled to a mechanically deforming specimen. Operating in constant current mode, this digitally controlled STM records detailed topographies of specimen surfaces with a resolution of 10 nm in-plane and 7 nm out-of-plane over a 10 μ × 10 μ area. Three-dimensional displacement field information is extracted by comparing topographies of the same specimen area before and after deformation by way of a modified digital image correlation algorithm. The resolution of this (combined) displacement measuring method was assessed on translation and uniaxial tensile tests to be 5 nm for in-plane displacement components and 1.5 nm for out-of-plane motion over the same area. This is the first paper in a series of three in which the authors delineate the main features of this specially designed microscope and describe how it is constituted, calibrated and used with the improved version of the digital image correlation method to determine deformations in a test specimen at the nanoscale.

Vertical Deflection of a Pre-Stressed Concrete Bridge Obtained Using Deformation Sensors and Inclinometer Measurements

Abstract: The serviceability of a bridge is generally analyzed by a comparison between the vertical deflections expected by the engineer and those measured during a load test or in the long term. The existing methods do not allow the determination of the vertical displacements from the measurements carried out by a network of deformation sensors placed inside the bridge. The mathematical model presented allows the determination of the displacement field from internal horizontal deformation measurements and helps in the design of the required sensor network. This model was tested on an experimental model and on the Lutrive Highway Bridge in Switzerland by comparing the changes in vertical displacements under daily temperature variations obtained with the proposed method, with those measured directly using an absolute hydrostatic leveling system. Fiber optic deformation sensors and electrical inclinometers were used to carry out the measurements. With this deformation monitoring system, featuring a precision of 10 micrometers on 1 m long deformation sensors, it is possible to retrieve the vertical displacement field of a beam with a global error less than 8%.

Development of Stresses in Cohesionless Poured Sand

Abstract: The pressure distribution beneath a conical sandpile, created by pouring sand from a point source onto a rough rigid support, shows a pronounced minimum below the apex (`the dip'). Recent work of the authors has attempted to explain this phenomenon by invoking local rules for stress propagation that depend on the local geometry, and hence on the construction history, of the medium. We discuss the fundamental difference between such approaches, which lead to hyperbolic differential equations, and elastoplastic models, for which the equations are elliptic within any elastic zones present .... This displacement field appears to be either ill-defined, or defined relative to a reference state whose physical existence is in doubt. Insofar as their predictions depend on physical factors unknown and outside experimental control, such elastoplastic models predict that the observations should be intrinsically irreproducible .... Our hyperbolic models are based instead on a physical picture of the material, in which (a) the load is supported by a skeletal network of force chains ("stress paths") whose geometry depends on construction history; (b) this network is `fragile' or marginally stable, in a sense that we define. .... We point out that our hyperbolic models can nonetheless be reconciled with elastoplastic ideas by taking the limit of an extremely anisotropic yield condition.

Deformation of the Japanese Islands and seismic coupling: an interpretation based on GSI permanent GPS observations

Abstract: SUMMARY The entire area of the Japanese Islands has been covered by the permanent GPS observation network of the Geographical Survey Institute since 1994. In this paper we use a solution for the vectors of motion during 1995 for a selection of 116 stations to discuss the origin of the observed deformation field. We refer the displacement field to Eurasia using the VLBI-determined motion of Kashima and demonstrate that other choices such as the Okhotsk or North American plates for north Japan are not compatible with the data. 1 yr GPS velocities are much higher than geological constraints would allow because these short-term measurements include transient elastic deformation. However, the good qualitative agreement between the observed geodetic deformation tensors and those inferred from active faults and earthquakes suggests that the Quaternary permanent deformation is essentially the result of the transfer of part of the subduction-induced elastic deformation into permanent plastic deformation. We then compute the elastic deformation of the Japanese Islands caused by interseismic loading of the Pacific and Philippine subduction planes. The geometry of the coupled zone and its downward extension are determined from the distribution of earthquakes for the Pacific slab. For the Philippine slab we use the geometry proposed by Hyndman et al. (1995). These elastic models account for most of the observed velocity field if the subduction movement of the Philippine Sea Plate is 100 per cent locked and if that of the Pacific Plate is 75‐85 per cent locked. We note that the boundaries of the areas where significant elastic deformation is predicted (more than 10 mm yr’1 of motion with respect to Eurasia) coincide with the main zones of permanent deformation: the Eastern Japan Sea deformation zone for the Pacific subduction elastic deformation field and the Setouchi/MTL deformation zone for the Nankai field. Each zone probably accommodates 10‐15 mm yr’1 of motion in the long term (convergence in the Eastern Japan Sea; strike-slip in the Setouchi/MTL zone). To account for this deformation, the eVect of elastic loading from the trench must be combined with 5‐10 mm yr’1 of motion of the Amur Plate with respect to Eurasia. Because loading during the subduction earthquake cycle causes an increase in stress in the Eastern Japan Sea and Setouchi/MTL deformation zones, the probability of earthquake occurrence in these zones may be higher near the end of the cycle.

A 3-D, symmetric, finite element formulation of the Biot equations with application to acoustic wave propagation through an elastic porous medium

Abstract: A weak solution of the coupled, acoustic-elastic, wave propagation problem for a flexible porous material is proposed for a 3-D continuum. Symmetry in the matrix equations; with respect to both volume, i.e. ‘porous frame’–‘pore fluid’, and surface, i.e. ‘porous frame/pore fluid’–‘non-porous media’, fluid–structure interaction; is ensured with only five unknowns per node; fluid pore pressure, fluid-displacement potential and three Cartesian components of the porous frame displacement field. Taking Biot's general theory as starting point, the discretized form of the equations is derived from a weighted residual statement, using a standard Galerkin approximation and iso-parametric interpolation of the dependent variables. The coupling integrals appearing along the boundary of the porous medium are derived for a number of different surface conditions. The primary application of the proposed symmetric 3-D finite element formulation is modelling of noise transmission in typical transportation vehicles, such as aircraft, cars, etc., where porous materials are used for both temperature and noise insulation purposes. As an example of an application of the implemented finite elements, the noise transmission through a double panel with porous filling and different boundary conditions at the two panel boundaries are analysed. © 1998 John Wiley & Sons, Ltd.

Nonlinearly Elastic Shell Models: A Formal Asymptotic Approach II. The Flexural Model

Abstract: This paper is the sequel of Part I, in which the limiting displacement field of a thin shell when its thickness approaches zero is identified as the solution of a two‐dimensional nonlinear membrane shell model. When the geometry of the middle surface of the shell and the boundary conditions allow non‐zero “inextensional displacements”, the previous membrane limit model is not relevant. In this case, we show how to “update” the assumptions on the applied forces acting on the shell so that a limiting model can be derived by an asymptotic analysis. Furthermore, we identify this limit as the two‐dimensional nonlinear flexural shell model.

Applying voltage sources to a Luttinger liquid with arbitrary transmission

Abstract: The Landauer approach to transport in mesoscopic conductors has been generalized to allow for strong electronic correlations in a single-channel quantum wire. We describe in detail how to account for external voltage sources in adiabatic contact with a quantum wire containing a backscatterer of arbitrary strength. Assuming that the quantum wire is in the Luttinger liquid state, voltage sources lead to radiative boundary conditions applied to the displacement field employed in the bosonization scheme. We present the exact solution of the transport problem for arbitrary backscattering strength at the special Coulomb interaction parameter $g=1/2.$

Postbuckling analysis of thin rectangular laminated plates by spline FSM

Abstract: Description is given of a versatile spline finite strip method for analysing the geometrically non-linear response of rectangular, composite laminated plates of arbitrary lay-up to progressive end shortening in their plane. The plates are assumed to be thin, thus allowing the analysis to be based on the use of classical plate theory, and the non-linearity is introduced in the strain-displacement equations in the manner of the von Karman assumption. A number of finite strip models have been developed but attention is concentrated on a particular model whose displacement field uses cubic B-splines longitudinally and quadratic crosswise interpolation of the in-plane displacements. Description is given of the use of this model in applications involving plates which have simply supported ends and which either are made of homogeneous, isotropic material or of anistropic material or are laminates with unbalanced cross-ply or angle-ply lamination.

Asymptotics of arbitrary order for a thin elastic clamped plate, II. Analysis of the boundary layer terms

Abstract: This paper is the last of a series of two, where we study the asymptotics of the displacement in a thin clamped plate as its thickness tends to 0 . In Part I, relying on the structure at infinity of the solutions of certain model problems posed on unbounded domains, we proved that the combination of a polynomial Ansatz (outer expansion) and of a boundary layer Ansatz (inner expansion) yields a complete multiscale asymptotics of the displacement and optimal estimates in energy norm. The “profiles” for the boundary layer terms are solutions of such model problems. In this paper, adapting Saint-Venant’s principle to our framework, we prove the results which we used in Part I. Investigating more precisely the structure of the boundary layer terms, we go further in the analysis performed in Part I: the introduction of edge layer terms along the intersections of the clamped face with the top and the bottom of the plate respectively, allows estimates in higher order norms. These edge layer terms are constructed with the help of stable asymptotics, and are the singular parts of the boundary layer terms. As a by-product of all these investigations, we obtain expansions and estimates for the stress tensor in various anisotropic norms, and also estimates in L norm form the displacement field. To appear in Asymptotic Analysis

Utility of elastic models in predicting fault displacement fields

Abstract: Although elastic models have long been used to model earthquake deformation, their application to fault problems is questionable, as accumulated fault strain is higher and the relevant timescales are longer. We test the utility of using elastic models to predict fault displacement fields by independently measuring the three-dimensional slip (offset) distribution and displacement field of small normal faults. The displacement field is constrained from the topography of the deformed bedding planes; the slip distribution is constrained from stratal offsets in multiple sections of fault-normal saw-cuts. Using the observed slip distribution, we calculate both one- and three-dimensional elastic displacement fields. We find that the large strain associated with fault growth can be accommodated with linear elastic models. Much of the remaining misfit between the data and the model may result from elastic interaction with other nearby faults, the inelastic zone around surrounding fault tips, and prefaulting irregularities in the measured bedding plane surface.