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Several Numerical Examples (several + numerical_example)
Selected AbstractsOn the C1 continuous discretization of non-linear gradient elasticity: A comparison of NEM and FEM based on Bernstein,Bézier patchesINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 10 2010P. Fischer Abstract In gradient elasticity, the appearance of strain gradients in the free energy density leads to the need of C1 continuous discretization methods. In the present work, the performances of C1 finite elements and the C1 Natural Element Method (NEM) are compared. The triangular Argyris and Hsieh,Clough,Tocher finite elements are reparametrized in terms of the Bernstein polynomials. The quadrilateral Bogner,Fox,Schmidt element is used in an isoparametric framework, for which a preprocessing algorithm is presented. Additionally, the C1 -NEM is applied to non-linear gradient elasticity. Several numerical examples are analyzed to compare the convergence behavior of the different methods. It will be illustrated that the isoparametric elements and the NEM show a significantly better performance than the triangular elements. Copyright © 2009 John Wiley & Sons, Ltd. [source] Transient heat conduction in a medium with multiple circular cavities and inhomogeneitiesINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 11 2009Elizaveta Gordeliy Abstract A two-dimensional transient heat conduction problem of multiple interacting circular inhomogeneities, cavities and point sources is considered. In general, a non-perfect contact at the matrix/inhomogeneity interfaces is assumed, with the heat flux through the interface proportional to the temperature jump. The approach is based on the use of the general solutions to the problems of a single cavity and an inhomogeneity and superposition. Application of the Laplace transform and the so-called addition theorem results in an analytical transformed solution. The solution in the time domain is obtained by performing a numerical inversion of the Laplace transform. Several numerical examples are given to demonstrate the accuracy and the efficiency of the method. The approximation error decreases exponentially with the number of the degrees of freedom in the problem. A comparison of the companion two- and three-dimensional problems demonstrates the effect of the dimensionality. Copyright © 2009 John Wiley & Sons, Ltd. [source] A hypersingular time-domain BEM for 2D dynamic crack analysis in anisotropic solidsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 2 2009M. Wünsche Abstract A hypersingular time-domain boundary element method (BEM) for transient elastodynamic crack analysis in two-dimensional (2D), homogeneous, anisotropic, and linear elastic solids is presented in this paper. Stationary cracks in both infinite and finite anisotropic solids under impact loading are investigated. On the external boundary of the cracked solid the classical displacement boundary integral equations (BIEs) are used, while the hypersingular traction BIEs are applied to the crack-faces. The temporal discretization is performed by a collocation method, while a Galerkin method is implemented for the spatial discretization. Both temporal and spatial integrations are carried out analytically. Special analytical techniques are developed to directly compute strongly singular and hypersingular integrals. Only the line integrals over an unit circle arising in the elastodynamic fundamental solutions need to be computed numerically by standard Gaussian quadrature. An explicit time-stepping scheme is obtained to compute the unknown boundary data including the crack-opening-displacements (CODs). Special crack-tip elements are adopted to ensure a direct and an accurate computation of the elastodynamic stress intensity factors from the CODs. Several numerical examples are given to show the accuracy and the efficiency of the present hypersingular time-domain BEM. Copyright © 2008 John Wiley & Sons, Ltd. [source] Accurate eight-node hexahedral elementINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 6 2007Magnus Fredriksson Abstract Based on the assumed strain method, an eight-node hexahedral element is proposed. Consistent choice of the fundamental element stiffness guarantees convergence and fulfillment of the patch test a priori. In conjunction with a ,-projection operator, the higher order strain field becomes orthogonal to rigid body and linear displacement fields. The higher order strain field in question is carefully selected to preserve correct rank for the element stiffness matrix, also for distorted elements. Volumetric locking is also removed effectively. By considerations of the bending energy, improved accuracy is obtained even for coarse element meshes. The choice of local co-ordinate system aligned with the principal axes of inertia makes it possible to improve the performance even for distorted elements. The strain-driven format obtained is well suited for materials with non-linear stress,strain relations. Several numerical examples are presented where the excellent performance of the proposed eight-node hexahedral is verified. Copyright © 2007 John Wiley & Sons, Ltd. [source] Hybrid and enhanced finite element methods for problems of soil consolidationINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 2 2007X. X. Zhou Abstract Hybrid and enhanced finite element methods with bi-linear interpolations for both the solid displacements and the pore fluid pressures are derived based on mixed variational principles for problems of elastic soil consolidation. Both plane strain and axisymmetric problems are studied. It is found that by choosing appropriate interpolation of enhanced strains in the enhanced method, and by choosing appropriate interpolations of strains, effective stresses and enhanced strains in the hybrid method, the oscillations of nodal pore pressures can be eliminated. Several numerical examples demonstrating the capability and performance of the enhanced and hybrid finite element methods are presented. It is also shown that for some situations, such as problems involving high Poisson's ratio and in other related problems where bending effects are evident, the performance of the enhanced and hybrid methods are superior to that of the conventional displacement-based method. The results from the hybrid method are better than those from the enhanced method for some situations, such as problems in which soil permeability is variable or discontinuous within elements. Since all the element parameters except the nodal displacements and nodal pore pressures are assumed in the element level and can be eliminated by static condensation, the implementations of the enhanced method and the hybrid method are basically the same as the conventional displacement-based finite element method. The present enhanced method and hybrid method can be easily extended to non-linear consolidation problems. Copyright © 2006 John Wiley & Sons, Ltd. [source] Radial point interpolation based finite difference method for mechanics problemsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 7 2006G. R. Liu Abstract A radial point interpolation based finite difference method (RFDM) is proposed in this paper. In this novel method, radial point interpolation using local irregular nodes is used together with the conventional finite difference procedure to achieve both the adaptivity to irregular domain and the stability in the solution that is often encountered in the collocation methods. A least-square technique is adopted, which leads to a system matrix with good properties such as symmetry and positive definiteness. Several numerical examples are presented to demonstrate the accuracy and stability of the RFDM for problems with complex shapes and regular and extremely irregular nodes. The results are examined in detail in comparison with other numerical approaches such as the radial point collocation method that uses local nodes, conventional finite difference and finite element methods. Copyright © 2006 John Wiley & Sons, Ltd. [source] Structural topology optimization of vibrating structures with specified eigenfrequencies and eigenmode shapesINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 5 2006Y. Maeda Abstract In vibration optimization problems, eigenfrequencies are usually maximized in the optimization since resonance phenomena in a mechanical structure must be avoided, and maximizing eigenfrequencies can provide a high probability of dynamic stability. However, vibrating mechanical structures can provide additional useful dynamic functions or performance if desired eigenfrequencies and eigenmode shapes in the structures can be implemented. In this research, we propose a new topology optimization method for designing vibrating structures that targets desired eigenfrequencies and eigenmode shapes. Several numerical examples are presented to confirm that the method presented here can provide optimized vibrating structures applicable to the design of mechanical resonators and actuators. Copyright © 2006 John Wiley & Sons, Ltd. [source] Robust adaptive remeshing strategy for large deformation, transient impact simulationsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 13 2006Tobias Erhart Abstract In this paper, an adaptive approach, with remeshing as essential ingredient, towards robust and efficient simulation techniques for fast transient, highly non-linear processes including contact is discussed. The necessity for remeshing stems from two sources: the capability to deal with large deformations that might even require topological changes of the mesh and the desire for an error driven distribution of computational resources. The overall computational approach is sketched, the adaptive remeshing strategy is presented and the crucial aspect, the choice of suitable error indicator(s), is discussed in more detail. Several numerical examples demonstrate the performance of the approach. Copyright © 2005 John Wiley & Sons, Ltd. [source] Strong and weak arbitrary discontinuities in spectral finite elementsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 8 2005A. Legay Abstract Methods for constructing arbitrary discontinuities within spectral finite elements are described and studied. We use the concept of the eXtended Finite Element Method (XFEM), which introduces the discontinuity through a local partition of unity, so there is no requirement for the mesh to be aligned with the discontinuities. A key aspect of the implementation of this method is the treatment of the blending elements adjacent to the local partition of unity. We found that a partition constructed from spectral functions one order lower than the continuous approximation is optimal and no special treatment is needed for higher order elements. For the quadrature of the Galerkin weak form, since the integrand is discontinuous, we use a strategy of subdividing the discontinuous elements into 6- and 10-node triangles; the order of the element depends on the order of the spectral method for curved discontinuities. Several numerical examples are solved to examine the accuracy of the methods. For straight discontinuities, we achieved the optimal convergence rate of the spectral element. For the curved discontinuity, the convergence rate in the energy norm error is suboptimal. We attribute the suboptimality to the approximations in the quadrature scheme. We also found that modification of the adjacent elements is only needed for lower order spectral elements. Copyright © 2005 John Wiley & Sons, Ltd. [source] Simple modifications for stabilization of the finite point methodINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 3 2005B. Boroomand Abstract A stabilized version of the finite point method (FPM) is presented. A source of instability due to the evaluation of the base function using a least square procedure is discussed. A suitable mapping is proposed and employed to eliminate the ill-conditioning effect due to directional arrangement of the points. A step by step algorithm is given for finding the local rotated axes and the dimensions of the cloud using local average spacing and inertia moments of the points distribution. It is shown that the conventional version of FPM may lead to wrong results when the proposed mapping algorithm is not used. It is shown that another source for instability and non-monotonic convergence rate in collocation methods lies in the treatment of Neumann boundary conditions. Unlike the conventional FPM, in this work the Neumann boundary conditions and the equilibrium equations appear simultaneously in a weight equation similar to that of weighted residual methods. The stabilization procedure may be considered as an interpretation of the finite calculus (FIC) method. The main difference between the two stabilization procedures lies in choosing the characteristic length in FIC and the weight of the boundary residual in the proposed method. The new approach also provides a unique definition for the sign of the stabilization terms. The reasons for using stabilization terms only at the boundaries is discussed and the two methods are compared. Several numerical examples are presented to demonstrate the performance and convergence of the proposed methods. Copyright © 2005 John Wiley & Sons, Ltd. [source] Fast and accurate 4-node quadrilateralINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 11 2004Magnus Fredriksson Abstract An accurate and variationally consistent 4-node quadrilateral element is introduced where high coarse mesh accuracy and low mesh distortion sensitivity are characteristic qualities, even when incompressibility is approached for plane strain. One-point quadrature integration procedure is adopted and a new improved stabilization technique is developed. Orthogonality conditions are utilized so that the patch test is satisfied for arbitrary quadrilaterals. Several numerical examples including a convergence rate study are presented which confirm the excellent performance of this element. Copyright © 2004 John Wiley & Sons, Ltd. [source] On discontinuous Galerkin methodsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 8 2003O. C. Zienkiewicz Abstract Discontinuous Galerkin methods have received considerable attention in recent years for problems in which advection and diffusion terms are present. Several alternatives for treating the diffusion and advective fluxes have been introduced. This report summarizes some of the methods that have been proposed. Several numerical examples are included in the paper. These present discontinuous Galerkin solutions of one-dimensional problems with a scalar variable. Results are presented for diffusion,reaction problems and advection,diffusion problems. We discuss the performance of various formulations with respect to accuracy as well as stability of the method. Copyright © 2003 John Wiley & Sons, Ltd. [source] Explicit calculation of smoothed sensitivity coefficients for linear problemsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 2 2003R. A. Bia, ecki Abstract A technique of explicit calculation of sensitivity coefficients based on the approximation of the retrieved function by a linear combination of trial functions of compact support is presented. The method is applicable to steady state and transient linear inverse problems where unknown distributions of boundary fluxes, temperatures, initial conditions or source terms are retrieved. The sensitivity coefficients are obtained by solving a sequence of boundary value problems with boundary conditions and source term being homogeneous except for one term. This inhomogeneous term is taken as subsequent trial functions. Depending on the type of the retrieved function, it may appear on boundary conditions (Dirichlet or Neumann), initial conditions or the source term. Commercial software and analytic techniques can be used to solve this sequence of boundary value problems producing the required sensitivity coefficients. The choice of the approximating functions guarantees a filtration of the high frequency errors. Several numerical examples are included where the sensitivity coefficients are used to retrieve the unknown values of boundary fluxes in transient state and volumetric sources. Analytic, boundary-element and finite-element techniques are employed in the study. Copyright © 2003 John Wiley & Sons, Ltd. [source] Arbitrary placement of local meshes in a global mesh by the interface-element method (IEM)INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 15 2003Hyun-Gyu KimArticle first published online: 25 FEB 200 Abstract A new method is proposed to place local meshes in a global mesh with the aid of the interface-element method (IEM). The interface-elements use moving least-square (MLS)-based shape functions to join partitioned finite-element domains with non-matching interfaces. The supports of nodes are defined to satisfy the continuity condition on the interfaces by introducing pseudonodes on the boundaries of interface regions. Particularly, the weight functions of nodes on the boundaries of interface regions span only neighbouring nodes, ensuring that the resulting shape functions are identical to those of adjoining finite-elements. The completeness of the shape functions of the interface-elements up to the order of basis provides a reasonable transfer of strain fields through the non-matching interfaces between partitioned domains. Taking these great advantages of the IEM, local meshes can be easily inserted at arbitrary places in a global mesh. Several numerical examples show the effectiveness of this technique for modelling of local regions in a global domain. Copyright © 2003 John Wiley & Sons, Ltd. [source] A Galerkin boundary integral method for multiple circular elastic inclusionsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 10 2001S. G. Mogilevskaya Abstract The problem of an infinite, isotropic elastic plane containing an arbitrary number of circular elastic inclusions is considered. The analysis procedure is based on the use of a complex singular integral equation. The unknown tractions at each circular boundary are approximated by a truncated complex Fourier series. A system of linear algebraic equations is obtained by using the classical Galerkin method and the Gauss,Seidel algorithm is used to solve the system. Several numerical examples are considered to demonstrate the effectiveness of the approach. Copyright © 2001 John Wiley & Sons, Ltd. [source] Optimal service rates of a service facility with perishable inventory itemsNAVAL RESEARCH LOGISTICS: AN INTERNATIONAL JOURNAL, Issue 5 2002O. Berman In this paper we optimally control service rates for an inventory system of service facilities with perishable products. We consider a finite capacity system where arrivals are Poisson-distributed, lifetime of items have exponential distribution, and replenishment is instantaneous. We determine the service rates to be employed at each instant of time so that the long-run expected cost rate is minimized for fixed maximum inventory level and capacity. The problem is modelled as a semi-Markov decision problem. We establish the existence of a stationary optimal policy and we solve it by employing linear programming. Several numerical examples which provide insight to the behavior of the system are presented. © 2002 Wiley Periodicals, Inc. Naval Research Logistics 49: 464,482, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/nav.10021 [source] A posteriori error estimator for expanded mixed hybrid methods,NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 2 2007Dongho Kim Abstract In this article, we construct an a posteriori error estimator for expanded mixed hybrid finite-element methods for second-order elliptic problems. An a posteriori error analysis yields reliable and efficient estimate based on residuals. Several numerical examples are presented to show the effectivity of our error indicators. © 2006 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 23: 330,349, 2007 [source] Pricing American exchange options in a jump-diffusion modelTHE JOURNAL OF FUTURES MARKETS, Issue 3 2007Snorre Lindset A way to estimate the value of an American exchange option when the underlying assets follow jump-diffusion processes is presented. The estimate is based on combining a European exchange option and a Bermudan exchange option with two exercise dates by using Richardson extrapolation as proposed by R. Geske and H. Johnson (1984). Closed-form solutions for the values of European and Bermudan exchange options are derived. Several numerical examples are presented, illustrating that the early exercise feature may have a significant economic value. The results presented should have potential for pricing over-the-counter options and in particular for pricing real options. © 2007 Wiley Periodicals, Inc. Jrl Fut Mark 27:257,273, 2007 [source] Modelling of hygro-thermal behaviour and damage of concrete at temperature above the critical point of waterINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 6 2002D. Gawin Abstract In this paper, a model for the analysis of the behaviour of concrete at temperature largely exceeding critical point of water, is presented. In this temperature range liquid phase, i.e. capillary phase, and gas phase cannot be distinguished and only the latter exists. Consequently, capillary pressure has no more physical meaning above this point and liquid water is present only as physically adsorbed water. In this work, we give a different physical interpretation to the capillary pressure and use it still for the description of the hygrometric state of concrete in the zone, where temperature exceeds the critical point of water. Considerable thermal dilatation of the liquid water and the real behaviour of water vapour close to critical temperature are taken into account. Moreover, a special switching procedure in order to avoid the Stefan-like problem, which subsequently arises, is described and employed in the calculations. Finally, several numerical examples demonstrating the robustness of the adopted solution have been shown. Copyright © 2002 John Wiley & Sons, Ltd. [source] Fast multipole boundary element analysis of two-dimensional elastoplastic problemsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 10 2007P. B. Wang Abstract This paper presents a fast multipole boundary element method (BEM) for the analysis of two-dimensional elastoplastic problems. An incremental iterative technique based on the initial strain approach is employed to solve the nonlinear equations, and the fast multipole method (FMM) is introduced to achieve higher run-time and memory storage efficiency. Both of the boundary integrals and domain integrals are calculated by recursive operations on a quad-tree structure without explicitly forming the coefficient matrix. Combining multipole expansions with local expansions, computational complexity and memory requirement of the matrix,vector multiplication are both reduced to O(N), where N is the number of degrees of freedom (DOFs). The accuracy and efficiency of the proposed scheme are demonstrated by several numerical examples. Copyright © 2006 John Wiley & Sons, Ltd. [source] Heat conduction and radiative heat exchange in cellular structures using flat shell elementsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 3 2006J. B. Colliat Abstract We developed in this paper a variational formulation of heat diffusion equation applicable to the flat shell context and cellular structures. For this purpose, we introduce the average mid-surface temperature field, through-the-thickness gradient and their dual generalized fluxes. Moreover, we introduced radiative heat exchange in the same way, which leads to a non-linear and unsymmetrical thermal discrete problem. The model performance is illustrated by several numerical examples concerning cellular structures like hollow clay bricks submitted to thermal loading. Thermo-mechanical coupling for such structure which is well adapted to the shell-like modelling approach, is presented in the elastic regime with the numerical results concerning temperature field and forces. Copyright © 2005 John Wiley & Sons, Ltd. [source] Complete semi-analytical treatment of weakly singular integrals on planar triangles via the direct evaluation methodINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 12 2010Athanasios G. Polimeridis Abstract A complete semi-analytical treatment of the four-dimensional (4-D) weakly singular integrals over coincident, edge adjacent and vertex adjacent triangles, arising in the Galerkin discretization of mixed potential integral equation formulations, is presented. The overall analysis is based on the direct evaluation method, utilizing a series of coordinate transformations, together with a re-ordering of the integrations, in order to reduce the dimensionality of the original 4-D weakly singular integrals into, respectively, 1-D, 2-D and 3-D numerical integrations of smooth functions. The analytically obtained final formulas can be computed by using typical library routines for Gauss quadrature readily available in the literature. A comparison of the proposed method with singularity subtraction, singularity cancellation and fully numerical methods, often used to tackle the multi-dimensional singular integrals evaluation problem, is provided through several numerical examples, which clearly highlights the superior accuracy and efficiency of the direct evaluation scheme. Copyright © 2010 John Wiley & Sons, Ltd. [source] Molecular mechanics in the context of the finite element methodINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 7 2009Jens Wackerfuß Abstract In molecular mechanics, the formalism of the finite element method can be exploited in order to analyze the behavior of atomic structures in a computationally efficient way. Based on the atom-related consideration of the atomic interactions, a direct correlation between the type of the underlying interatomic potential and the design of the related finite element is established. Each type of potential is represented by a specific finite element. A general formulation that unifies the various finite elements is proposed. Arbitrary diagonal- and cross-terms dependent on bond length, valence angle, dihedral angle, improper dihedral angle and inversion angle can also be considered. The finite elements are formulated in a geometrically exact setting; the related formulas are stated in detail. The mesh generation can be performed using well-known procedures typically used in molecular dynamics. Although adjacent elements overlap, a double counting of the element contributions (as a result of the assembly process) cannot occur a priori. As a consequence, the assembly process can be performed efficiently line by line. The presented formulation can easily be implemented in standard finite element codes; thus, already existing features (e.g. equation solver, visualization of the numerical results) can be employed. The formulation is applied to various interatomic potentials that are frequently used to describe the mechanical behavior of carbon nanotubes. The effectiveness and robustness of this method are demonstrated by means of several numerical examples. Copyright © 2008 John Wiley & Sons, Ltd. [source] Theoretical aspects of the internal element connectivity parameterization approach for topology optimizationINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 6 2008Gil Ho Yoon Abstract The internal element connectivity parameterization (I-ECP) method is an alternative approach to overcome numerical instabilities associated with low-stiffness element states in non-linear problems. In I-ECP, elements are connected by zero-length links while their link stiffness values are varied. Therefore, it is important to interpolate link stiffness properly to obtain stably converging results. The main objective of this work is two-fold (1) the investigation of the relationship between the link stiffness and the stiffness of a domain-discretizing patch by using a discrete model and a homogenized model and (2) the suggestion of link stiffness interpolation functions. The effects of link stiffness penalization on solution convergence are then tested with several numerical examples. The developed homogenized I-ECP model can also be used to physically interpret an intermediate design variable state. Copyright © 2008 John Wiley & Sons, Ltd. [source] Meshfree point collocation method for elasticity and crack problemsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 1 2004Sang-Ho Lee Abstract A generalized diffuse derivative approximation is combined with a point collocation scheme for solid mechanics problems. The derivatives are obtained from a local approximation so their evaluation is computationally very efficient. This meshfree point collocation method has other advantages: it does not require special treatment for essential boundary condition nor the time-consuming integration of a weak form. Neither the connectivity of the mesh nor differentiability of the weight function is necessary. The accuracy of the solutions is exceptional and generally exceeds that of element-free Galerkin method with linear basis. The performance and robustness are demonstrated by several numerical examples, including crack problems. Copyright © 2004 John Wiley & Sons, Ltd. [source] Finite element of slender beams in finite transformations: a geometrically exact approachINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 5 2004Frédéric Boyer Abstract This article is devoted to the modelling of thin beams undergoing finite deformations essentially due to bending and torsion and to their numerical resolution by the finite element method. The solution proposed here differs from the approaches usually implemented to treat thin beams, as it can be qualified as ,geometrically exact'. Two numerical models are proposed. The first one is a non-linear Euler,Bernoulli model while the second one is a non-linear Rayleigh model. The finite element method is tested on several numerical examples in statics and dynamics, and validated through comparison with analytical solutions, experimental observations and the geometrically exact approach of the Reissner beam theory initiated by Simo. The numerical result shows that this approach is a good alternative to the modelling of non-linear beams, especially in statics. Copyright © 2003 John Wiley & Sons, Ltd. [source] Efficient preconditioning techniques for finite-element quadratic discretization arising from linearized incompressible Navier,Stokes equationsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 12 2010A. El Maliki Abstract We develop an efficient preconditioning techniques for the solution of large linearized stationary and non-stationary incompressible Navier,Stokes equations. These equations are linearized by the Picard and Newton methods, and linear extrapolation schemes in the non-stationary case. The time discretization procedure uses the Gear scheme and the second-order Taylor,Hood element P2,P1 is used for the approximation of the velocity and the pressure. Our purpose is to develop an efficient preconditioner for saddle point systems. Our tools are the addition of stabilization (penalization) term r,(div(·)), and the use of triangular block matrix as global preconditioner. This preconditioner involves the solution of two subsystems associated, respectively, with the velocity and the pressure and have to be solved efficiently. Furthermore, we use the P1,P2 hierarchical preconditioner recently proposed by the authors, for the block matrix associated with the velocity and an additive approach for the Schur complement approximation. Finally, several numerical examples illustrating the good performance of the preconditioning techniques are presented. Copyright © 2009 John Wiley & Sons, Ltd. [source] A centroid-based sampling strategy for kriging global modeling and optimizationAICHE JOURNAL, Issue 1 2010Eddie Davis Abstract A new sampling strategy is presented for kriging-based global modeling. The strategy is used within a kriging/response surface (RSM) algorithm for solving NLP containing black-box models. Black-box models describe systems lacking the closed-form equations necessary for conventional gradient-based optimization. System optima can be alternatively found by building iteratively updated kriging models, and then refining local solutions using RSM. The application of the new sampling strategy results in accurate global model generation at lower sampling expense relative to a strategy using randomized and heuristic-based sampling for initial and subsequent model construction, respectively. The new strategy relies on construction of an initial kriging model built using sampling data obtained at the feasible region's convex polytope vertices and centroid. Updated models are constructed using additional sampling information obtained at Delaunay triangulation centroids. The new sampling algorithm is applied within the kriging-RSM framework to several numerical examples and case studies to demonstrate proof of concept. © 2009 American Institute of Chemical Engineers AIChE J, 2010 [source] Testing for Local Spatial Autocorrelation in the Presence of Global AutocorrelationJOURNAL OF REGIONAL SCIENCE, Issue 3 2001J. Keith Ord A fundamental concern of spatial analysts is to find patterns in spatial data that lead to the identification of spatial autocorrelation or association. Further, they seek to identify peculiarities in the data set that signify that something out of the ordinary has occurred in one or more regions. In this paper we provide a statistic that tests for local spatial autocorrelation in the presence of the global autocorrelation that is characteristic of heterogeneous spatial data. After identifying the structure of global autocorrelation, we introduce a new measure that may be used to test for local structure. This new statistic Oi is asymptotically normally distributed and allows for straightforward tests of hypotheses. We provide several numerical examples that illustrate the performance of this statistic and compare it with another measure that does not account for global structure. [source] A kinetic scheme for the Savage,Hutter equationsMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 16 2008Christine Kaland Abstract The Savage,Hutter (SH) equations describe the motion of granular material under the influence of friction. Based on the kinetic formulation of the SH equations, we present a kinetic scheme in one dimension, which describes the deformation of the mass profile and allows it to start and to stop. Moreover the method is able to preserve the steady states of granular masses at rest. The method is tested on several numerical examples. 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