Showing papers on "Displacement field published in 2000"
TL;DR: In this paper, the authors developed a new paradigm for thin-shell finite-element analysis based on the use of subdivision surfaces for describing the geometry of the shell in its undeformed configuration, and generating smooth interpolated displacement fields possessing bounded energy within the strict framework of the Kirchhoff-love theory of thin shells.
Abstract: We develop a new paradigm for thin-shell finite-element analysis based on the use of subdivision surfaces for (i) describing the geometry of the shell in its undeformed configuration, and (ii) generating smooth interpolated displacement fields possessing bounded energy within the strict framework of the Kirchhoff–Love theory of thin shells. The particular subdivision strategy adopted here is Loop's scheme, with extensions such as required to account for creases and displacement boundary conditions. The displacement fields obtained by subdivision are H2 and, consequently, have a finite Kirchhoff–Love energy. The resulting finite elements contain three nodes and element integrals are computed by a one-point quadrature. The displacement field of the shell is interpolated from nodal displacements only. In particular, no nodal rotations are used in the interpolation. The interpolation scheme induced by subdivision is non-local, i.e. the displacement field over one element depend on the nodal displacements of the element nodes and all nodes of immediately neighbouring elements. However, the use of subdivision surfaces ensures that all the local displacement fields thus constructed combine conformingly to define one single limit surface. Numerical tests, including the Belytschko et al. [10] obstacle course of benchmark problems, demonstrate the high accuracy and optimal convergence of the method.
656 citations
TL;DR: In this paper, a simple constitutive proposal is discussed where incompatibility only enters the instantaneous hardening relations, and thus the incremental moduli, which preserves the classical structure of the incremental boundary value problem.
Abstract: In the finite-deformation, continuum theory of crystal plasticity, the lattice is assumed to distort only elastically, while generally the elastic deformation itself is not compatible with a single-valued displacement field. Lattice incompatibility is shown to be characterized by a certain skew-symmetry property of the gradient of the elastic deformation field, and this measure can play a natural role in a nonlocal, gradient-type theory of crystal plasticity. A simple constitutive proposal is discussed where incompatibility only enters the instantaneous hardening relations, and thus the incremental moduli, which preserves the classical structure of the incremental boundary value problem.
446 citations
TL;DR: In this paper, a second-order approximation of the displacement gradients is proposed to directly measure both the first-and secondorder displacement gradient resulting from nonlinear deformation, which can be used to obtain more accurate strain measurements in large deformation situations.
Abstract: This paper outlines the procedure for refining the digital image correlation (DIC) method by implementing a second-order approximation of the displacement gradients. The second-order approximation allows the DIC method to directly measure both the first- and second-order displacement gradients resulting from nonlinear deformation. Thirteen unknown parameters, consisting of the components of displacement, the first- and second-order displacement gradients and the gray-scale value offset, are determined through optimization of a correlation coefficient. The previous DIC method assumes that the local deformation in a subset of pixels is represented by a first-order Taylor series approximation for the displacement gradient terms, so actual deformations consisting of higher order displacement gradients tend to distort the infinitesimal strain measurements. By refining the method to measure both the first- and second-order displacement gradients, more accurate strain measurements can be achieved in large-deformation situations where second-order deformations are also present. In most cases, the new refinements allow the DIC method to maintain an accuracy of ±0.0002 for the first-order displacement gradients and to reach ±0.0002 per pixel for the second-order displacement gradients.
370 citations
TL;DR: In this article, a finite element model for strain localization analysis of elastoplastic solids subjected to discontinuous displacement fields based on standard Galerkin approximation is presented, which does not require static condensation to be performed on the element level.
199 citations
TL;DR: In this article, a linear theory for elastic materials with inner structure whose particles, in addition to the classical displacement and temperature fields, possess microtemperatures is presented, which is illustrated with the solution of the problem of thermal stresses in an elastic space with a spherical cavity.
Abstract: The article is concerned with a linear theory for elastic materials with inner structure whose particles, in addition to the classical displacement and temperature fields, possess microtemperatures. In the first part of the article we derive an existence result for the dynamical theory and establish the continuous dependence of solutions on the initial data and body loads. Then we consider the equilibrium theory and present a uniqueness result and a solution for the field equations. The theory is illustrated with the solution of the problem of thermal stresses in an elastic space with a spherical cavity.
138 citations
TL;DR: In this article, the debonding mechanism of soft viscoelastic adhesives from a hard interface can be described using an instrumented probe-tack device, and a semiquantitative model of how the lateral growth of these cavities is controlled by the competition between a critical energy-release rate at the interface G c and the elastic modulus of the film E.
Abstract: Because of recent experiments (H. Lakrout et al., J Adhes 1999, 69, 307) conducted with an instrumented probe-tack device, a better description of the debonding mechanisms of soft viscoelastic adhesives from a hard interface can be proposed. Because the deformed volume is about the magnitude of the sample size and the deformation is highly inhomogeneous, adhesion cannot be studied independently of the geometry of the test. One of the simplest geometries is that of the debonding of a cylindrical flat-ended probe from a thin film. In this case, a uniform displacement field is applied over the entire top surface of the film, and the stress field at the probe-film interface is strongly dependent on the degree of confinement of the film characterized by the ratio between the probe radius a and the film thickness h. For a very confined film, the nucleation of interfacial cavities is predicted to occur over most of the surface of the probe. These cavities will grow in the plane of the film and can be assimilated to multiple penny-shaped interfacial cracks. We present a semiquantitative model of how the lateral growth of these cavities is controlled by the competition between a critical energy-release rate at the interface G c and the elastic modulus of the film E. Finally, either these cavities coalesce and the film is debonded from the surface or the walls between these cavities become elongated in the tensile direction and form a fibrillar structure. The conditions for the formation of this fibrillar structure are qualitatively discussed.
131 citations
TL;DR: In this article, the authors generalized the multiscale approach to higher dimensions by identifying the fine scale field with a component of the displacement that has a large gradient and then interpolating fine scale interpolations to ensure sharp resolution of localized displacement.
103 citations
TL;DR: In this paper, a comprehensive analysis of available models and techniques to evaluate transverse shear and normal stresses in multilayered orthotropic plates is given in a comprehensive manner.
102 citations
TL;DR: In this article, the authors present experimental evidence to show that a size/geometry dependence is observed in the shrinkage cracking behavior of restrained concrete structures, and a theoretical model is developed to explain this behavior.
Abstract: This paper presents experimental evidence to show that a size/geometry dependence is observed in the shrinkage cracking behavior of restrained concrete structures. A theoretical model is developed to explain this behavior. First, a solution is presented to compute the stress and displacement fields of an aging, linear, viscoelastic cylinder by assuming that a uniformly distributed shrinkage strain is perfectly restrained in the radial direction at the internal surface of the cylinder. Second, a fracture mechanics failure criterion is implemented to develop time and geometry-dependent tensile stress resistance (strength) curves. Third, this model is used to illustrate the role of specimen size/geometry and material composition on the failure response. Finally, experimentally measured ages of cracking are compared with the theoretical modeling predictions.
95 citations
TL;DR: In this paper, a refined laminated plate theory and a three-dimensional finite element based on first-order zig-zag sublaminate approximations has been developed, where the in-plane displacement fields in each sub-laminate are assumed to be piecewise linear functions and vary in a zigzag fashion through the thickness of the sublaminates.
94 citations
TL;DR: In this paper, Gao et al. presented a fully anisotropic analysis of strip electric saturation model for piezoelectric materials, which revealed that the critical fracture stresses for a crack perpendicular to the poling axis is linearly decreased with the increase of the positive applied electric field and increases linearly with the increasing of the negative applied electric displacement field.
TL;DR: A spectrally formulated element that has three degrees of freedom (axial motion, transverse motion and rotation) per node for analysis of slender multiply connected composite beams under high-frequency impact loading is presented in this article.
TL;DR: In this article, a method for elastic and viscoelastic imaging of multicomponent seismic data is presented based on Claerbout's survey-sinking concept and the (visco)elastic Kirchhoff integral for the displacement field.
Abstract: This paper presents a method for elastic and viscoelastic imaging of multicomponent seismic data. The method is based on Claerbout’s survey‐sinking concept and the (visco)elastic Kirchhoff integral for the displacement field. Assuming a multishot and multireceiver experiment, the migration process is formulated as a wavefield reconstruction problem, using the (visco)elastic Kirchhoff integral twice. First, the receiver coordinates are downward continued. Second, the source coordinates are downward continued. The multicomponent seismic data are treated as a vector wavefield in which the data measurements may be displacement velocity or traction (pressure). The theoretical formulation is based on the viscoelastic Hooke’s law and Newton’s equation of motion as the physical model for seismic wave propagation. It is valid for linear viscoelastic media with any anisotropic symmetry. When the lowest‐order ray approximation is introduced, the migration equation takes a form similar to conventional Kirchhoff migra...
TL;DR: In this article, a closed-form description for the effective inplane core stiffnesses including the thickness effect is given based on an approximate representation for the displacement field within the core cell walls, the effective core stiffness are derived by energetical considerations.
TL;DR: In this paper, a digital speckle pattern interferometry and hole drilling combined system is developed to determine the magnitude of the residual stress in a aluminum thin plate subjected to an uniform uniaxial tensile load.
TL;DR: This paper proposes to model the spatio-temporal myocardial displacement field by a cosine series model fitted to the entire tagged dataset and provides an analytical and hierarchical model of the 2D+time deformation inside the myocardium.
TL;DR: A multi-layer shell-element family capable to deal with the prediction of interlaminar stresses playing an important role in the design, particularly in the failure analysis of these structures is developed.
TL;DR: In this paper, a combined numerical-experimental method for the identification of six elastic material modulus of generally thick composite plates is proposed, which can be used in composite plates made of different materials and with general stacking sequences.
TL;DR: In this paper, a higher order displacement theory is used to define the mechanical displacement field, which satisfies the thermal surface boundary conditions, necessary for accurate modeling of temperature distribution through the thickness of laminated structures.
TL;DR: Additional, discontinuous functions are added to the displacement field of standard finite elements in order to capture highly localised zones of intense straining and compared with smeared type models for brittle fracture.
TL;DR: In this article, the performance of a curved beam finite element with coupled polynomial distributions for normal displacement and tangential displacement was investigated for in-plane flexural vibration of arches.
TL;DR: In this paper, the Young's modulus of the equivalent continuum is found to be very low (of the order of 1 GPa), a feature which suggests that a viscoelastic behavior may be more appropriate for this rock mass, given the observed seismic velocities for the domain of interest.
Abstract: The displacement field has been monitored in the vicinity of the crater rim at Mount Merapi (Indonesia) from 1993 to 1997. During this period the volcanic activity has been quasicontinuous with dome growth, explosions, and pyroclastic flows. We measured a nine-point network every year with the Global Positioning System static method. Interpretation of results is conducted with a three-dimensional elastostatic boundary elements code that takes into account topography, fractures, and complex magma source geometry. The inversion technique yields an estimate of the variation with time of the boundary conditions at the magma duct interface together with the probability associated with the best model. The Young's modulus of the equivalent continuum is found to be very low (of the order of 1 GPa), a feature which suggests that a viscoelastic behavior may be more appropriate for this rock mass, given the observed seismic velocities for the domain of interest. A striking compatibility is outlined between observed deformations and the rate of occurrence of multiphase seismic events, once the main fractures of the structure have been taken into consideration. This suggests that the summit elastic (or viscoelastic) deformation field is controlled by the magma flux within the duct rather than by magma pressure variations. In addition, a nonelastic displacement has been identified at the westernmost point of the network. This was considered critical for the stability of the summit structure, a concern whose validity has been verified a posteriori by the July 1998 explosion.
TL;DR: In this paper, a finite element formulation for refined linear analysis of multilayered shell structures of moderate thickness is presented, which is a direct extension of the first-order shear-deformation theory of Reissner-Mindlin type.
Abstract: A finite element formulation for refined linear analysis of multilayered shell structures of moderate thickness is presented An underlying shell model is a direct extension of the first-order shear-deformation theory of Reissner–Mindlin type A refined theory with seven unknown kinematic fields is developed: (i) by introducing an assumption of a zig-zag (ie layer-wise linear) variation of displacement field through the thickness, and (ii) by assuming an independent transverse shear stress fields in each layer in the framework of Reissner's mixed variational principle The introduced transverse shear stress unknowns are eliminated on the cross-section level At this process, the interlaminar equilibrium conditions (ie the interlaminar shear stress continuity conditions) are imposed As a result, the weak form of constitutive equations (the so-called weak form of Hooke's law) is obtained for the transverse strains–transverse stress resultants relation A finite element approximation is based on the four-noded isoparametric element To eliminate the shear locking effect, the assumed strain variational concept is used Performance of the derived finite element is illustrated with some numerical examples The results are compared with the exact three-dimensional solutions, as well as with the analytical and numerical solutions obtained by the classical, the first-order and some representative refined models Copyright © 2000 John Wiley & Sons, Ltd
TL;DR: In this paper, a finite element method for 3D vibration analysis of annular and circular plates is presented. But the method is different from the traditional 3D finite element analysis and is reduced to a sequence of 2-D analyses one for each circumferential wave number.
TL;DR: In this article, a theoretical formulation for modeling composite smart structures, in which the piezoelectric actuators and sensors are treated as constituent parts of the entire structural system, is presented.
TL;DR: In this article, a new theoretical model for the analysis of the mass sensitivity of the Love wave device was proposed. The model is based on Love wave propagation in an isotropic, non-piezoelectric quartz substrate over-layered by a silica waveguiding layer and immersed in a viscous liquid.
Abstract: This paper describes a new theoretical model for the analysis of the mass sensitivity of the Love wave device. We use this model along with calculations from perturbation theory to calculate sensitivity. The model is based on Love wave propagation in an isotropic, non-piezoelectric quartz substrate over-layered by a silica waveguiding layer and immersed in a viscous liquid. The analysis considers power flow in the three-layered system, comprising the quartz substrate, the silica over-layer and the viscous liquid. The model fully accounts for the first time for the power that flows through the liquid phase and assesses its effect on mass sensitivity. Mass sensitivity values were obtained by determining the displacement field throughout the viscous liquid and the Love waveguide device. The resulting velocity field was used to generate a number of trial functions that had solutions assuming stress and strain continuity at the boundaries, and the complex dispersion relation was evaluated numerically. The resulting wavevector k and propagation constant β values were used to calculate the power in both the Love wave device and the liquid layer and the velocity amplitude at the surface. The model predicts that the mass sensitivity of the Love wave device will increase in the presence of a viscous solution due to power flow into the liquid.
TL;DR: In this article, the simulation of delaminations in composite structures is considered and a 3D-shell element is proposed to describe the global as well as the local behaviour in laminates.
TL;DR: In this article, a non-hypersingular boundary integral equation is derived for the time-domain analysis of the dynamics of a 3D non-planar crack, located in an infinite homogeneous isotropic medium.
Abstract: We derive a non-hypersingular boundary integral equation, in a fully explicit form, for the time-domain analysis of the dynamics of a 3-D non-planar crack, located in an infinite homogeneous isotropic medium. The hypersingularities, existent in the more straightforward expression, are removed by way of a technique of regularization based on integration by parts. The variables are denoted in terms of a local Cartesian coordinate system, one of the axes of which is always held locally perpendicular to the potentially curved surface of the crack. Also given, in a fully explicit form, are the expressions for the off-fault stress and displacement field, as well as the special form of the equations for the case in which the fault is planar.
TL;DR: In this article, a general framework for obtaining analytic solutions for finite elastic isotropic solid cylinders subjected to arbitrary surface load is presented, which uses the displacement function approach to uncouple the equations of equilibrium.
TL;DR: In this paper, the authors investigated the effect of warping of an initially plane-free surface, at a corner point, on crack profiles in the vicinity of a crack front intersecting a free surface.
Abstract: Crack profiles in the vicinity of a crack tip were investigated both theoretically by using standard displacement field equations, and by experiments using foam plastic models. Particular attention was paid to crack profiles in the vicinity of a corner point where a crack front intersects a free surface. Crack profiles for single-mode and mixed-mode cracks, calculated from standard displacement field equations, are incorrect in the vicinity of a corner point. The use of foam plastic models permits the visualization of crack profiles in the vicinity of a corner point. Strictly speaking, stress intensity factors have no meaning in the vicinity of a corner point, but for practical purposes it is possible to calculate representative values. Failure to take into account warping of an initially plane-free surface, at a corner point, has led to some confusion in the finite element calculation of representative K III values.