Uncertainty in material properties can have large effect oil numerical modeling of solids and Structures. This is particularly true as all natural and man-made materials exhibit spatial non-Uniformity and point-wise uncertainty in their behaviors.A methodology that accounts for the probabilistic yielding of elastic-plastic materials is presented. The recently developed Eulerian-Lagrangian form of the Fokker-Planck-Kolmogorov equation is used to obtain a second-order exact solution to elastic-plastic constitutive differential equations. In this paper that solution is used in deriving the weighted probabilities of elastic, elastic-plastic behavior and yielding, A number of examples for two commonly used material models, von Mises and Drucker-Prager, illustrated the findings. Copyright (C) 2008 John Wiley & Sons, Ltd.
In this paper, the extended finite element method (X-FEM) is investigated for the solution of hydraulic fracture problems. The presence of an internal pressure inside the crack is taken into account. Special tip functions encapsulating tip asymptotics typically encountered in hydraulic fractures are introduced. We are especially interested in the two limiting tip behaviour for the impermeable case: the classical LEFM square root asymptote in fracture width for the toughness-dominated regime of propagation and the so-called ⅔ asymptote in fracture width for the viscosity-dominated regime. Different variants of the X-FEM are tested for the case of a plane-strain hydraulic fracture propagation in both the toughness and the viscosity dominated regimes. Fracture opening and fluid pressure are compared at each nodes with analytical solutions available in the literature. The results demonstrate the importance of correcting for the loss of partition of unity in the transition zone between the enriched part and the rest of the mesh. A point-wise matching scheme appears sufficient to obtain accurate results. Proper integration of the singular terms introduced by the enrichment functions is also critical for good performance. Copyright © 2008 John Wiley & Sons, Ltd.
Many classes of engineering fluid dynamics simulation require the tracking of discrete elements, for example, dispersed particles in a solvent, a spray of diesel injected into an internal Combustion engine, or the dynamics of granular materials. Realistic simulations often require complex, 3D geometries, generated from CAD models and meshed With unstructured polyhedra, which may be deforming, in motion or spatially decomposed for parallel computation. We present an algorithm to track the motion of particles in such geometries which is designed to be computationally efficient and robust in imperfect 3D meshes where small holes or overlaps are present. It has been applied to a wide range of engineering problems ranging from injected fuel sprays in internal combustion engines to molecular dynamics modelling of nanoscale flows. Copyright (C) 2008 John Wiley & Sons, Ltd.
We propose a simple stopping criterion for the conjugate gradient (CG) algorithm in the framework of anisotropic, adaptive finite elements for elliptic problems. The goal of the adaptive algorithm is to find a triangulation such that the estimated relative error is close to a given tolerance TOL. We propose to stop the CG algorithm whenever the residual vector has Euclidian norm less than a small fraction of the estimated error. This stopping criterion is based on a posteriori error estimates between the true solution u and the computed solution u(h)(n) (the superscript n stands for the CG iteration number, the subscript It for the typical mesh size) and on heuristics to relate the error between u(h) and u(h)(n) to the residual vector.Numerical experiments with anisotropic adaptive meshes show that the total number of CG iterations can be divided by 10 without significant discrepancy in the computed results. Copyright (C) 2008 John Wiley & Sons, Ltd.
The extended finite element method (X-FEM), in conjunction with the level set method, is applied to sloshing analysis of a rigid container filled with liquid. The governing equations for liquid with a free surface based on the potential flow theory are discretized using the framework of level set X-FEM. Once the space domain of a container is modeled by tetrahedral elements, sloshing analysis for arbitrary liquid levels and configurations can be performed without remeshing. Natural frequencies of free surface sloshing motion in rigid containers of various shapes were computed by the proposed method and the results were compared with those obtained by theoretical solutions and experiments. The proposed method was demonstrated to perform sloshing analysis efficiently for rigid containers with various liquid levels and configurations. Copyright (C) 2008 John Wiley & Sons, Ltd.
The adaptive variational multiscale method is an extension of the variational multiscale method where the line-scale part of the solution is approximated by a sum of numerically computed solutions to localized subgrid problems. Furthermore, the crucial discretization parameters are chosen automatically by an adaptive algorithm based on a posteriori error estimates. This method has been developed for diffusion-dominated problems and applied to multiscale problems that arise in oil reservoir Simulation. In this paper, we extend the method to convection-diffusion problems. We present it duality based a posteriori error representation formula and an adaptive algorithm that tunes the fine-scale mesh size and the patch sizes of the local problems. Numerical results show rapid convergence of the adaptive algorithm. Copyright (c) 2008 John Wiley & Sons, Ltd.
In this paper we extend the method of inter-modality image registration using the maximization of normalized mutual information (NMI) for the registration of [F-18]-2-fluoro-deoxy-D-glucose (FDG)-positron emission tomography (PET) with T1-weighted magnetic resonance (MR) Volumes. We investigate the impact on the NMI maximization with respect to using coarse-to-fine grained B-spline bases and to the number of bills required for the voxel intensity histograms of each volume. Our results demonstrate that the efficiency and accuracy of elastic, as well as rigid body, registration is improved both through the use of a reduced number of bins in the PET and MR histograms, and of a limited coarse-to-fine grain interpolation of the volume data. To determine the appropriate number of bins prior to registration, we consider the NMI between the two volumes, the mutual information content of the two volumes, as a function of the binning of each volume. Simulated data sets are used for validation and the registration improves that obtained with a standard approach based oil the Statistical Parametric Mapping software. Copyright (C) 2008 John Wiley & Sons, Ltd.
We analyze localized textural consistencies in high-resolution X-ray (computed tomography) CT scans of coronary arteries to identify the appearance of diagnostically relevant changes in tissue. For the efficient and accurate processing of CT volume data, we use fast wavelet algorithms associated with three-dimensional isotropic multiresolution wavelets that implement a redundant, frame-based image encoding without directional preference. Our algorithm identifies textural consistencies by correlating coefficients in the wavelet representation. Copyright (C) 2009 John Wiley & Sons, Ltd.
Wave-based numerical methods often require to integrate products of polynomials and exponentials. With quadrature methods, this task can be particularly expensive at high frequencies as large numbers of integration points are required. This paper presents a set of closed-form Solutions for the integrals of polynomial-exponential products in two and three dimensions. These results apply to arbitrary polygons in two dimensions, and for arbitrary polygonal surfaces or polyhedral volumes in three dimensions. Quadrature methods are therefore not required for this class of integrals that can be evaluated quickly and exactly. Copyright (C) 2008 John Wiley & Sons, Ltd.
The variational multiscale (VMS) method sets a general framework for stabilization methods. By splitting the exact solution into coarse (grid) and fine (subgrid) scales, one can obtain a system of two equations for these unknowns. The grid scale equation is solved using the Galerkin method and contains an additional term involving the subgrid scale. At this stage, several options are usually considered to deal with the subgrid scale equation: this includes the choice of the space where the subgrid scale would be defined as well as the simplifications leading to compute the subgrid scale analytically or numerically. The present study proposes to develop a two-scale variational method for the advection-diffusion-reaction equation. On the one hand, a family of weak forms are obtained by integrating by parts a fraction of the advection term. On the other hand, the solution of the subgrid scale equation is found using the following. First, a two-scale variational method is applied to the one-dimensional problem. Then, a series of approximations are assumed to solve the subgrid space equation analytically. This allows to devise expressions for the,stabilization parameter' tau, in the context of VMS (two-scale) method. The proposed method is equivalent to the traditional Green's method used in the literature to solve residual-free bubbles, although it offers another point of view, as the strong form of the subgrid scale equation is solved explicitly. In addition, the authors apply the methodology to high-order elements, namely quadratic and cubic elements. The proposed model consists in assuming that the subgrid scale vanishes also on interior nodes of the element and applying the strategy used for linear element in the segment between these interior nodes. The proposed scheme is compared with existing ones through the solution of a one-dimensional numerical example for linear, quadratic and cubic elements. In addition, the mesh convergence is checked for high-order elements through the solution of an exact solution in two dimensions. Copyright (C) 2008 John Wiley & Sons, Ltd.
The flow-field immediately downstream of it collapsible tube during oscillation onset starting from the collapsed state was measured using two-dimensional high-speed particle image velocimetry. Both tube and fluid were chosen to produce oscillation at the lowest possible Reynolds number, of just over 300. The flow was examined in the plane formed by the tube axis extended into the downstream pipe and the major axis of the tube collapse cross-section. The resulting time-series of spatial fields of 2D velocity vectors was analysed by frequency content and by proper orthogonal decomposition. Areas of the flow where oscillation initially occurs were identified. Flow disturbances centred at various frequencies were identified, some associated with the growing oscillation arising from the instability of the fluid-structure interaction between the main flow and the tube and others associated with the instability of the confined twin jets emanating from the collapsed-tube throat. Copyright (C) 2009 John Wiley & Sons, Ltd.
Accurate prediction of the position of flow separation along a constriction is important to model fluid-structure interaction phenomena in the upper airways such as phonation and obstructive sleep apnea. Flow assumptions underlying common flow descriptions along the upper airways are formulated. Flow separation positions, obtained from theories with different degrees of complexity are qualitatively and quantitatively discussed. In particular, geometrical and flow features determining the influence of viscosity are varied. Increasing the constriction degree and the constriction length is shown to affect the position of flow separation. Boundary layer solutions and simulations with the two-dimensional Navier Stokes equations result in an accurate quantitative prediction of flow separation. Furthermore, Jeffery-Hamel flow solutions qualitatively predict the effect of both constriction height and length on the position of flow,separation. The ad hoc assumption applied in quasi-one-dimensional flow descriptions does not accurately predict flow separation. Copyright (C) 2008 John Wiley & Sons, Ltd.
To obtain a very fast solution for finite element models used in surgical simulations low order elements such as the linear tetrahedron or the linear under-integrated hexahedron must be used. Automatic hexahedral mesh generation for complex geometries remains a challenging problem, and therefore tetrahedral or mixed meshes are often necessary. Unfortunately the standard formulation of the linear tetrahedral element exhibits volumetric locking in case of almost incompressible materials. In this paper we extend the average nodal pressure tetrahedral element proposed by Bonet and Burton for a better handling of multiple material interfaces. The new formulation can handle multiple materials in a uniform way, with better accuracy, while requiring only a small additional computation effort. We discuss some implementation issues and show how easy an existing TLED (Total Lagrangian Explicit Dynamics) algorithm can be modified in order to support the new element formulation. The performance evaluation of the new element shows the clear improvement in reaction forces and displacements predictions compared to the average nodal pressure element in case of models consisting of multiple materials.
This paper promotes the development of a novel family of finite elements with smoothed strains, offering remarkable properties. In the smoothed finite element method (FEM), elements are divided into subcells. The strain at a point is defined as a weighted average of the standard strain field over a representative domain.This yields superconvergent stresses, both in regular and singular settings, as well as increased accuracy. with slightly lower computational cost than the standard FEM.The one-subcell version that does not exhibit volumetric locking yields more accurate stresses but less accurate displacements and is equivalent to a quasi-equilibrium FEM. It is also subject to instabilities. In the limit where the number of subcells goes to infinity, the standard FEM is recovered, which yields more accurate displacements and less accurate stresses.The specific contribution of this paper is to show that expressing the volumetric part of the strain field using a one-subcell formulation is sufficient to get rid of volumetric locking and increase the displacement accuracy compared with the standard FEM when the single subcell version is used to express both the volumetric and deviatoric parts of the strain. Selective integration also alleviates instabilities associated with the single subcell element, which are due to rank deficiency.Numerical examples on various compressible and incompressible linear elastic test cases show that high accuracy is retained compared with the standard FEM without increasing computational cost. Copyright (c) 2008 John Wiley & Sons, Ltd.
In this paper, a method is presented for the coupling of three-dimensional (3D) and one-dimensional (1D) fluid-structure-interaction models for wave propagation phenomena in flexible vessels. The method is based on the hyperbolic nature of the 1D problem. More specifically, the two Riemann invariants of the 1D problem are expressed in terms of average velocity and pressure and the value of the invariant that approaches the 3D domain provides a non-linear constraint between the two variables that is used as a boundary conditions for the 3D problem. It is assumed that the distribution of the Riemann invariant is uniform in the vessel cross section. The implementation of the boundary condition in the context of a pressure-correction solution method in a finite volume mesh is described in detail. Computations of pressure pulse propagation within an elastic cylindrical vessel showed that the wave propagates smoothly from the 3D to the 1D domain. Copyright (C) 2009 John Wiely & Sons, Ltd.
This paper describes an approach to smooth the surface and improve the quality of quadrilateral/hexahedral meshes with feature preserved using geometric flow. For quadrilateral surface meshes, the surface diffusion flow is selected to remove noise by relocating vertices in the normal direction, and the aspect ratio is improved with feature preserved by adjusting vertex positions in the tangent direction. For hexahedral meshes, besides the surface vertex movement in the normal and tangent directions, interior vertices are relocated to improve the aspect ratio. Our method has the properties of noise removal, feature preservation and quality improvement of quadrilateral/hexahedral meshes, and it is especially suitable for biomolecular meshes because the surface diffusion flow preserves sphere accurately if the initial surface is close to a sphere. Several demonstration examples are provided from a wide variety of application domains. Some extracted meshes have been extensively used in finite element simulations.
Full understanding of the fluid-object interactions subcomputation technique (FOIST) and the related fundamental concepts in dynamics and fluid mechanics is essential in using this technique in a meaningful way. We explain what constitutes a correct implementation of the FOIST and give a published example of what does not. Copyright (C) 2009 John Wiley & Sons, Ltd.
The moment-of-fluid (MOF) method is a new volume-tracking method that accurately treats evolving material interfaces. The MOF method uses moment data, namely the material volume fraction, as well as the centroid, for a more accurate representation of the material configuration, interfaces and concomitant volume advection. In contrast, the volume-of-fluid method uses only volume fraction data for interface reconstruction and advection. Based on the moment data for each material, the material inter-faces are reconstructed with second-order spatial accuracy in a strictly conservative manner. The MOF method is Coupled with a stabilized finite element incompressible Navier-Stokes solver for two materials. The effectiveness of the MOF method is demonstrated with a free-surface dam-break and a two-material Rayleigh-Taylor problem. Copyright (C) 2008 John Wiley & Sons, Ltd.
When solving parabolic partial differential equations using finite difference non-overlapping domain decomposition methods, one often uses the stripwise decomposition of spatial domain and it can be extended to the rectangular decomposition without further analysis. In this paper, we analyze the rectangular decomposition when the modified implicit prediction (MIP) algorithm is used. We show that the performance of the rectangular decomposition and the stripwise decomposition is different. We compare spectral radius, maximum error, efficiency, and total operations of the rectangular and the stripwise decompositions. We investigate the accuracy of the interface of the rectangular decomposition and the effects of the correction phase of the rectangular decomposition. Numerical experiments have been done in both two and three spatial dimensions and show that the rectangular decomposition is not better than the stripwise decomposition. Copyright © 2008 John Wiley & Sons, Ltd.
Circular plates are important structural elements in modern engineering structures. In this paper a computationally efficient and accurate numerical model is presented for the study of free vibration and bending behavior of thick circular plates based on Mindlin plate theory. The approach developed is based on the discrete singular convolution method and the use of regularized Shannon's delta kernel. Frequency parameters, deflections and bending moments are obtained for different geometric parameters of the circular plate. Comparisons are made with existing numerical and analytical Solutions in the literature. It is found that the DSC method yields accurate results for the free vibration and bending problems of thick circular plates. Copyright (C) 2008 John Wiley & Sons, Ltd.
