Showing papers on "Displacement field published in 2004"
TL;DR: In this article, the authors show that the Frechet derivatives of the objective function can be obtained for tomographic and (finite) source inversions based on just two numerical simulations for each earthquake: one calculation for the current model and a second, "adjoint" calculation that uses time-reversed signals at the receivers as simultaneous, fictitious sources.
Abstract: SUMMARY
We draw connections between seismic tomography, adjoint methods popular in climate and ocean dynamics, time-reversal imaging and finite-frequency ‘banana-doughnut’ kernels. We demonstrate that Frechet derivatives for tomographic and (finite) source inversions may be obtained based upon just two numerical simulations for each earthquake: one calculation for the current model and a second, ‘adjoint’, calculation that uses time-reversed signals at the receivers as simultaneous, fictitious sources. For a given model, m, we consider objective functions χ(m) that minimize differences between waveforms, traveltimes or amplitudes. For tomographic inversions we show that the Frechet derivatives of such objective functions may be written in the generic form , where δ ln m=δm/m denotes the relative model perturbation. The volumetric kernel Km is defined throughout the model volume V and is determined by time-integrated products between spatial and temporal derivatives of the regular displacement field s and the adjoint displacement field s†; the latter is obtained by using time-reversed signals at the receivers as simultaneous sources. In waveform tomography the time-reversed signal consists of differences between the data and the synthetics, in traveltime tomography it is determined by synthetic velocities, and in amplitude tomography it is controlled by synthetic displacements. For each event, the construction of the kernel Km requires one forward calculation for the regular field s and one adjoint calculation involving the fields s and s†. In the case of traveltime tomography, the kernels Km are weighted combinations of banana-doughnut kernels. For multiple events the kernels are simply summed. The final summed kernel is controlled by the distribution of events and stations. Frechet derivatives of the objective function with respect to topographic variations δh on internal discontinuities may be expressed in terms of 2-D kernels Kh and Kh in the form , where Σ denotes a solid-solid or fluid-solid boundary and ΣFS a fluid–solid boundary, and ∇Σ denotes the surface gradient. We illustrate how amplitude anomalies may be inverted for lateral variations in elastic and anelastic structure. In the context of a finite-source inversion, the model vector consists of the time-dependent elements of the moment-density tensor m(x, t). We demonstrate that the Frechet derivatives of the objective function χ may in this case be written in the form , where e† denotes the adjoint strain tensor on the finite-fault plane Σ. In the case of a point source this result reduces further to the calculation of the time-dependent adjoint strain tensor e† at the location of the point source, an approach reminiscent of an acoustic time-reversal mirror. The theory is illustrated for both tomographic and source inversions using a 2-D spectral-element method.
904 citations
27 Aug 2004
TL;DR: The physical model is derived from continuum mechanics, which allows the specification of common material properties such as Young's Modulus and Poisson's Ratio and it is demonstrated how to solve the equations of motion based on these forces, with both explicit and implicit integration schemes.
Abstract: We present a method for modeling and animating a wide spectrum of volumetric objects, with material properties anywhere in the range from stiff elastic to highly plastic. Both the volume and the surface representation are point based, which allows arbitrarily large deviations form the original shape. In contrast to previous point based elasticity in computer graphics, our physical model is derived from continuum mechanics, which allows the specification of common material properties such as Young's Modulus and Poisson's Ratio.In each step, we compute the spatial derivatives of the discrete displacement field using a Moving Least Squares (MLS) procedure. From these derivatives we obtain strains, stresses and elastic forces at each simulated point. We demonstrate how to solve the equations of motion based on these forces, with both explicit and implicit integration schemes. In addition, we propose techniques for modeling and animating a point-sampled surface that dynamically adapts to deformations of the underlying volumetric model.
453 citations
TL;DR: A normal mode analysis of the nonaffine elastic displacement field allows it to clarify its relation to the zero-frequency mode at the onset of failure and to the cracklike pattern which results from the subsequent relaxation of energy.
Abstract: We show that, in the athermal quasistatic deformation of amorphous materials, the onset of failure is accompanied by universal scalings associated with a divergence of elastic constants. A normal mode analysis of the nonaffine elastic displacement field allows us to clarify its relation to the zero-frequency mode at the onset of failure and to the cracklike pattern which results from the subsequent relaxation of energy.
201 citations
TL;DR: Introducing a smoothness constraint into motion field estimation helped solve ambiguities due to incoherent motion, leading to elastograms less degraded by decorrelation noise than the ones obtained from correlation-based techniques.
Abstract: Elasticity imaging is based on the measurements of local tissue deformation. The approach to ultrasound elasticity imaging presented in this paper relies on the estimation of dense displacement fields by a coarse-to-fine minimization of an energy function that combines constraints of conservation of echo amplitude and displacement field continuity. The multiscale optimization scheme presents several characteristics aimed at improving and accelerating the convergence of the minimization process. This includes the nonregularized initialization at the coarsest resolution and the use of adaptive configuration spaces. Parameters of the energy model and optimization were adjusted using data obtained from a tissue-like phantom material. Elasticity images from normal in vivo breast tissue were subsequently obtained with these parameters. Introducing a smoothness constraint into motion field estimation helped solve ambiguities due to incoherent motion, leading to elastograms less degraded by decorrelation noise than the ones obtained from correlation-based techniques.
182 citations
TL;DR: This paper examines the performance of a new adjoint equation based iterative method for evaluating the spatial distribution of the elastic modulus of tissue based on the knowledge of its displacement field under a deformation, and concludes that it is robust and accurate, and a good candidate for clinical application because of its computational speed and efficiency.
Abstract: Recently a new adjoint equation based iterative method was proposed for evaluating the spatial distribution of the elastic modulus of tissue based on the knowledge of its displacement field under a deformation. In this method the original problem was reformulated as a minimization problem, and a gradient-based optimization algorithm was used to solve it. Significant computational savings were realized by utilizing the solution of the adjoint elasticity equations in calculating the gradient. In this paper, we examine the performance of this method with regard to measures which we believe will impact its eventual clinical use. In particular, we evaluate its abilities to (1) resolve geometrically the complex regions of elevated stiffness; (2) to handle noise levels inherent in typical instrumentation; and (3) to generate three-dimensional elasticity images. For our tests we utilize both synthetic and experimental displacement data, and consider both qualitative and quantitative measures of performance. We conclude that the method is robust and accurate, and a good candidate for clinical application because of its computational speed and efficiency.
162 citations
TL;DR: VBFM has the potential to increase the robustness and reliability of micromanipulation and biomanipulation tasks where force sensing is essential for success and is demonstrated for both a microcantilever beam and a microgripper.
Abstract: This paper demonstrates a method to visually measure the force distribution applied to a linearly elastic object using the contour data in an image. The force measurement is accomplished by making use of the result from linear elasticity that the displacement field of the contour of a linearly elastic object is sufficient to completely recover the force distribution applied to the object. This result leads naturally to a deformable template matching approach where the template is deformed according to the governing equations of linear elasticity. An energy minimization method is used to match the template to the contour data in the image. This technique of visually measuring forces we refer to as vision-based force measurement (VBFM). VBFM has the potential to increase the robustness and reliability of micromanipulation and biomanipulation tasks where force sensing is essential for success. The effectiveness of VBFM is demonstrated for both a microcantilever beam and a microgripper. A sensor resolution of less than +/-3 nN for the microcantilever and +/-3 mN for the microgripper was achieved using VBFM. Performance optimizations for the energy minimization problem are also discussed that make this algorithm feasible for real-time applications.
153 citations
TL;DR: In this article, a finite element model for the static and dynamic analysis of a piezoelectric bimorph is proposed, which combines a 2D single-layer representation model (finite 2D isoparametric elements) for the mechanical displacement field with a layerwise-like approximation for the electric potential field to achieve the accurate prediction of both mechanical displacement and electric potential fields.
144 citations
TL;DR: In this article, the authors used a white light speckle technique for deformation analysis of a magnetorheological elastomer (MRE) and the elastic fiberromagnet composite (EFC) while the magnetic field is turned on.
Abstract: Magnetorheological elastomer (MRE) is a new class of smart materials, whose modulus can be controlled by the applied magnetic field. In this paper, using a white light speckle technique for deformation analysis, we present the real-time dynamic deformation progress (the vector diagram of the displacement or the whole-field quantitative displacement distribution) of the MRE and the elastomer?ferromagnet composite (EFC) while the magnetic field is turned on. The experimental results verify the prediction presented in a recently published paper, (Borcea and Bruno 2001 J.?Mech.?Phys.?Solids 49 2877?919), and reveals some interesting phenomena which will give us a deeper understanding for such smart materials.
143 citations
TL;DR: In this paper, an analysis of the mesh dependence of results from numerical failure analyses using the strong discontinuity approach (SDA) based on an analytical and numerical comparison with a standard plasticity model, pertaining to the classical fracture energy based smeared crack concept using a consistent characteristic length.
111 citations
TL;DR: In this article, a higher order zig-zag plate theory is developed to refine the prediction of the mechanical, thermal, and electric behaviors fully coupled, where both in-plane displacement and temperature fields through the thickness are constructed by superimposing linear zigzag field to the smooth globally cubic varying field.
109 citations
TL;DR: In this article, a three-node triangular finite element based on cubic zig-zag plate theory is developed to refine the predictions of the mechanical, thermal, and electric behaviors fully coupled.
01 Jan 2004
TL;DR: In this paper, the inverse problem of real-time reconstruction of full-field structural displacements is addressed through the application of a new variational formulation leading to versatile, robust and computationally efficient inverse shell finite element analysis.
Abstract: The inverse problem of real-time reconstruction of full-field structural displacements is addressed through the application of a new variational formulation leading to versatile, robust and computationally efficient inverse shell finite element analysis. Utilizing surface strain measurements from strain sensors mounted on the load-carrying structural components, the methodology enables accurate computations of the three-dimensional displacement field. This high fidelity computational technology is essential for providing feedback to the actuation and control systems of the next generation of aerospace vehicles.
TL;DR: In this paper, the authors developed a method of controlling the friction and wear affecting the contact pair in rolling-sliding contact, which is in small-scale tribology by which mechanism of wear would be clarified on first hand by Archard's law.
TL;DR: In this article, a new higher order Zigzag theory for laminated plates under thermal loading is presented, which is modified by replacing the uniform across the thickness approximation for the deflection with a layer-wise variable approximation for deflection which explicitly accounts for the transverse thermal strain.
TL;DR: In this article, numerical solution procedures for coupled chemo-mechanical simulations of concrete structures subjected to calcium leaching and mechanical damage are concerned with numerical solutions for coupled concrete structures.
TL;DR: The proposed smoothing method can render morphometric analysis methods that are based on displacement field of shape transformations more robust to noise without removing important morphologic characteristics.
Abstract: We propose a method for enforcing topology preservation and smoothness onto a given displacement field. We first analyze the conditions for topology preservation on two- and three-dimensional displacement fields over a discrete rectangular grid. We then pose the problem of finding the closest topology preserving displacement field in terms of its complete set of gradients, which we later solve using a cyclic projections framework. Adaptive smoothing of a displacement field is then formulated as an extension of topology preservation, via constraints imposed on the Jacobian of the displacement field. The simulation results indicate that this technique is a fast and reliable method to estimate a topology preserving displacement field from a noisy observation that does not necessarily preserve topology. They also show that the proposed smoothing method can render morphometric analysis methods that are based on displacement field of shape transformations more robust to noise without removing important morphologic characteristics.
TL;DR: In this article, the problem of determining true stress-strain curves from flat tensile specimens beyond the onset of necking has been investigated based on finite element analyses under consideration of experimental accessible data using digital image correlation (DIC).
Abstract: The problem of determining true stress-strain curves from flat tensile specimens beyond the onset of necking has been investigated based on finite element analyses under consideration of experimental accessible data using digital image correlation (DIC). The displacement field on the specimen surface is determined by in-situ deformation field measurement. A three-dimensional finite element study with different stress-strain-curves has been carried out to develop a formula, with which it is possible to calculate the true stress subject to the strain in the necking region. The method has been used to evaluate the true stress-strain curve with a so-called micro flat tensile specimen, which is normally used to determine the material properties in the material gradient around thin weldments.
TL;DR: In this paper, a variational formulation of the Coulomb's law of dry friction was derived for the static frictional contact between a piezoelectric body and an obstacle.
Abstract: We consider a mathematical model which describes the static frictional contact between a piezoelectric body and an obstacle. The constitutive relation of the material is assumed to be electroelastic and involves a nonlinear elasticity operator. The contact is modelled with a version of Coulomb's law of dry friction in which the coefficient of friction depends on the slip. We derive a variational formulation for the model which is in form of a coupled system involving as unknowns the displacement field and the electric potential. Then we provide the existence of a weak solution to the model and, under a smallness assumption, we provide its uniqueness. The proof is based on a result obtained in [14] in the study of elliptic quasi‐variational inequalities.
TL;DR: In this paper, the linear response of two-dimensional amorphous elastic bodies to an external delta force is determined in analogy with recent experiments on granular aggregates, and strong relative fluctuations of order 1 close to the source, which, however, average out readily to the classical predictions of isotropic continuum elasticity.
Abstract: The linear response of two-dimensional amorphous elastic bodies to an external delta force is determined in analogy with recent experiments on granular aggregates. For the generated forces, stress, and displacement fields, we find strong relative fluctuations of order 1 close to the source, which, however, average out readily to the classical predictions of isotropic continuum elasticity. The stress fluctuations decay (essentially) exponentially with distance from the source. Only beyond a surprisingly large distance, $b\ensuremath{\approx}30$ interatomic distances, self-averaging dominates, and the quenched disorder becomes irrelevant for the response of an individual configuration. We argue that this self-averaging length $b$ also sets the lower wavelength bound for the applicability of classical eigenfrequency calculations. Particular attention is paid to the displacements of the source, allowing a direct measurement of the local rigidity. The algebraic correlations of these displacements demonstrate the existence of domains of slightly different rigidity without, however, revealing a characteristic length scale, at least not for the system sizes we are able to probe.
TL;DR: In this article, a Cosserat shell model of the interphase is derived which successfully models the original interphase in a unified manner, for the full range of its material parameters relative to those of the neighboring media.
Abstract: This study is concerned with the modeling of interphases in elastic media in general, and in composite materials in particular. The aim is to replace a boundary value problem consisting of a three-phase configuration, say that of fiber–interphase–matrix, by a simpler problem which involves the fiber and matrix only, plus certain matching conditions which simulate the interphase. The simplest of such known representations replaces a thin interphase by a “perfect contact interface” (a single surface) across which the displacements and tractions are assumed to be continuous. Another classical model replaces a thin and soft interphase by a “spring-type interface”, across which the tractions are continuous, but the displacement field undergoes a discontinuity. In the present paper, a Cosserat shell model of the interphase is derived which successfully models the original interphase in a unified manner, for the full range of its material parameters relative to those of the neighboring media. The model is derived in the setting of three-dimensional linear elasticity with small deformations and displacements. Comparisons with an existing exact solution of a coated fiber in an infinite matrix show that it performs extremely well even for moderately thick interphases.
TL;DR: In this paper, the exact response sensitivity of material nonlinear beam-column elements is derived for the displacement-and force-based formulations, in which the displacement field is not specified along the element.
Abstract: Response sensitivity is needed for simulation applications such as optimization, reliability, and system identification. The exact response sensitivity of material nonlinear beam-column elements is derived for the displacement- and force-based formulations. For displacement-based beam.column elements the response sensitivity is straightforward to compute because the displacement field is specified along the element. A new approach is presented for computing the response sensitivity of force-based beam-column elements, in which the displacement field is not specified. In this approach, the response sensitivity depends on the derivative of unbalanced section forces because the element displacement field changes with the element state. Example nonlinear static analyses of steel and reinforced concrete structural systems verify the exact response sensitivity for force-based elements using the new approach.
TL;DR: It is found that a first-order algorithm can significantly reduce strain measurement error, and that an image "roughness" index correlates with displacement measurement error for a variety of imaging conditions and tissue types.
Abstract: Mechanical factors such as deformation and strain are thought to play important roles in the maintenance, repair, and degeneration of soft tissues. Determination of soft tissue static deformation has traditionally only been possible at a tissue's surface, utilizing external markers or instrumentation. Texture correlation is a displacement field measurement technique which relies on unique image patterns within a pair of digital images to track displacement. The technique has recently been applied to MR images, indicating the possibility of high-resolution displacement and strain field determination within the mid-substance of soft tissues. However, the utility of MR texture correlation analysis may vary amongst tissue types depending on their underlying structure, composition, and contrast mechanism, which give rise to variations in texture with MRI. In this study, we investigate the utility of a texture correlation algorithm with first-order displacement mapping terms for use with MR images, and suggest a novel index of image "roughness" as a way to decrease errors associated with the use of texture correlation for intra-tissue strain measurement with MRI. We find that a first-order algorithm can significantly reduce strain measurement error, and that an image "roughness" index correlates with displacement measurement error for a variety of imaging conditions and tissue types.
TL;DR: In this paper, a detailed 3D model of the Jura arc was reconstructed using the UNFOLD surface-balanced program, based on a block mosaic method, which results in a displacement field divergent toward the deformation front.
Abstract: [1] The mechanism of arcuate mountain range formation is a matter of debate. Here we perform a map view restoration of a detailed three-dimensional model of the Jura arc, a typical arcuate mountain range in the foothills of the Swiss and French Alps. This retrodeformation is performed using the UNFOLD surface-balanced program, based on a “block mosaic” method. It results in a displacement field divergent toward the deformation front. This displacement field suggests counterclockwise rigid rotations in the horizontal plane up to 30° in the southern Internal Jura and a corresponding vertical axis rotation or shear strain of the Savoie molasse basin hinterlandward. We also predict a 10° clockwise, vertical axis rotation of the molasse basin in Switzerland. All these rotations agree with those documented by paleomagnetic data. The former are taken to result from a substantial decrease in shortening at the southern Jura end, while the divergence of displacements is interpreted to result from variations in the detachment level distribution.
TL;DR: In this article, an enrichment technique for accurately modeling two dimensional crack propagation within the framework of the finite element method is presented, which uses an enriched basis that spans the asymptotic dynamic crack-tip solution.
Abstract: An enrichment technique for accurately modeling two dimensional crack propagation within the framework of the finite element method is presented. The technique uses an enriched basis that spans the asymptotic dynamic crack-tip solution. The enrichment functions and their spatial derivatives are able to exactly reproduce the asymptotic displacement field and strain field for a moving crack. The stress intensity factors for Mode I and Mode II are taken as additional degrees of freedom. An explicit time integration scheme is used to solve the resulting discrete equations. Numerical simulations of linear elastodynamic problems are reported to demonstrate the accuracy and potential of the technique.
TL;DR: A new method for reconstructing three-dimensional (3-D) left ventricular myocardial strain from tagged magnetic resonance (MR) image data with a 3-D B-spline deformation model based on a cylindrical coordinate system that more closely fits the morphology of the myocardium than previously proposed Cartesian B- Spline models.
Abstract: In this paper, we present a new method for reconstructing three-dimensional (3-D) left ventricular myocardial strain from tagged magnetic resonance (MR) image data with a 3-D B-spline deformation model. The B-spline model is based on a cylindrical coordinate system that more closely fits the morphology of the myocardium than previously proposed Cartesian B-spline models and does not require explicit regularization. Our reconstruction method first fits a spatial coordinate B-spline displacement field to the tag line data. This displacement field maps each tag line point in the deformed myocardium back to its reference position (end-diastole). The spatial coordinate displacement field is then converted to material coordinates with another B-spline fit. Finally, strain is computed by analytically differentiating the material coordinate B-spline displacement field with respect to space. We tested our method with strains reconstructed from an analytically defined mathematical left ventricular deformation model and ten human imaging studies. Our results demonstrate that a quadratic cylindrical B-spline with a fixed number of control points can accurately fit a physiologically realistic range of deformations. The average 3-D reconstruction computation time is 20 seconds per time frame on a 450 MHz Sun Ultra80 workstation.
TL;DR: In this paper, the free vibration of laminated two-side simply-supported cylindrical panels is analyzed by the mesh-free kp-Ritz method, where the reproducing kernel particle estimation is employed in hybridized form with harmonic functions to approximate the two-dimensional displacement field.
19 Apr 2004
TL;DR: In this paper, a reduced-order model for the prediction of the response of aircraft panels subjected to a severe thermo-acoustic loading is presented, where a partial static condensation approach is proposed for the numerically efficient integration of the reduced order model governing equations.
Abstract: This paper focuses on the formulation and validation of a reduced order model for the prediction of the response - displacements, stresses, fatigue life - of aircraft panels subjected to a severe thermo-acoustic loading. The reduced order modeling starts with a finite element model from a standard package (MSC.NASTRAN) and produces a set of cubic nonlinear differential equations which are efficiently marched in time. The basis for the representation of the displacement field includes transverse deflection modes of the linear panel and some associated in-plane modes (the dual modes). A partial static condensation approach is proposed for the numerically efficient integration of the reduced order model governing equations. Validation cases demonstrate the accuracy of the proposed static condensation and of the good to excellent reliability of the reduced order model for the prediction of the displacements and stresses of panels in the nonlinear range in static and dynamic cases. The computational efficiency of the reduced order model permits the generation of time histories of stresses long enough for the accurate assessment of the fatigue life of panels.
Patent•
13 Sep 2004TL;DR: In this paper, the authors proposed a method of randomizing elements into a random pattern on a surface so the random pattern of elements substantially entirely consumes a region of the surface, wherein neighboring elements overlap by the overlap distance.
Abstract: A method of randomizing elements into a random pattern on a surface so the random pattern of elements substantially entirely consumes a region of the surface includes choosing an overlap distance and creating an initial pattern of elements that substantially entirely consumes a region of the surface, wherein neighboring elements overlap by the overlap distance. The method also includes choosing a maximum displacement distance, and displacing the elements by random displacement distances from their positions in the initial pattern, the random displacement distances being less than the maximum displacement distance. Moreover, a signed difference in displacement between two neighboring elements is not greater than the overlap distance. An apparatus including the elements is also disclosed.
TL;DR: In this paper, a new zig-zag coupled theory was developed for hybrid cross-ply plates with some piezoelectric layers using third-order zigzag approximation for the inplane displacements and sublayer wise piecewise linear approximation for electric potential.
Abstract: A new zig-zag coupled theory is developed for hybrid cross-ply plates with some piezoelectric layers using third-order zig-zag approximation for the inplane displacements and sublayer wise piecewise linear approximation for the electric potential. The theory considers all electric field components and can model open and closed-circuit boundary conditions. The deflection field accounts for the transverse normal strain due to the piezoelectric d 33 coefficient. The displacement field is expressed in terms of five displacement variables (which are the same as in FSDT) and electric potential variables by satisfying exactly the conditions of zero shear stresses at the top and bottom, and their continuity at layer interfaces. The governing equations are derived from the principle of virtual work. Comparison of the Navier solutions for the simply-supported plates with the analytical three-dimensional piezoelasticity solutions establishes that the present efficient zig-zag theory is quite accurate for moderately thick plates.
TL;DR: In this article, a theoretical model is developed to predict the dynamic stability of a power transmission belt excited by an eccentric pulley, and an experimental investigation is performed on a beltpulley system with a pulley eccentricity; a laser displacement transducer is used to measure the transverse displacement.