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Showing papers on "Displacement field published in 1992"


Journal ArticleDOI
TL;DR: In this article, a methodology to improve the quality of the finite element calculations in the regions of unacceptable errors has been developed, where the superimposed regions can be of arbitrary shape, unlimited by the problem geometry, boundary conditions and the underlying mesh topography.

329 citations


Journal ArticleDOI
TL;DR: In this article, the authors developed the equations governing the elastodynamic behavior of moderately thick multilayered anisotropic plates by making use of a displacement field which allows a nonlinear variation of the inplane displacements through the laminate thickness and fulfils a priori the static and geometric continuity conditions.

244 citations


Journal ArticleDOI
TL;DR: In this paper, a variationally and asymptotically consistent theory is developed in order to derive the governing equations of anisotropic thin-walled beams with closed sections.

204 citations


Journal ArticleDOI
TL;DR: In this article, a higher-order plate theory for symmetric laminated composites is developed by superposing a cubic varying displacement field on a zig-zag linearly varying displacement.

201 citations


Journal ArticleDOI
TL;DR: In this paper, the weakly nonlinear evolution of particle trajectories in Friedmann-leemaitre models with zero cosmological constant is investigated, where the matter is assumed to be a nonrelativistic pressureless fluid.
Abstract: The weakly nonlinear evolution of particle trajectories in Friedmann-Lemaitre models with zero cosmological constant is investigated. The matter is assumed to be a nonrelativistic pressureless fluid. A perturbative expansion in Lagrangian coordinates is used and analytic expressions for the second-order solutions with arbitary density parameter Ω are derived. This perturbative expansion is valid provided the gradients of the displacement field are small, a much weaker condition than the usual Eulerian requirement of smallness of the density perturbations

194 citations


Journal ArticleDOI
TL;DR: In this article, a theory for modeling the effects of postseismic relaxation on a spherically symmetric earth is presented for two simple earthquake sources: a strike slip fault and a uniaxial thrust fault.
Abstract: Postseismic displacements and strains observed at the earth9s surface can be explained through the relaxation of a viscoelastic asthenosphere underlying a purely elastic crust. A theory is presented for modeling the effects of postseismic relaxation on a spherically symmetric earth. For an earthquake point source located in the upper elastic layer, the displacement field is decomposed into its toroidal and spheroidal components. A linear (Maxwell) rheology in the viscoelastic layers is assumed, enabling the use of the correspondence principle for the solutions of the equations of static equilibrium. Displacement and strain fields are then calculated using normal mode summation. Computational results are presented for two simple earthquake sources: a strike slip fault and a uniaxial thrust fault. The patterns of postseismic displacements and strains are found to depend strongly on both the earth model and earthquake source geometry. In particular, the elastic plate thickness, asthenosphere thickness, fault type, and fault length each play a major role in determining the spatial pattern of postseismic relaxation effects. Asthenospheric viscosity controls the temporal pattern of relaxation.

168 citations


Journal ArticleDOI
TL;DR: In this paper, the bending behavior of a general sandwich beam, delaminated (debonded) at one of the skin-core interfaces, with transversely flexible core, based on variational principles is analytically investigated.

119 citations


Journal ArticleDOI
TL;DR: In this paper, a family of p-method plane elasticity elements is derived based on the hybrid Trefftz formulation, where exact solutions of the Lame-Navier equations are used for the intra-element displacement field together with an independent displacement frame function field along the element boundary.
Abstract: A family of p-method plane elasticity elements is derived based on the hybrid Trefftz formulation.1 Exact solutions of the Lame-Navier equations are used for the intra-element displacement field together with an independent displacement frame function field along the element boundary. The final unknowns are the parameters of the frame function field consisting of the usual degrees of freedom at corner nodes and an optional number of hierarchic degrees of freedom associated with the mid-side nodes. Since the element matrices do not involve integration over the element area, the elements have a polygonal contour with an optional number of curved sides. The quadrilateral element has the same external appearance as the conventional p-method plane elasticity element.2,3 But unlike in the conventional p-method approach, suitable special-purpose Trefftz functions are generally used to handle the singularity and/or stress concentration problems rather than a local mesh refinement. The practical efficiency of the new elements is assessed through a series of examples.

109 citations


Journal ArticleDOI
TL;DR: In this paper, a new refined hut simple shear deformation theory of elastic shells is developed for shells laminated of orthotropic layers and the boundary value problem is formulated by making use of the principle of virtual power in conjunction with the assumed consistent displacement field.

100 citations


Journal ArticleDOI
TL;DR: In this paper, a method of modeling material damping and modulus in structural dynamics analysis is presented, based on the use of augmenting thermodynamic fields (ATF) to interact with the mechanical displacement field of continuum mechanics.

94 citations


Journal ArticleDOI
TL;DR: In this paper, a methodology was developed to accurately resolve the stress field in the vicinity of free edges as well as the overall response of laminated plates without significantly affecting the computational cost.
Abstract: SUMMARY A methodology has been developed to accurately resolve the stress field in the vicinity of free edges as well as the overall response of laminated plates without significantly affecting the computational cost. This is accomplished by enriching a set of classical smooth interpolants throughout the thickness direction with Co continuous displacement interpolants (piecewise continuous strain field) in the regions where the most critical behaviour is anticipated. Co continuity of the displacement field is maintained by imposing homogeneous boundary conditions on the superimposed field in the portion of the boundary which is not contained within the boundary of the problem. Numerical experiments for both cylindrical bending and uniform extension of cross-ply laminates are presented to validate the present formulation.

Journal ArticleDOI
TL;DR: In this paper, an experimental study of the near tip deformation fields for a single edge-cracked specimen (SEC) has been completed, and the results indicate that the value of the J-integral obtained from the measured surface deformation, and under the assumption of plane stress linearly elastic behavior, is essentially path independent over a region that is considered to be within the crack tip three-dimensional zone by researchers who have performed tests on other materials.
Abstract: An experimental study of the near tip deformation fields for a Single Edge-Cracked specimen (SEC) has been completed. The surface deformation fields for a thin SEC plexiglas specimen have been obtained in the region 0.15 <- r/t <- 0.60, where r is radial distance from the crack tip and t is the specimen thickness, by using a novel computer vision method. The results of the study indicate that the value of the J-Integral obtained from the measured surface deformation, and under the assumption of plane stress linearly elastic behavior, is essentially path independent over a region that is considered to be within the crack tip three-dimensional zone by researchers who have performed tests on other materials. However, the near-tip, in-plane displacement field does show a deviation from the traditional linear elastic crack tip singularity over the same region, suggesting the need for further studies to address this inconsistency.

Journal ArticleDOI
TL;DR: In this article, a guided ultrasonic interface wave was used for metal-metal and metal-ceramic interface studies, and the propagation parameters of these waves were measured and several of these modes were used to obtain direct acoustic images of the interfaces between two solids.
Abstract: When a guided ultrasonic interface wave travels along the interface between two materials, acoustic energy is radiated from each point on the interface, producing a displacement field at the outer surface of the material. We show how this unique feature of guided interface waves may be used for metal–metal and metal–ceramic interface studies. The propagation parameters of these waves were measured and several of these modes were used to obtain direct acoustic images of the interfaces between two solids.

Journal ArticleDOI
TL;DR: In this article, the lateral deflection and the cross-sectional rotation are represented by B-spline functions of equal order and the calculated natural frequencies are of good accuracy for stocky beams but can overestimate the true frequencies very considerably for slender beams.
Abstract: B-spline functions are used as trial functions in a Rayleigh-Ritz analysis of the free vibration of shear-deformable Timoshenko beams. In a first approach it is demonstrated in numerical applications that when the lateral deflection and the cross-sectional rotation are represented by functions of equal order the calculated natural frequencies are of good accuracy for stocky beams but can overestimate the true frequencies very considerably for slender beams. This is identified as a shear-locking difficulty and consideration of its causes points clearly to the adoption of a new displacement field in which the deflection is represented by a B-spline function which is one order higher than that used to represent the rotation. Numerical results using this new displacement field demonstrate good accuracy for both stocky and slender beams: the shear-locking difficulty is completely eliminated. This has clear significance for the analysis of shear-deformable plates and shells when using B-spline functions.

Journal ArticleDOI
TL;DR: In this paper, a quantitative model using elastic dislocation theory has been developed to model the near-field subsurface displacement field associated with faults and fault arrays within an elastic layer above an elastic half-space.
Abstract: SUMMARY A quantitative model using elastic dislocation theory has been developed to model the near-field subsurface displacement field associated with faults and fault arrays within an elastic layer above an elastic half-space. A fault is modelled as a surface across which there is a discontinuity in prescribed displacements. Fault displacements may be oblique as well as dip-slip. The mathematical expressions for the surface and subsurface displacements are formed using the Thomson-Haskell matrix technique. Faults may intersect the free surface or may be blind. The model has been used to determine the 3-D surface and subsurface displacement fields for a rectangular fault with constant slip and for an elliptical fault on which the slip varies from a point of maximum displacement at the centre to zero displacement at an elliptical tip-line. The 3-D displacement field and associated strain tensor may be determined for individual slip events on a fault or for cumulative fault displacements. Displacement contour maps may be constructed for either originally horizontal, vertical or inclined horizons. The model has also been applied to multiple fault arrays.

Journal ArticleDOI
TL;DR: In this article, the authors derived the Muskhelishvili potentials in conformal representation and the displacement field around cavities or cracks, and the shape of the deformed crack is in agreement with the one directly computed by Theocaris et al.

Journal ArticleDOI
TL;DR: In this paper, a method of analysis for the elastic behavior of three-dimensional solids with a large number of embedded fiber inclusions has been developed, where the resulting integrals are then treated semi-analytically.

Journal ArticleDOI
TL;DR: In this article, a distinction is made between infinitesimal and finite mechanisms, the former being characterized by one or several directions of lower stiffness, whereas the latter show at least one finite admissible displacement for which none of the bars undergoes any elongation.
Abstract: Structures presenting kinematical inderterminacy are usually called mechanisms. This paper is entirely concerned with assemblies which reveal themselves to be mechanisms at a null value of the load. Among them a first distinction is made between infinitesimal and finite ones, the former being characterized by one or several directions of lower (but not zero) stiffness, whereas the latter show at least one finite admissible displacement for which none of the bars undergoes any elongation. Moreover, there exists the possibility to make a further distinction among the infinitesimal mechanisms, according to which is the order of the stiffness along the direction considered above. The way of evaluating this order is to perform a local analysis of the strain energy of the assembly, once the displacement field is parametrized in terms of a suitable parameter. By means of a finite element technique, this analysis can be easily performed through the numerical approach presented in this report.

Journal ArticleDOI
Y. Q. Sun1
TL;DR: In this paper, the displacement field associated with a circular APB tube was calculated using isotropic elasticity under the assumption of APB energy, and the image contrast formed by this displacement field in dark-field Bragg reflections in the transmission electron microscope is calculated using the two-beam dynamical theory.
Abstract: In a transmission electron microscope, antiphase-domain-boundary (APB) tubes have been found to produce contrast not only in superlattice reflections satisfying g · R ¦ integer, as previously known, but also in a range of reflections, superlattice or fundamental, which contain large components normal to the tube axis. This observation is explained by a continuous lattice distortion in and around the tube caused by the surface tension of the APB. The displacement field associated with a circular APB tube is calculated using isotropic elasticity under the assumption of isotropic APB energy. The image contrast formed by this displacement field in dark-field Bragg reflections in the transmission electron microscope is calculated using the two-beam dynamical theory. The image contrast of an APB tube is shown to be substantially weaker than that of a dislocation owing to its much smaller lattice distortions. This contrast mechanism is shown to explain the images of APB tubes observed in deformed L12 or...

Journal ArticleDOI
TL;DR: In this paper, a bending theory for thin shells undergoing finite deformations is presented, and its associated finite element model is described, and the kinematic assumptions are of Reissner-Mindlin type.
Abstract: A bending theory for thin shells undergoing finite deformations is presented, and its associated finite element model is described. The kinematic assumptions are of Reissner-Mindlin type. The formulation is based on the introduction of a mixed functional with independent in-plane rotation field and skew-symmetric part of membrane forces. The resulting Euler-Lagrangian equations yield the equilibrium of stress resultants and the couple resultant with respect to the surface normal. Furthermore, the equality of the independent rotation field with the displacement dependent rotation field is enforced. Hence, the symmetry of the stress resultants is fulfilled in a weak sence. Naturally, the development of a quadrilateral finite element includes drilling degrees of freedom. The displacement field is approximated using an Allman-type interpolation.

Journal ArticleDOI
TL;DR: In this article, the fracture process zone in compact tension specimens of Indiana limestone was investigated to study its effect on the fracture mechanics parameters in such materials, including ligament connections and micro-cracks.
Abstract: The Fracture process zone in compact tension specimens of Indiana limestone was investigated to study its effect on the fracture mechanics parameters in such materials. Specimens were tested up to the peak load, and propagation of the crack from a preexisting notch was monitored. Experiments were designed to study the two features of the fracture process zone in rocks: ligament connections and microcracking. To observe this zone with high sensitivity and accuracy, laser interferometry methods were adopted. Holographic Interferometry was used to observe initial crack propagation. To obtain more quantitative measurements of the displacement field, in realtime, the recently developed technique of electronic speckle pattern interferometry was applied. This technique can provide continuous video recording of the interferometric fringe pattern, depict the evolution of the fracture process, and measure profiles of crack opening displacements. The macroscopic observations of full-field displacement by the laser techniques were supplemented by post mortem observation of the fracture region under a scanning electron microscope. Regions around the crack were studied after the test for possible presence of microcracks. An interactive finite element code was used to compute the stress intensity factors of the propagating crack-tip and displacements. Finite element computations were used to evaluate the effect of the process zone on crack propagation.


Journal ArticleDOI
TL;DR: In this paper, a numerical experiment and an analytical calculation are made to study self-localized modes for the displacement field of a pure one-dimensional lattice with hard quartic anharmonicity.
Abstract: A numerical experiment and an analytical calculation are made to study self-localized modes for the displacement field of a pure one-dimensional lattice with hard quartic anharmonicity. Approximate analytical solutions are obtained for moving localized modes with eigenfrequencies above the top of the harmonic frequency band. The envelope of the displacement field itself is of the form of the conventional sech function, depending on the wave vector of carrier waves. By using approximate analytical solutions as input, numerical experiments are made to explore the space-time evolution of the localized modes by taking the localized mode height and the wave vector of carrier waves as parameters. It is shown that the moving localized modes obtained here are identifiable as lattice solitons under favorable conditions.

Journal ArticleDOI
S. H. Lo1
TL;DR: The beam element formulation presented in this article allows large rotation angles to be made within a load increment by using nodal displacements and tangent vectors instead of rotation angles at the two ends of the beam element.

Journal ArticleDOI
TL;DR: Motion estimation is cast as a problem in energy minimization by modeling the displacement field as a Markov random field using the Mean Field Annealing algorithm, a technique which finds the global or near global minima in nonconvex optimization problems.

Journal ArticleDOI
TL;DR: In this paper, a simple and accurate method for estimating the three-dimensional effective moduli of symmetric and orthotropic laminated composites is presented, which is based on obtaining the exact displacement field of three boundary value problems of laminate composites using the Airy stress function solution technique.
Abstract: A simple and accurate method for estimating the three-dimensional effective moduli of symmetric and orthotropic laminated composites is presented. The method is based on obtaining the exact displacement field of three boundary value problems of laminated composites using the Airy stress function solution technique. The effective moduli are estimated by matching the boundary displacements of the equivalent homogeneous system with those of the laminated system. Among the estimated effective moduli, those associated with the interlaminar direction are of special interest. It is found that the effective interlaminar normal stiffness in extensional deformation is independent of laminae stacking sequence which is consistent with the finding of Pagano (1974). However, the laminate interlaminar shear stiffness is dependent on stacking sequence, and it is shown that the rule of mixtures can not predict the interlaminar shear stiffness accurately.

Journal ArticleDOI
TL;DR: In this article, the critical buckling load of simply supported, unsymmetric cross-ply and antisymmetric angle-ply laminates, under linearly varying in-plane biaxial loads, combined with shear, was determined.

Journal ArticleDOI
Sun-Hoon Kim, Chang-Koon Choi1
TL;DR: In this paper, a finite element based on the Mindlin plate concept is proposed for the analysis of plate bending structures, which is shown to overcome the shear locking problem completely in a very thin plate situation, even for irregular meshes.
Abstract: The present paper is concerned with the improvement of a finite element for the analysis of plate bending structures. The element formulation is based upon the Mindlin plate concept. The displacement field of this element is formed by adding non-conforming modes to two rotational displacement components of an 8-node plate element. The element has the requisite numbers of zero eigenvalues associated with rigid body modes to avoid the spurious zero energy mode. It is shown that the results obtained by the element converged to the exact solutions very rapidly as the mesh is refined and exhibited reliable solutions through numerical studies for standard benchmark problems. This element is shown to overcome the shear locking problem completely in a very thin plate situation, even for irregular meshes.

Journal ArticleDOI
TL;DR: In this paper, an asymptotic analysis is carried out in order to calculate the elastostatic field near the tip of a crack for the finite plane deformation of Hadamard materials.
Abstract: SUMMARY An asymptotic analysis is carried out in order to calculate the elastostatic field near the tip of a crack for the finite plane deformation of Hadamard materials. A general body configuration containing a crack and loading conditions is considered. It is shown that the singular field near the crack tip can be obtained by applying a rigid-body rotation with a subsequent parallel translation to a so-called canonical field. The adjective canonical is adopted here to denote the field in which the crack faces open symmetrically, with the most singular term of order A, just resembling the displacement field of the symmetric mode in linear fracture mechanics. No analogy with the antisymmetric mode is possible, and the crack-equilibrium criterion requires only one stress-intensity factor to be known.