Showing papers on "Displacement field published in 1989"
TL;DR: In this paper, the authors examined the theoretical ranges and distributions of rates of change of displacement on fault surfaces using a limited number of displacement gradient measurements, based on a knowledge of the effective shear modulus of the rocks containing a fault.
202 citations
TL;DR: In this article, a thermoplastic theory of fluid-filled porous materials is established, which incorporates the heat transportation by fluid flow through pores in addition to the difference between the thermal expansibility of the pore fluid and that of the solid skeleton.
142 citations
TL;DR: In this article, the authors derived exact analytical solutions to problems of SH line force and line dislocation operating at the interface between two quarter spaces and showed that the resulting fields differ from that of a homogeneous half space in the distribution of travel times, wave amplitudes and polarity of first motions.
Abstract: SUMMARY Exact analytical solutions to problems of SH line force and line dislocation operating at the interface between two quarter spaces are derived and discussed. It is shown that the resulting fields differ from that of a homogeneous half space in the distribution of travel times, wave amplitudes and polarity of first motions. These effects are documented in the literature. It is, therefore, suggested that when constructing theoretical seismic displacement fields from source, path and site effects, it is important to use response functions that account for material heterogeneity in the source region. An extension of the formulation used in the case of SH line dislocation leads to a 3-D representation theorem which gives the displacement field in terms of the displacement discontinuities along the rupture area. The resulting overall sue scaling parameter is the ‘potency’, which does not suffer from an ambiguity associated with seismic moment in the case of heterogeneous source region.
97 citations
TL;DR: Friedmann-Lemaitre-Robertson-Walker (FLRW) cosmological models were derived in Lyra's manifold assuming a time dependent displacement field in this paper, which solved the singularity, entropy and horizon problems which exist in the standard models of cosmology based on Riemannian geometry.
Abstract: Friedmann-Lemaitre-Robertson-Walker (FLRW) cosmological models are derived in Lyra's manifold assuming a time dependent displacement field. The models obtained solve the singularity, entropy and horizon problems which exist in the standard models of cosmology based on Riemannian geometry. The asymptotic behaviour of the models is also examined. 1.
74 citations
TL;DR: In this article, the authors measured mean values of the displacement gradients for the deformation, and if the gradients are approximately constant, calculate bulk strain values from a natural fault array in the Tennessee Appalachians.
64 citations
TL;DR: In this paper, a twenty-node hexahedron element is employed in each layer for the displacement field, and the equilibrium equation is enforced by the variational principle, which is derived from the Hellinger-Reissner principle.
Abstract: The variational principle of this element can be derived from the Hellinger-Reissner principle through dividing six stress components into a flexural part (σ x , σ y , τ xy , σ z ) and a transverse shear part (τ xy , τ yz ). The element stiffness matrix can be formulated by assuming a stress field only for transverse shear stresses, while all the others are obtained from an assumed displacement field. A twenty-node hexahedron element is employed in each layer for the displacement field. The equilibrium equation is enforced by the variational principle
58 citations
TL;DR: In this paper, a geometrically non-linear formulation for the three dimensional curved beam elements using the total Lagrangian approach is presented, where the element geometry is constructed using co-ordinates of the nodes on the centroidal or reference axis and the orthogonal nodal vectors representing the principal bending directions.
Abstract: This paper presents a geometrically non-linear formulation (GNL) for the three dimensional curved beam elements using the total Lagrangian approach. The element geometry is constructed using co-ordinates of the nodes on the centroidal or reference axis and the orthogonal nodal vectors representing the principal bending directions. The element displacement field is described using three translations at the element nodes and three rotations about the local axes . The GNL three dimensional beam element formulations based on these element approximations are restricted to small nodal rotations between two successive load increments. The element formulation presented here removes such restrictions. This is accomplished by retaining non-linear nodal terms in the definition of the element displacement field, and the consistent derivation of the element properties. The formulation presented here is very general and yet can be made specific by selecting proper non-linear functions representing the effects of nodal rotations. The details of the element properties are presented and discussed. Numerical examples are also presented to demonstrate the behaviour and the accuracy of the elements. A comparison of the results obtained from the present formulation with those available in the literature using a linearized element approximation clearly demonstrate the superiority of the formulation in terms of large load steps, large rotations between two load steps and extremely good convergence characteristics during equilibrium iterations. The displacement approximation of these elements is fully compatible with the isoparametric curved shell elements (with large rotations), and since the elements possess offset capability, these elements can also serve as stiffeners for the curved shells.
55 citations
TL;DR: In this paper, the problem of finding the response of a thick infinite plate to the application of body forces is considered, and transform techniques are employed to reduce the problem to that of an initial boundary value problem for a one-dimensional hyperbolic system.
54 citations
TL;DR: In this article, the effect of bearing shell deformation on the static and dynamic performance characteristics of a four pocket capillary-compensated hydrostatic journal bearing have been studied, where the finite element method has been used to solve the Reynold's equation governing the lubricant flow in the clearance space of a hydrostatic bearing and the three-dimensional elasticity equations governing the displacement field in the bearing shell.
43 citations
TL;DR: In this article, a 150 lines mm-1 specimen grating is imaged onto a reference grating with a specially modified camera lens and the resulting real-time moire fringes are recorded with a high speed image converter camera.
Abstract: The techniques of high resolution moire photography and high speed photography have been combined to allow simultaneous measurement of both in-plane components of a transient displacement field with microsecond time resolution. A 150 lines mm-1 specimen grating is imaged onto a reference grating with a specially modified camera lens. The resulting real-time moire fringes are recorded with a high speed image converter camera. An automatic fringe analysis technique based on the 2-D Fourier transform method is used to extract the displacement information from the high speed sequences. The techniques are illustrated by the results of an investigation into the transient deformation of polymethyl methacrylate caused by solid particle impact.
36 citations
TL;DR: In this article, the set of singular integral equations which relates unknown fields on the surface of the scatterer to a time-harmonic incident wave is solved by the boundary element method.
Abstract: The set of singular integral equations which relates unknown fields on the surface of the scatterer to a time-harmonic incident wave is solved by the boundary element method. The general method of solution is discussed in some detail for scattering by an inclusion. Results are presented for a spherical cavity, and for a soft and a stiff spherical inclusion. Fields on the surface of the scatterer are compared with previous results obtained by different methods. Back-scattered and forward-scattered displacement fields are presented, both as a function of position at fixed frequency, and as a function of frequency at fixed position. The quasi-static approximation is briefly discussed.
TL;DR: In this paper, the problem of determining the resulting stress and displacement fields throughout the disc was solved (within the two-dimensional linear theory) exactly and in closed form, in particular the stress intensity factor and the crack opening displacement were evaluated for both the plane stress and plane strain cases with any crack length b (0
Abstract: A circular disc of radius a, made of homogeneous, isotropic, linearly elastic material, contains a radial edge crack of length b. The disc is rotating with constant angular velocity about an axis through its centre and perpendicular to its plane. The problem of determining the resulting stress and displacement fields throughout the disc is solved (within the two-dimensional linear theory) exactly and in closed form. In particular the stress intensity factor and the crack opening displacement are evaluated for both the plane stress and plane strain cases with any crack length b (0
01 Jan 1989
TL;DR: In this article, the authors apply an extended theory to a complete system of nondestructive evaluation, taking into account the structure of different laser modes, the optical, thermal and elastic material properties as well as the finite area of a capacitance transducer.
Abstract: The basic work of R. M. White [1] on the generation of elastic waves by transient surface heating was followed by numerous theoretical and experimental investigations, to understand the nature of the strange elastic waveforms obtained and to make this technique available for practical applications [2]. The theoretical considerations of L. R. F. Rose [3] about a point of dilation just below the surface of an elastic halfspace leads to a reasonable qualitative agreement with experiments, but do not relate all relevant material and laser beam parameters to the displacement field. This contributions outlines the application of an extended theory to a complete system of nondestructive evaluation, taking into account the structure of different laser modes, the optical, thermal and elastic material properties as well as the finite area of a capacitance transducer.
TL;DR: In this paper, the approximate analytical determination of the crack opening displacement field from the reference stress intensity factor is outlined in detail, in the absence of a reference solution the FE-method is used in some special applications.
Abstract: The weight function method is an important procedure to determine stress intensity factors for complex stress distributions. This approach is based on the knowledge of the crack opening displacement field for a reference load case. The approximate analytical determination of the crack opening field from the reference stress intensity factor is outlined in detail. In the absence of a reference solution the FE-method is used in some special applications. The general treatment is illustrated by a number of examples, which have been obtained by the authors in the last years.
TL;DR: In this paper, the use of digital image processing equipment was used to determine the displacement fields in an internally pressurized composite cylinder, and the results of actual experiments performed by the authors on both a Plexiglas and a composite cylinder.
Abstract: The lack of a quick, nondestructive method of flaw detection in composite materials is a hindrance to their use. Optical methods of determining displacements hold promise as a method of detection of these flaws. This paper illustrates the use of digital-image-processing equipment to determine the displacement fields in an internally pressurized composite cylinder. Included are results of actual experiments performed by the authors on both a Plexiglas and a composite cylinder.
TL;DR: In this paper, a plane strain model using a boundary method is investigated for the scattering of elastic waves by dipping layers of arbitrary shape embedded within an elastic half-space, where unknown scattered waves are expressed in the frequency domain in terms of wave functions which satisfy the equations of motion and appropriate radiation conditions at infinity.
Abstract: Scattering of elastic waves by dipping layers of arbitrary shape embedded within an elastic half-space is investigated for a plane strain model by using a boundary method. Unknown scattered waves are expressed in the frequency domain in terms of wave functions which satisfy the equations of motion and appropriate radiation conditions at infinity. The steady state displacement field is evaluated throughout the elastic medium for different incident waves so that the continuity conditions along the interfaces between the layers and the traction-free conditions along the surface of the half-space are satisfied in the least-squares sense. Transient response is constructed from the steady state one through the Fourier synthesis.
The results presented show that scattering of waves by dipping layers may cause locally very large amplification of surface ground motion. This amplification depends upon the type and frequency of the incident wave, impedance contrast between the layers, component of displacement which is being observed, location of the observation station and the geometry of the subsurface irregularity. These results are in agreement with recent experimental observations.
TL;DR: In this paper, a higher-order theory of laminated composites under in-plane loads is developed and the displacement field is expanded in terms of the thickness co-ordinate, satisfying the zero shear stress condition at the surfaces of the laminate.
03 Apr 1989
TL;DR: In this article, a new method of modeling frequency-dependent material damping in structural dynamics analysis is reported, motivated by results from materials science, augmenting thermodynamic fields (ATF) are introduced to interact with the usual mechanical displacement field.
Abstract: A new method of modeling frequency-dependent material damping in structural dynamics analysis is reported. Motivated by results from materials science, augmenting thermodynamic fields (ATF) are introduced to interact with the usual mechanical displacement field. The methods of irreversible thermodynamics are used to develop coupled material constitutive relations and partial differential equations of evolution (PDE). The resulting PDE are implemented for numerical solution within the computational framework of the finite element method. The ATF modeling method is illustrated using several examples including longitudinal vibration of a rod, transverse vibration of a beam, and vibration of a large space truss structure.
TL;DR: The evaluation of double-exposure records in optical metrology is simplified by using two-step optical processing that is performed on many interrogation areas simultaneously by a 2-D array of narrow focused light beams.
Abstract: The evaluation of double-exposure records in optical metrology (speckle photography or particle image velocimetry) is simplified by using two-step optical processing that is performed on many interrogation areas simultaneously by a 2-D array of narrow focused light beams. A first application of this procedure to the original record, if dimensioned properly, produces an array of small nonoverlapping Young’s fringe systems. The photographic record of these patterns is subjected to the same operation once more, each beam illuminating precisely one pattern. The resulting output is an array of autocorrelation functions that are a direct representation of the displacement field since the spacing of respective side peaks gives the displacement. A single whole-field interrogation of the array of fringe systems produces an optical representation of accumulated displacement values thus rendering the statistics of the displacement field. The required matrix of light beams is generated by holographic optical elements.
TL;DR: In this paper, it was shown that the Murnaghan's displacement field is the more general form for a cylindrical tube (or rod) of isotropic material submitted to a load having the same symmetries.
Abstract: It is shown that the Murnaghan's displacement field is the more general form for a cylindrical tube (or rod) of isotropic material submitted to a load having the same symmetries. The use of this field enables us to analyse correctly the data furnished by strain gages. This is particularly useful in the case of torsion: the influence of a small misorientation, which actually always exists, can then be explained and taken into account.
TL;DR: By imaginal method the solution of displacement discontinuity for anisotropic half-plane is derived in this paper, according to the Betti's reciprocal theorem, the relationship between the stress intensity factor KI and the increment ΔvΔa is established and numerical results of KI are obtained by the twice calculation method.
TL;DR: In this article, the scattering of elastic plane harmonic SH, SV, P, and Rayleigh waves by three-dimensional nonaxisymmetric dipping layers embedded in an elastic half-space was investigated.
Abstract: Using a boundary method, we investigated the scattering of elastic plane harmonic SH, SV, P, and Rayleigh waves by three-dimensional nonaxisymmetric dipping layers embedded in an elastic half-space. The valley was subjected to incident Rayleigh wave and oblique incident SH, SV, and P waves. The method utilized spherical wave functions to express the unknown scattered field. These functions satisfy the equation of motion and radiation conditions at infinity but they do not satisfy the stress-free boundary conditions at the surface of the half-space. The boundary and continuity conditions are imposed locally in the least-square-sense at several points on the layer interface and on the surface of the half-space. A comparative study was done to examine the validity and limitations of the two-dimensional approximations (antiplane and plane strain models) of three-dimensional models. It is demonstrated that the two-dimensional approximations may be inadequate to represent actual displacement field for three-dimensional irregularities.
TL;DR: In this paper, an embedded elliptical crack is investigated for the application of Cruse and Besuner's method to calculate approximative energy release rates or averaged weighted stress intensity factors.
TL;DR: In this article, the Bubnov-Galerkin method of weighted residuals is used to transform the coupled differential equations to a set of algebraic equations which can be readily solved.
Patent•
15 Mar 1989
TL;DR: In this article, a displacement sensor, particularly for monitoring angular displacement over 360°, uses two transducers whose moving parts (2, 3, 26) are coupled for synchronous displacement over respective paths.
Abstract: A displacement sensor, particularly for monitoring angular displacement over 360°, uses two transducers (1, 2 and 1, 3; 1, 2 and 3, 14, 16; 24-26) whose moving parts (2, 3; 26) are coupled for synchronous displacement over respective paths. Each transducer has a measurable parameter. For the first transducer (1, 2; 24-26), the path has a plurality of equal portions (AB, BA) in each of which the parameter varies uniformly over the same range. For the second transducer, the values or ranges of its parameter are characteristic of the portions. Thus they can provide a logic signal for indicating the path portion so that the parameter value of the first transducer determines the displacement position uniquely. For example, the first transducer may be a rotary potentiometer (1, 2) with 180° taps (A, B). The second transducer (3, 14, 15) may employ two 180° contact plates (14, 15) held at high and low potential (respectively), and a sliding contact (3) rotationally fast with the contact (2) of the potentiometer.
TL;DR: In this paper, the spherically symmetric deformation of a hollow sphere which has a traction-free inner wall and a prescribed radial displacement δ at its outer wall is studied.
TL;DR: In this paper, a pair of quartic polynomials in the tangent of the output angular displacement were derived for two TTTR mechanisms designed in such a way that the serially connected pairs of Hooke joints had their successive transverse axes parallel or mutually perpendicular.
Abstract: A pair of quartic polynomials in the tangent of the output angular displacement were derived for two TTTR mechanisms designed in such a way that the serially connected pairs of Hooke joints have their successive transverse axes parallel or mutually perpendicular. These results form the basis for an efficient reverse displacement analysis and for the design of a new group of robots with three serially connected Hooke joints which may prove to be attractive to industry
TL;DR: In this article, the use of displacement potentials in terms of second order elasticity for equilibrium problems of homogeneous and isotropic materials is discussed, and the authors use the representations in obtaining complete solutions for equilibrium boundary-value problems.
Abstract: This paper is concerned with the use of a representation in terms of displacement potentials in second order elasticity for equilibrium problems of homogeneous and isotropic materials. After justifying the adoption of an existing representation for linear elasticity for the purpose at hand, appropriate representations for solutions of second order elasticity problems in terms of displacement potentials (for both compressible and incompressible materials) are discussed. The use of the representations in obtaining complete solutions for equilibrium boundary-value problems is then illustrated by application to two examples of plane strain problems of compressible materials.
TL;DR: In this paper, a new laminated composite plate finite element is proposed that is numerically stable and accurate in displacements and stresses, including transverse shear stress, based on the Hellinger-Reissner principle with Mindlin kinematics.
Abstract: A new laminated composite plate finite element is proposed that is numerically stable and accurate in displacements and stresses, including transverse shear stress. The formulation is based on the Hellinger—Reissner principle with Mindlin kinematics. All stress components are given independent approximations and do not satisfy equilibrium conditions a priori. A novel feature of the formulation is the additive decomposition of the displacement field into two parts corresponding to nodal interpolations and independent local basis functions. The additional basis functions and their associated parameters play an important role in characterizing the accuracy of the element. These functions eliminate shear locking in the lower order elements and provide additional variational constraints on the stresses, leading to very accurate results. A 4‐node and a 9‐node version are developed and it is shown that both elements pass the patch test suggested by Zienkiewicz et al. and are stable in the sense of the Babuska—Brezzi condition. The special structure of the element flexibility matrix provides computational efficiency approaching that of displacement based formulations.
TL;DR: In this paper, the displacement and stress fields generated by semi-ellipsoidal surface inclusions containing uniform transformation strains or eigenstrains were analyzed for special cases and numerical results for general cases.
Abstract: This paper presents calculations of the displacement and stress fields generated by semi-ellipsoidal surface inclusions containing uniform transformation strains or eigenstrains. The inclusion is assumed to have the same elastic constants as the rest of the material. This is a reasonable assumption for modeling transformed zones in transformation toughened ceramics and localized plasticity in individual surface grains in alloys. Analytical results are obtained for special cases and numerical results for general cases