Home About us Contact
|
Home About us Contact | ||
|
|
||
Integration Scheme (integration + scheme)
Kinds of Integration Scheme Selected AbstractsIntegration schemes for von-Mises plasticity models based on exponential maps: numerical investigations and theoretical considerationsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 9 2005E. Artioli Abstract We consider three different exponential map algorithms for associative von-Mises plasticity with linear isotropic and kinematic hardening. The first scheme is based on a different formulation of the time continuous plasticity model, which automatically grants the yield consistency of the method in the numerical solution. The second one is the quadratically accurate but non-yield consistent method already proposed in Auricchio and Beirão da Veiga (Int. J. Numer. Meth. Engng 2003; 56: 1375,1396). The third method is an improved version of the second one, in which the yield consistency condition is enforced a posteriori. We also compare the performance of the three methods with the classical radial return map algorithm. We develop extensive numerical tests which clearly show the main advantages and disadvantages of the three methods. Copyright © 2005 John Wiley & Sons, Ltd. [source] A Rosenbrock-W method for real-time dynamic substructuring and pseudo-dynamic testingEARTHQUAKE ENGINEERING AND STRUCTURAL DYNAMICS, Issue 9 2009C. P. Lamarche Abstract A variant of the Rosenbrock-W integration method is proposed for real-time dynamic substructuring and pseudo-dynamic testing. In this variant, an approximation of the Jacobian matrix that accounts for the properties of both the physical and numerical substructures is used throughout the analysis process. Only an initial estimate of the stiffness and damping properties of the physical components is required. It is demonstrated that the method is unconditionally stable provided that specific conditions are fulfilled and that the order accuracy can be maintained in the nonlinear regime without involving any matrix inversion while testing. The method also features controllable numerical energy dissipation characteristics and explicit expression of the target displacement and velocity vectors. The stability and accuracy of the proposed integration scheme are examined in the paper. The method has also been verified through hybrid testing performed of SDOF and MDOF structures with linear and highly nonlinear physical substructures. The results are compared with those obtained from the operator splitting method. An approach based on the modal decomposition principle is presented to predict the potential effect of experimental errors on the overall response during testing. Copyright © 2009 John Wiley & Sons, Ltd. [source] Output-only structural identification in time domain: Numerical and experimental studiesEARTHQUAKE ENGINEERING AND STRUCTURAL DYNAMICS, Issue 4 2008M. J. Perry Abstract By identifying changes in stiffness parameters, structural damage can be detected and monitored. Although considerable progress has been made in this research area, many challenges remain in achieving robust structural identification based on incomplete and noisy measurement signals. The identification task is made even more difficult if measurement of input force is to be eliminated. To this end, an output-only structural identification strategy is proposed to identify unknown stiffness and damping parameters. A non-classical approach based on genetic algorithms (GAs) is adopted. The proposed strategy makes use of the recently developed GA-based method of search space reduction, which has shown to be able to accurately and reliably identify structural parameters from measured input and output signals. By modifying the numerical integration scheme, input can be computed as the parameter identification task is in progress, thereby eliminating the need to measure forces. Numerical and experimental results demonstrate the power of the strategy in accurate and efficient identification of structural parameters and damage using only incomplete acceleration measurements. Copyright © 2007 John Wiley & Sons, Ltd. [source] Net primary productivity mapped for Canada at 1-km resolutionGLOBAL ECOLOGY, Issue 2 2002J Liu Abstract Aim To map net primary productivity (NPP) over the Canadian landmass at 1-km resolution. Location Canada. Methods A simulation model, the Boreal Ecosystem Productivity Simulator (BEPS), has been developed. The model uses a sunlit and shaded leaf separation strategy and a daily integration scheme in order to implement an instantaneous leaf-level photosynthesis model over large areas. Two key driving variables, leaf area index (every 10 days) and land cover type (annual), are derived from satellite measurements of the Advanced Very High Resolution Radiometer (AVHRR). Other spatially explicit input data are also prepared, including daily meteorological data (radiation, precipitation, temperature, and humidity), available soil water holding capacity (AWC) and forest biomass. The model outputs are compared with ground plot data to ensure that no significant systematic biases are created. Results The simulation results show that Canada's annual net primary production was 1.22 Gt C year,1 in 1994, 78% attributed to forests, mainly the boreal forest, without considering the contribution of the understorey. The NPP averaged over the entire landmass was ~140 g C m,2 year,1 in 1994. Geographically, NPP varied greatly among ecozones and provinces/territories. The seasonality of NPP is characterized by strong summer photosynthesis capacities and a short growing season in northern ecosystems. Conclusions This study is the first attempt to simulate Canada-wide NPP with a process-based model at 1-km resolution and using a daily step. The statistics of NPP are therefore expected to be more accurate than previous analyses at coarser spatial or temporal resolutions. The use of remote sensing data makes such simulations possible. BEPS is capable of integrating the effects of climate, vegetation, and soil on plant growth at a regional scale. BEPS and its parameterization scheme and products can be a basis for future studies of the carbon cycle in mid-high latitude ecosystems. [source] Explicit integration of bounding surface model for the analysis of earthquake soil liquefactionINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 15 2010Konstantinos I. Andrianopoulos Abstract This paper presents a new plasticity model developed for the simulation of monotonic and cyclic loading of non-cohesive soils and its implementation to the commercial finite-difference code FLAC, using its User-Defined-Model (UDM) capability. The new model incorporates the framework of Critical State Soil Mechanics, while it relies upon bounding surface plasticity with a vanished elastic region to simulate the non-linear soil response. Stress integration of constitutive relations is performed using a recently proposed explicit scheme with automatic error control and substepping, which so far has been employed in the literature only for constitutive models aiming at monotonic loading. The overall accuracy of this scheme is evaluated at element level by simulating cyclic loading along complex stress paths and by using iso-error maps for paths involving change of the Lode angle. The performance of the new constitutive model and its stress integration scheme in complex boundary value problems involving earthquake-induced liquefaction is evaluated, in terms of accuracy and computational cost, via a number of parametric analyses inspired by the successful simulation of the VELACS centrifuge Model Test No. 2 studying the lateral spreading response of a liquefied sand layer. Copyright © 2009 John Wiley & Sons, Ltd. [source] Implicit integration of a chemo-plastic constitutive model for partially saturated soilsINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 14 2008H. W. Zhang Abstract A chemo-plastic constitutive model for partially saturated soils is proposed in this paper based on the existing models developed in Hueckel (Int. J. Numer. Anal. Meth. Geomech. 1997; 21:43,72) and Gallipoli et al. (Geotechnique 2003; 53:123,135). The chemical softening effects due to the increase in contaminant mass concentration are considered based on Hueckel's chemo-plastic model. Gallipoli's model is used to simulate the effects of suction and degree of saturation on mechanical behavior of partially saturated porous materials. In order to implement the proposed model in a finite element code, a fully implicit backward-Euler integration algorithm is put forward. Numerical solutions for the tests at local level and the application of the algorithm to the real boundary value problem demonstrate the accuracy and convergence properties of the proposed integration scheme. Copyright © 2008 John Wiley & Sons, Ltd. [source] Finite element formulation and algorithms for unsaturated soils.INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 9 2003Part I: Theory Abstract This paper presents a complete finite-element treatment for unsaturated soil problems. A new formulation of general constitutive equations for unsaturated soils is first presented. In the incremental stress,strain equations, the suction or the pore water pressure is treated as a strain variable instead of a stress variable. The global governing equations are derived in terms of displacement and pore water pressure. The discretized governing equations are then solved using an adaptive time-stepping scheme which automatically adjusts the time-step size so that the integration error in the displacements and pore pressures lies close to a specified tolerance. The non-linearity caused by suction-dependent plastic yielding, suction-dependent degree of saturation, and saturation-dependent permeability is treated in a similar way to the elastoplasticity. An explicit stress integration scheme is used to solve the constitutive stress,strain equations at the Gauss point level. The elastoplastic stiffness matrix in the Euler solution is evaluated using the suction as well as the stresses and hardening parameters at the start of the subincrement, while the elastoplastic matrix in the modified Euler solution is evaluated using the suction at the end of the subincrement. In addition, when applying subincrementation, the same rate is applied to all strain components including the suction. Copyright © 2003 John Wiley & Sons, Ltd. [source] Numerical solution for consolidation and desiccation of soft soilsINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 2 2002Daniel T. C. Yao Abstract The consolidation and desiccation behaviour of soft soils can be described by two time-dependent non-linear partial differential equations using the finite strain theory. Analytical solutions do not exist for these governing equations. In this paper, we develop efficient numerical methods and software for finding the numerical solutions. We introduce a semi-implicit time integration scheme, and show numerically that our method converges. In addition, the numerical solution matches well with the experimental result. A boundary refinement method is also developed to improve the convergence and stability for the case of Neumann type boundary conditions. Interface governing equations are derived to maintain the continuity of consolidation and desiccation processes. This is useful because the soil column can undergo desiccation on top and consolidation on the bottom simultaneously. The numerical algorithms has been implemented into a computer program and the results have been verified with centrifuge test results conducted in our laboratory. Copyright © 2001 John Wiley & Sons, Ltd. [source] Analysis of adiabatic shear bands in heat-conducting elastothermoviscoplastic materials by the meshless local Bubnov,Galerkin methodINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 10 2009R. C. Batra Abstract Transient finite coupled thermomechanical simple shearing deformations of a block made of an elastothermoviscoplastic material that exhibits strain and strain-rate hardening, and thermal softening are studied by using the meshless local Bubnov,Galerkin method. A local nonlinear weak formulation and a semidiscrete formulation of the problem are derived. The prescribed velocity at the top and the bottom surfaces of the block is enforced by using a set of Lagrange multipliers. A homogeneous solution of the problem is perturbed by superimposing on it a temperature bump at the center of the block, and the resulting nonlinear initial-boundary-value problem is solved numerically. We have developed an integration scheme to numerically integrate the set of coupled nonlinear ordinary differential equations. The inhomogeneous deformations of the block are found to concentrate in a narrow region of intense plastic deformation usually called a shear band. For a material exhibiting enhanced thermal softening, it is shown that as the shear stress within the region of localization collapses, an unloading elastic shear wave emanates outward from the edges of the shear band. In the absence of an analytical solution, the computed results have been compared with those obtained by the finite element and the modified smoothed particle hydrodynamics methods. Copyright © 2008 John Wiley & Sons, Ltd. [source] Optimal time integration parameters for elastodynamic contact problemsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 6 2001A. Czekanski Abstract In this paper, we employ the generalized- , time integration scheme for treating elastodynamic contact problems. The criteria invoked for the selection of the four time integration parameters are motivated by our desire to ensure that the solution is unconditionally stable, second-order accurate, provides optimal high-frequency dissipation and preserves the energy and momentum transfer in dynamic rigid impact problems. New closed-form expressions for the time integration parameters are determined in terms of user-specified high-frequency spectral radius. The selected parameters help in avoiding the spurious high-frequency modes, which are present in the traditional Newmark method. Copyright © 2001 John Wiley & Sons, Ltd. [source] A new support integration scheme for the weakform in mesh-free methodsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 6 2010Yan Liu Abstract A new support integration technique is proposed, which is similar to those used in truly mesh-free methods. The contribution of this paper is to exploit the divergence-free condition for the support integrals to construct quadrature formulas that only require three integration points per particle in two dimensions. Numerical examples show that the proposed integration method can achieve results that agree with manufactured closed-form solutions. Copyright © 2009 John Wiley & Sons, Ltd. [source] Explicit coupled thermo-mechanical finite element model of steel solidificationINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 1 2009Seid Koric Abstract The explicit finite element method is applied in this work to simulate the coupled and highly non-linear thermo-mechanical phenomena that occur during steel solidification in continuous casting processes. Variable mass scaling is used to efficiently model these processes in their natural time scale using a Lagrangian formulation. An efficient and robust local,global viscoplastic integration scheme (Int. J. Numer. Meth. Engng 2006; 66:1955,1989) to solve the highly temperature- and rate-dependent elastic,viscoplastic constitutive equations of solidifying steel has been implemented into the commercial software ABAQUS/Explicit (ABAQUS User Manuals v6.7. Simulia Inc., 2007) using a VUMAT subroutine. The model is first verified with a known semi-analytical solution from Weiner and Boley (J. Mech. Phys. Solids 1963; 11:145,154). It is then applied to simulate temperature and stress development in solidifying shell sections in continuous casting molds using realistic temperature-dependent properties and including the effects of ferrostatic pressure, narrow face taper, and mechanical contact. Example simulations include a fully coupled thermo-mechanical analysis of a billet-casting and thin-slab casting in a funnel mold. Explicit temperature and stress results are compared with the results of an implicit formulation and computing times are benchmarked for different problem sizes and different numbers of processor cores. The explicit formulation exhibits significant advantages for this class of contact-solidification problems, especially with large domains on the latest parallel computing platforms. Copyright © 2008 John Wiley & Sons, Ltd. [source] Meshfree simulation of failure modes in thin cylinders subjected to combined loads of internal pressure and localized heatINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 8 2008Dong Qian Abstract This paper focuses on the non-linear responses in thin cylindrical structures subjected to combined mechanical and thermal loads. The coupling effects of mechanical deformation and temperature in the material are considered through the development of a thermo-elasto-viscoplastic constitutive model at finite strain. A meshfree Galerkin approach is used to discretize the weak forms of the energy and momentum equations. Due to the different time scales involved in thermal conduction and failure development, an explicit,implicit time integration scheme is developed to link the time scale differences between the two key mechanisms. We apply the developed approach to the analysis of the failure of cylindrical shell subjected to both heat sources and internal pressure. The numerical results show four different failure modes: dynamic fragmentation, single crack with branch, thermally induced cracks and cracks due to the combined effects of pressure and temperature. These results illustrate the important roles of thermal and mechanical loads with different time scales. Copyright © 2008 John Wiley & Sons, Ltd. [source] Smooth finite element methods: Convergence, accuracy and propertiesINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 2 2008Hung Nguyen-Xuan Abstract A stabilized conforming nodal integration finite element method based on strain smoothing stabilization is presented. The integration of the stiffness matrix is performed on the boundaries of the finite elements. A rigorous variational framework based on the Hu,Washizu assumed strain variational form is developed. We prove that solutions yielded by the proposed method are in a space bounded by the standard, finite element solution (infinite number of subcells) and a quasi-equilibrium finite element solution (a single subcell). We show elsewhere the equivalence of the one-subcell element with a quasi-equilibrium finite element, leading to a global a posteriori error estimate. We apply the method to compressible and incompressible linear elasticity problems. The method can always achieve higher accuracy and convergence rates than the standard finite element method, especially in the presence of incompressibility, singularities or distorted meshes, for a slightly smaller computational cost. It is shown numerically that the one-cell smoothed four-noded quadrilateral finite element has a convergence rate of 2.0 in the energy norm for problems with smooth solutions, which is remarkable. For problems with rough solutions, this element always converges faster than the standard finite element and is free of volumetric locking without any modification of integration scheme. Copyright © 2007 John Wiley & Sons, Ltd. [source] Numerical aspects of a real-time sub-structuring technique in structural dynamicsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 11 2007R. Sajeeb Abstract A time domain coupling technique, involving combined computational and experimental modelling, for vibration analysis of structures built-up of linear/non-linear substructures is developed. The study permits, in principle, one or more of the substructures to be modelled experimentally with measurements being made only on the interfacial degrees of freedom. The numerical and experimental substructures are allowed to communicate in real time within the present framework. The proposed strategy involves a two-stage scheme: the first is iterative in nature and is implemented at the initial stages of the solution in a non-real-time format; the second is non-iterative, employs an extrapolation scheme and proceeds in real time. Issues on time delays during communications between different substructures are discussed. An explicit integration procedure is shown to lead to solutions with high accuracy while retaining path sensitivity to initial conditions. The stability of the integration scheme is also discussed and a method for numerically dissipating the temporal growth of high-frequency errors is presented. For systems with non-linear substructures, the integration procedure is based on a multi-step transversal linearization method; and, to account for time delays, we employ a multi-step extrapolation scheme based on the reproducing kernel particle method. Numerical illustrations on a few low-dimensional vibrating structures are presented and these examples are fashioned after problems of seismic qualification testing of engineering structures using real-time substructure testing techniques. Copyright © 2007 John Wiley & Sons, Ltd. [source] Improved implementation and robustness study of the X-FEM for stress analysis around cracksINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 8 2005E. Béchet Abstract Numerical crack propagation schemes were augmented in an elegant manner by the X-FEM method. The use of special tip enrichment functions, as well as a discontinuous function along the sides of the crack allows one to do a complete crack analysis virtually without modifying the underlying mesh, which is of industrial interest, especially when a numerical model for crack propagation is desired. This paper improves the implementation of the X-FEM method for stress analysis around cracks in three ways. First, the enrichment strategy is revisited. The conventional approach uses a ,topological' enrichment (only the elements touching the front are enriched). We suggest a ,geometrical' enrichment in which a given domain size is enriched. The improvements obtained with this enrichment are discussed. Second, the conditioning of the X-FEM both for topological and geometrical enrichments is studied. A preconditioner is introduced so that ,off the shelf' iterative solver packages can be used and perform as well on X-FEM matrices as on standard FEM matrices. The preconditioner uses a local (nodal) Cholesky based decomposition. Third, the numerical integration scheme to build the X-FEM stiffness matrix is dramatically improved for tip enrichment functions by the use of an ad hoc integration scheme. A 2D benchmark problem is designed to show the improvements and the robustness. Copyright © 2005 John Wiley & Sons, Ltd. [source] Finite element formulation for modelling large deformations in elasto-viscoplastic polycrystalsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 14 2004Karel Matou Abstract Anisotropic, elasto-viscoplastic behaviour in polycrystalline materials is modelled using a new, updated Lagrangian formulation based on a three-field form of the Hu-Washizu variational principle to create a stable finite element method in the context of nearly incompressible behaviour. The meso-scale is characterized by a representative volume element, which contains grains governed by single crystal behaviour. A new, fully implicit, two-level, backward Euler integration scheme together with an efficient finite element formulation, including consistent linearization, is presented. The proposed finite element model is capable of predicting non-homogeneous meso-fields, which, for example, may impact subsequent recrystallization. Finally, simple deformations involving an aluminium alloy are considered in order to demonstrate the algorithm. Copyright © 2004 John Wiley & Sons, Ltd. [source] Meshless analysis of potential problems in three dimensions with the hybrid boundary node methodINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 9 2004Jianming Zhang Abstract Combining a modified functional with the moving least-squares (MLS) approximation, the hybrid boundary node method (Hybrid BNM) is a truly meshless, boundary-only method. The method may have advantages from the meshless local boundary integral equation (MLBIE) method and also the boundary node method (BNM). In fact, the Hybrid BNN requires only the discrete nodes located on the surface of the domain. The Hybrid BNM has been applied to solve 2D potential problems. In this paper, the Hybrid BNM is extended to solve potential problems in three dimensions. Formulations of the Hybrid BNM for 3D potential problems and the MLS approximation on a generic surface are developed. A general computer code of the Hybrid BNM is implemented in C++. The main drawback of the ,boundary layer effect' in the Hybrid BNM in the 2D case is circumvented by an adaptive face integration scheme. The parameters that influence the performance of this method are studied through three different geometries and known analytical fields. Numerical results for the solution of the 3D Laplace's equation show that high convergence rates with mesh refinement and high accuracy are achievable. Copyright © 2004 John Wiley & Sons, Ltd. [source] Singularity extraction technique for integral equation methods with higher order basis functions on plane triangles and tetrahedraINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 8 2003Seppo Järvenpää Abstract A numerical solution of integral equations typically requires calculation of integrals with singular kernels. The integration of singular terms can be considered either by purely numerical techniques, e.g. Duffy's method, polar co-ordinate transformation, or by singularity extraction. In the latter method the extracted singular integral is calculated in closed form and the remaining integral is calculated numerically. This method has been well established for linear and constant shape functions. In this paper we extend the method for polynomial shape functions of arbitrary order. We present recursive formulas by which we can extract any number of terms from the singular kernel defined by the fundamental solution of the Helmholtz equation, or its gradient, and integrate the extracted terms times a polynomial shape function in closed form over plane triangles or tetrahedra. The presented formulas generalize the singularity extraction technique for surface and volume integral equation methods with high-order basis functions. Numerical experiments show that the developed method leads to a more accurate and robust integration scheme, and in many cases also a faster method than, for example, Duffy's transformation. Copyright © 2003 John Wiley & Sons, Ltd. [source] On a new integration scheme for von-Mises plasticity with linear hardeningINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 10 2003Ferdinando Auricchio Abstract Limiting the discussion to an associative von-Mises plasticity model with linear kinematic and isotropic hardening, we compare the performance of the classical radial return map algorithm with a new integration scheme based on the computation of an integration factor. The numerical examples clearly show the improved accuracy of the new method. Copyright © 2003 John Wiley & Sons, Ltd. [source] A numerical integration scheme for special finite elements for the Helmholtz equationINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 4 2003Peter Bettess Abstract The theory for integrating the element matrices for rectangular, triangular and quadrilateral finite elements for the solution of the Helmholtz equation for very short waves is presented. A numerical integration scheme is developed. Samples of Maple and Fortran code for the evaluation of integration abscissæ and weights are made available. The results are compared with those obtained using large numbers of Gauss,Legendre integration points for a range of testing wave problems. The results demonstrate that the method gives correct results, which gives confidence in the procedures, and show that large savings in computation time can be achieved. Copyright © 2002 John Wiley & Sons, Ltd. [source] A control volume capacitance method for solidification modelling with mass transportINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 12 2002K. Davey Abstract Capacitance methods are popular methods used for solidification modelling. Unfortunately, they suffer from a major drawback in that energy is not correctly transported through elements and so provides a source of inaccuracy. This paper is concerned with the development and application of a control volume capacitance method (CVCM) to problems where mass transport and solidification are combined. The approach adopted is founded on theory that describes energy transfer through a control volume (CV) moving relative to the transporting mass. An equivalent governing partial differential equation is established, which is designed to be transformable into a finite element system that is commonly used to model transient heat-conduction problems. This approach circumvents the need to use the methods of Bubnov,Galerkin and Petrov,Galerkin and thus eliminates many of the stability problems associated with these approaches. An integration scheme is described that accurately caters for enthalpy fluxes generated by mass transport. Shrinkage effects are neglected in this paper as all the problems considered involve magnitudes of velocity that make this assumption reasonable. The CV approach is tested against known analytical solutions and is shown to be accurate, stable and computationally competitive. Copyright © 2002 John Wiley & Sons, Ltd. [source] Improved implicit integrators for transient impact problems,geometric admissibility within the conserving frameworkINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 2 2002T. A. Laursen Abstract The value of energy and momentum conserving algorithms has been well established for the analysis of highly non-linear systems, including those characterized by the nonsmooth non-linearities of an impact event. This work proposes an improved integration scheme for frictionless dynamic contact, seeking to preserve the stability properties of exact energy and momentum conservation without the heretofore unavoidable compromise of violating geometric admissibility as established by the contact constraints. The physically motivated introduction of a discrete contact velocity provides an algorithmic framework that ensures exact conservation locally while remaining independent of the choice of constraint treatment, thus making full conservation equally possible in conjunction with a penalty regularization as with an exact Lagrange multiplier enforcement. The discrete velocity effects are incorporated as a post-convergence update to the system velocities, and thus have no direct effect on the non-linear solution of the displacement equilibrium equation. The result is a robust implicit algorithmic treatment of dynamic frictionless impact, appropriate for large deformations and fully conservative for a range of geometric constraints. Copyright © 2001 John Wiley & Sons, Ltd. [source] Modelling of wetting and drying of shallow water using artificial porosityINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 11 2005B. van't Hof Abstract A new method for wetting and drying in two-dimensional shallow water flow models is proposed. The method is closely related to the artificial porosity method used by different authors in Boussinesq-type models, but is further extended for use in a semi-implicit (ADI-type) time integration scheme. The method is implemented in the simulation model WAQUA using general boundary fitted coordinates and is applied to realistic schematization for a portion of the river Meuse in the Netherlands. A large advantage of the artificial porosity method over traditionally used methods on the basis of ,screens' is a strongly reduced sensitivity of model results. Instead of blocking all water transport in grid points where the water level becomes small, as in screen-based methods, the flow is gradually closed off. Small changes in parameters such as the initial conditions or bottom topography therefore no longer lead to large changes in the model results. Copyright © 2005 John Wiley & Sons, Ltd. [source] Symplectic molecular dynamics integration using normal mode analysisINTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 1 2001anka Jane Abstract The split integration symplectic method (SISM) for molecular dynamics (MD) integration using normal mode analysis based on a factorization of the Liouville propagator is presented. This approach is quite distinct from others that use fractional-step methods, owing to the analytical treatment of high-frequency motions. The method involves splitting the total Hamiltonian of the system into a harmonic part and the remaining part. Then the Hamilton equations are solved using a second-order generalized leapfrog integration scheme in which the purely harmonic Hamiltonian (which represents the main contribution of the chemical bonds and angles) is treated analytically, i.e., independent of the step size of integration, by a normal mode analysis that is carried out only once, at the beginning of calculation. The whole integration step combines analytical evolution of the harmonic part of the Hamiltonian with a correction arising from the remaining part. The proposed algorithm requires only one force evaluation per integration step. The algorithm was tested on a simple system of linear chain molecules. Results demonstrate the method makes possible the integration of the MD equations over larger time steps without loss of stability while being economical in computer time. © 2001 John Wiley & Sons, Inc. Int J Quant Chem 84: 2,12, 2001 [source] An implementation of radiative transfer in the cosmological simulation code gadgetMONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY, Issue 3 2009Margarita Petkova ABSTRACT We present a novel numerical implementation of radiative transfer in the cosmological smoothed particle hydrodynamics (SPH) simulation code gadget. It is based on a fast, robust and photon-conserving integration scheme where the radiation transport problem is approximated in terms of moments of the transfer equation and by using a variable Eddington tensor as a closure relation, following the Optically Thin Variable Eddington Tensor suggestion of Gnedin & Abel. We derive a suitable anisotropic diffusion operator for use in the SPH discretization of the local photon transport, and we combine this with an implicit solver that guarantees robustness and photon conservation. This entails a matrix inversion problem of a huge, sparsely populated matrix that is distributed in memory in our parallel code. We solve this task iteratively with a conjugate gradient scheme. Finally, to model photon sink processes we consider ionization and recombination processes of hydrogen, which is represented with a chemical network that is evolved with an implicit time integration scheme. We present several tests of our implementation, including single and multiple sources in static uniform density fields with and without temperature evolution, shadowing by a dense clump and multiple sources in a static cosmological density field. All tests agree quite well with analytical computations or with predictions from other radiative transfer codes, except for shadowing. However, unlike most other radiative transfer codes presently in use for studying re-ionization, our new method can be used on-the-fly during dynamical cosmological simulation, allowing simultaneous treatments of galaxy formation and the re-ionization process of the Universe. [source] Modeling and numerical analysis of masonry structuresNUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 4 2007Mark Ainsworth Abstract We model masonry structures as elastodynamic systems assembled from a large number of elastic bodies (bricks or stone-blocks) in unilateral, frictional contact. The problem is formulated as a quasi-variational inequality and discretised using piecewise polynomial finite elements in conjunction with an energy consistent time integration scheme. At each time-step, the quasi-variational inequality is reformulated as a nonlinear complementarity problem. An iterative splitting of the contact problem into normal contact and frictional contact, together with a primal-dual active-set method is employed to calculate deformations and openings in the model structures. Numerical results are presented to illustrate the efficiency of the resulting approach in predicting the mechanical behaviour of a bidimensional arch-ring made of bricks, deformed due to body forces and surface tractions. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 23: 798,816, 2007 [source] One fragmentation procedure for brittle material crackingPROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2006S. H. Reese Realistic modeling of 3D fragmentation procedures with minimal incorporation of restrictions to the crack path is still a challenge in modern computational engineering simulations. The presented approach is used to model failure and cracking in concrete structures, applying an explicit finite element integration scheme. Within this model the Strong Discontinuity Approach (SDA) is used to handle the failure process until the material is fully damaged. At stage an adaptive refinement technique is incorporated in ordner to introduce real cracks which are suitable for DEM / FEM coupling or contact formulations. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Modelling and process development for gaseous separation with silicone-coated polymeric membranesTHE CANADIAN JOURNAL OF CHEMICAL ENGINEERING, Issue 2 2008Xin Jiang Abstract This paper proposes a permeance equation for vapour,permanent gas mixtures in a silicone-coated polymeric membrane. The equation was derived from the Arrhenius relationship by combining an apparent activation energy and interaction parameter. Accurate values of transmembrane flux were obtained by incorporating this proposed equation, which was dependent on temperature and feed composition. The equation parameters were correlated with the experimental data of eight mixtures consisting of hydrocarbons such as ethylene, ethane, propylene and propane with nitrogen covering a broad range of temperature and concentration. A numerical integration scheme was used for developing a crossflow model utilizing the above equation, which allowed the estimation of product properties including the membrane plasticization cases. The study also reports examples of implementation of this approach in potential industrial applications for the recovery of ethylene and propylene from nitrogen. Cet article propose une équation de permeance pour les mélanges vapeur,permanents de gaz dans une membrane polymère enduite de silicone. L'équation a été dérivée du rapport d'Arrhenius en combinant une énergie d'activation et un paramètre apparents d'interaction. Des valeurs précises du flux de transmembrane ont été obtenues en incorporant cette équation proposée, qui dépendait de la composition en température et en alimentation. Les paramètres de l'équation ont été corrélés avec les données expérimentales de huit mélanges se composant des hydrocarbures tels que l'éthylène, l'éthane, le propylène et le propane avec de l'azote couvrant une large gamme de la température et de concentration. Un arrangement numérique d'intégration a été employé pour développer un modèle de croisement de flux utilisant l'équation ci-dessus, qui a permis l'évaluation des propriétés de produit comprenant les cas de plasticization de membrane. L'étude indique également des exemples d'exécution de cette approche dans des demandes industrielles potentielles de rétablissement d'éthylène et de propylène de l'azote. [source] Spectral-element simulations of wave propagation in porous mediaGEOPHYSICAL JOURNAL INTERNATIONAL, Issue 1 2008Christina Morency SUMMARY We present a derivation of the equations describing wave propagation in porous media based upon an averaging technique which accommodates the transition from the microscopic to the macroscopic scale. We demonstrate that the governing macroscopic equations determined by Biot remain valid for media with gradients in porosity. In such media, the well-known expression for the change in porosity, or the change in the fluid content of the pores, acquires two extra terms involving the porosity gradient. One fundamental result of Biot's theory is the prediction of a second compressional wave, often referred to as ,type II' or ,Biot's slow compressional wave', in addition to the classical fast compressional and shear waves. We present a numerical implementation of the Biot equations for 2-D problems based upon the spectral-element method (SEM) that clearly illustrates the existence of these three types of waves as well as their interactions at discontinuities. As in the elastic and acoustic cases, poroelastic wave propagation based upon the SEM involves a diagonal mass matrix, which leads to explicit time integration schemes that are well suited to simulations on parallel computers. Effects associated with physical dispersion and attenuation and frequency-dependent viscous resistance are accommodated based upon a memory variable approach. We perform various benchmarks involving poroelastic wave propagation and acoustic,poroelastic and poroelastic,poroelastic discontinuities, and we discuss the boundary conditions used to deal with these discontinuities based upon domain decomposition. We show potential applications of the method related to wave propagation in compacted sediments, as one encounters in the petroleum industry, and to detect the seismic signature of buried landmines and unexploded ordnance. [source] | ||||||||||||||||