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Zdzis&#x;aw Wi&#x;ckowski Sung‐Kie Youn Jeoung‐Heum Yeon 《International journal for numerical methods in engineering》1999,45(9):1203-1225
The problem of flow of a granular material during the process of discharging a silo is considered in the present paper. The mechanical behaviour of the material is described by the use of the model of the elastic–plastic solid with the Drucker–Prager yield condition and the non‐associative flow rule. The phenomenon of friction between the stored material and the silo walls is taken into account—the Coulomb model of friction is used in the analysis. The problem is analysed by means of the particle‐in‐cell method—a variant of the finite element method which enables to solve the pertinent equations of motion on an arbitrary computational mesh and trace state variables at points of the body chosen independently of the mesh. The method can be regarded as an arbitrary Lagrangian–Eulerian formulation of the finite element method, and overcomes the main drawback of the updated Lagrangian formulation of FEM related to mesh distortion. The entire process of discharging a silo can be analysed by this approach. The dynamic problem is solved by the use of the explicit time‐integration scheme. Several numerical examples are included. The plane strain and axisymmetric problems are solved for silos with flat bottoms and conical hoppers. Some results are compared with experimental ones. Copyright © 1999 John Wiley & Sons, Ltd. 相似文献
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Carsten Carstensen Kerstin Weinberg 《International journal for numerical methods in engineering》2003,56(15):2313-2330
Adaptive algorithms are important tools for efficient finite‐element mesh design. In this paper, an error controlled adaptive mesh‐refining algorithm is proposed for a non‐conforming low‐order finite‐element method for the Reissner–Mindlin plate model. The algorithm is controlled by a reliable and efficient residual‐based a posteriori error estimate, which is robust with respect to the plate's thickness. Numerical evidence for this and the efficiency of the new algorithm is provided in the sense that non‐optimal convergence rates are optimally improved in our numerical experiments. Copyright © 2003 John Wiley & Sons, Ltd. 相似文献
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Alessandro Franci Eugenio Oñate Josep Maria Carbonell 《International journal for numerical methods in engineering》2016,107(11):970-990
We present three velocity‐based updated Lagrangian formulations for standard and quasi‐incompressible hypoelastic‐plastic solids. Three low‐order finite elements are derived and tested for non‐linear solid mechanics problems. The so‐called V‐element is based on a standard velocity approach, while a mixed velocity–pressure formulation is used for the VP and the VPS elements. The two‐field problem is solved via a two‐step Gauss–Seidel partitioned iterative scheme. First, the momentum equations are solved in terms of velocity increments, as for the V‐element. Then, the constitutive relation for the pressure is solved using the updated velocities obtained at the previous step. For the VPS‐element, the formulation is stabilized using the finite calculus method in order to solve problems involving quasi‐incompressible materials. All the solid elements are validated by solving two‐dimensional and three‐dimensional benchmark problems in statics as in dynamics. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
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Josef Synka Alexander Kainz Robert Maringer Andreas Obereder 《International journal for numerical methods in engineering》2005,62(5):616-638
A finite element code for steady‐state hot rolling processes of rigid–visco‐plastic materials under plane–strain conditions was developed in a mixed Eulerian–Lagrangian framework. This special set up allows for a direct calculation of the local deformations occurring at the free surfaces outside the contact region between the strip and the work roll. It further simplifies the implementation of displacement boundary conditions, such as the impenetrability condition. When applied to different practical hot rolling situations, ranging from thick slab to ultra‐thin strip rolling, the velocity–displacement based model (briefly denoted as vu‐model) in this mixed Eulerian–Lagrangian reference system proves to be a robust and efficient method. The vu‐model is validated against a solely velocity‐based model (vv‐model) and against elementary methods based on the Kármán–Siebel and Orowan differential equations. The latter methods, when calibrated, are known to be in line with experimental results for homogeneous deformation cases. For a massive deformation it is further validated against the commercial finite‐element software package Abaqus/Explicit. It is shown that the results obtained with the vu‐model are in excellent agreement with the predictions of the vv‐model and that the vu‐model is even more robust than its vv‐counterpart. Throughout the study we assumed a rigid cylindrical work roll; only for the homogeneous test case, we also investigated the effect of an elastically deformable work roll within the frame of the Jortner Green's function method. The new modelling approach combines the advantages of conventional Eulerian and Lagrangian modelling concepts and can be extended to three dimensions in a straightforward manner. Copyright © 2004 John Wiley & Sons, Ltd. 相似文献
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M. de Buhan P. Frey 《International journal for numerical methods in engineering》2011,86(13):1544-1557
In this paper, we consider a non‐linear viscoelastic model with internal variable, thoroughly analyzed by Le Tallecit et al. (Comput. Methods Appl. Mech. Engrg 1993; 109 :233–258). Our aim is to study here the implementation in three dimensions of a generalized version of this model. Computational results will be analyzed to validate our model on toy problems without geometric complexity, for which pseudo‐analytical solutions are known. At the end, we present a three‐dimensional numerical simulation on a mechanical device. Copyright © 2011 John Wiley & Sons, Ltd. 相似文献
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Q. V. Bui 《International journal for numerical methods in engineering》2007,70(2):127-162
In the context of the time‐finite element method, algorithmic stresses, which enable the conservation of energy, are designed for temporal integrators derived from the midpoint and trapezoidal schemes. This is achieved through an appropriate modification of the standard midpoint and trapezoidal quadrature rules used for the numerical integration of time integrals. Either scalar scaling or vectorial adjustments can be employed for the modification, and well‐designed simple tests allow to investigate the quality of these different strategies of energy‐conserving enforcements. Numerical examples with semi‐discrete elasto‐dynamics problems are presented to show the superior stability of energy‐conserving schemes. Copyright © 2006 John Wiley & Sons, Ltd. 相似文献
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Adrian E. Croucher Michael J. O'Sullivan 《International journal for numerical methods in engineering》2005,62(5):682-699
Standard Eulerian treatment of source terms in Eulerian–Lagrangian numerical simulations results in poor performance at higher Courant numbers. To regain the customary high accuracy of Eulerian–Lagrangian methods under these conditions, a Lagrangian treatment of source terms is needed. It is also important to include the effects of fluid sources as well as contaminant sources. A new Lagrangian source formulation is presented, which has been implemented in a finite element simulator for contaminant transport in rivers and estuaries. Test problems demonstrate the high accuracy of the technique under a range of conditions, and its applicability to general multi‐dimensional problems and unstructured grids. Copyright © 2004 John Wiley & Sons, Ltd. 相似文献
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Saeid Abbasbandy 《International journal for numerical methods in engineering》2007,70(7):876-881
In this paper, numerical solution of non‐linear Klein–Gordon equations with power law non‐linearities are obtained by the new application of He's variational iteration method. Numerical illustrations that include non‐linear Klein–Gordon equations and non‐linear partial differential equations are investigated to show the pertinent features of the technique. Copyright © 2006 John Wiley & Sons, Ltd. 相似文献
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Using a Representative volume element (RVE) to represent the microstructure of periodic composite materials, this paper develops a non‐linear numerical technique to calculate the macroscopic shakedown domains of composites subjected to cyclic loads. The shakedown analysis is performed using homogenization theory and the displacement‐based finite element method. With the aid of homogenization theory, the classical kinematic shakedown theorem is generalized to incorporate the microstructure of composites. Using an associated flow rule, the plastic dissipation power for an ellipsoid yield criterion is expressed in terms of the kinematically admissible velocity. By means of non‐linear mathematical programming techniques, a finite element formulation of kinematic shakedown analysis is then developed leading to a non‐linear mathematical programming problem subject to only a small number of equality constraints. The objective function corresponds to the plastic dissipation power which is to be minimized and an upper bound to the shakedown load of a composite is then obtained. An effective, direct iterative algorithm is proposed to solve the non‐linear programming problem. The effectiveness and efficiency of the proposed numerical method have been validated by several numerical examples. This can serve as a useful numerical tool for developing engineering design methods involving composite materials. Copyright © 2005 John Wiley & Sons, Ltd. 相似文献
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L. Noels 《International journal for numerical methods in engineering》2009,78(3):296-323
Discontinuous Galerkin (DG) methods provide a means of weakly enforcing the continuity of the unknown‐field derivatives and have particular appeal in problems involving high‐order derivatives. This feature has previously been successfully exploited (Comput. Methods Appl. Mech. Eng. 2008; 197 :2901–2929) to develop a formulation of linear Kirchhoff–Love shells considering only the membrane and bending responses. In this proposed one‐field method—the displacements are the only unknowns, while the displacement field is continuous, the continuity in the displacement derivative between two elements is weakly enforced by recourse to a DG formulation. It is the purpose of the present paper to extend this formulation to finite deformations and non‐linear elastic behaviors. While the initial linear formulation was relying on the direct linear computation of the effective membrane stress and effective bending couple‐stress from the displacement field at the mid‐surface of the shell, the non‐linear formulation considered implies the evaluation of the general stress tensor across the shell thickness, leading to a reformulation of the internal forces of the shell. Nevertheless, since the interface terms resulting from the discontinuous Galerkin method involve only the resultant couple‐stress at the edges of the shells, the extension to non‐linear deformations is straightforward. Copyright © 2008 John Wiley & Sons, Ltd. 相似文献
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H. R. Ronagh M. A. Bradford 《International journal for numerical methods in engineering》1999,46(4):535-552
The paper presents a means of determining the non‐linear stiffness matrices from expressions for the first and second variation of the Total Potential of a thin‐walled open section finite element that lead to non‐linear stiffness equations. These non‐linear equations can be solved for moderate to large displacements. The variations of the Total Potential have been developed elsewhere by the authors, and their contribution to the various non‐linear matrices is stated herein. It is shown that the method of solution of the non‐linear stiffness matrices is problem dependent. The finite element procedure is used to study non‐linear torsion that illustrates torsional hardening, and the Newton–Raphson method is deployed for this study. However, it is shown that this solution strategy is unsuitable for the second example, namely that of the post‐buckling response of a cantilever, and a direct iteration method is described. The good agreement for both of these problems with the work of independent researchers validates the non‐linear finite element method of analysis. Copyright © 1999 John Wiley & Sons, Ltd. 相似文献
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Pedro Ribeiro 《International journal for numerical methods in engineering》2003,56(5):715-738
A p‐version, hierarchical finite element for doubly curved, moderately thick, isotropic shallow shells is derived and geometrically non‐linear free vibrations of panels with rectangular planform are investigated. The geometrical non‐linearity is due to large displacements, and the effects of the rotatory inertia and transverse shear are considered. The time domain equations of motion are obtained by applying the principle of virtual work and the d'Alembert's principle. These equations are mapped to the frequency domain by the harmonic balance method, and are finally solved by a predictor–corrector method. The convergence properties of the element proposed and the influence of several parameters on the dynamic response are studied. These parameters are the shell's thickness, the width‐to‐length ratio, the curvature‐to‐width ratio and the ratio between curvature radii. The first and higher order modes are analysed. Some results are compared with results published or calculated using a commercial finite element package. It is demonstrated that with the proposed element low‐dimensional, accurate models are obtained. Copyright © 2002 John Wiley & Sons, Ltd. 相似文献
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Pompiliu Donescu Lawrence N. Virgin 《International journal for numerical methods in engineering》2001,51(4):379-412
In this work, a new comprehensive method has been developed which enables the solution of large, non‐linear motions of rigid bodies in a fluid with a free surface. The application of the modern Eulerian–Lagrangian approach has been translated into an implicit time‐integration formulation, a development which enables the use of larger time steps (where accuracy requirements allow it). Novel features of this project include: (1) an implicit formulation of the rigid‐body motion in a fluid with a free surface valid for both two or three dimensions and several moving bodies; (2) a complete formulation and solution of the initial conditions; (3) a fully consistent (exact) linearization for free surface flows valid for any boundary elements such that optimal convergence properties are obtained when using a Newton–Raphson solver. The proposed framework has been completed with details on implementation issues referring mainly to the computation of the complete initial conditions and the consistent linearization of the formulation for free surface flows. The second part of the paper demonstrates the mathematical and numerical formulation through numerical results simulating large free surface flows and non‐linear fluid structure interaction. The implicit formulation using a fully consistent linearization based on the boundary element method and the generalized trapezoidal rule has been applied to the solution of free surface flows for the evolution of a triangular wave, the generation of tsunamis and the propagation of a wave up to overturning. Fluid–structure interaction examples include the free and forced motion of a circular cylinder and the sway, heave and roll motion of a U‐shaped body in a tank with a flap wave generator. The presented examples demonstrate the applicability and performance of the implicit scheme with consistent linearization. Copyright © 2001 John Wiley & Sons. Ltd. 相似文献
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Frdric Boyer Dominique Primault 《International journal for numerical methods in engineering》2004,59(5):669-702
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. 相似文献
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K. Wisniewski P. Kowalczyk E. Turska 《International journal for numerical methods in engineering》2003,57(2):271-300
This paper concerns design sensitivity analysis (DSA) for an elasto–plastic material, with material parameters depending on, or serving as, design variables. The considered constitutive model is Huber–Mises deviatoric plasticity with non‐linear isotropic/kinematic hardening, one which is applicable to metals. The standard radial return algorithm for linear hardening is generalized to account for non‐linear hardening functions. Two generalizations are presented; in both the non‐linearity is treated iteratively, but the iteration loop contains either a scalar equation or a group of tensorial equations. It is proven that the second formulation, which is the one used in some parallel codes, can be equivalently brought to a scalar form, more suitable for design differentiation. The design derivatives of both the algorithms are given explicitly, enabling thus calculation of the ‘explicit’ design derivative of stresses entering the global sensitivity equation. The paper addresses several issues related to the implementation and testing of the DSA module; among them the concept of verification tests, both outside and inside a FE code, as well as the data handling implied by the algorithm. The numerical tests, which are used for verification of the DSA module, are described. They shed light on (a) the accuracy of the design derivatives, by comparison with finite difference computations and (b) the effect of the finite element formulation on the design derivatives for an isochoric plastic flow. Copyright © 2003 John Wiley & Sons, Ltd. 相似文献
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M. I. Asensio L. Ferragut 《International journal for numerical methods in engineering》2002,54(1):137-157
The 2‐D simplified wildland fire model presented here is based on conservation laws and takes into account radiation as the dominant thermal transfer mechanism, as well as convection, which represents the effect of the wind and the slope. The non‐dimensional equations are obtained using the Frank–Kamenestkii change of variables. The existence of weak solutions of the non‐linear reaction diffusion problem obtained is established as a particular case of more general existence results using a compactness method. The uniqueness of the weak solution is shown for a given initial data and fixed parameters of the equations. The approximate solution is obtained using a mixed finite element method. This preserves the continuity of the flux through the inter‐element boundaries and allows to represent high gradients in the solution. Semi‐discrete error estimation is presented. The convective term is solved by a splitting technique using Godunov's method. The numerical examples show the efficiency of the algorithm in capturing the fire front, even for critical values of the parameters. Copyright © 2002 John Wiley & Sons, Ltd. 相似文献
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Hyun‐Gyu Kim 《International journal for numerical methods in engineering》2003,56(15):2279-2312
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. 相似文献
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Kristian Krabbenhoft Lars Damkilde 《International journal for numerical methods in engineering》2003,56(2):165-184
The non‐linear programming problem associated with the discrete lower bound limit analysis problem is treated by means of an algorithm where the need to linearize the yield criteria is avoided. The algorithm is an interior point method and is completely general in the sense that no particular finite element discretization or yield criterion is required. As with interior point methods for linear programming the number of iterations is affected only little by the problem size. Some practical implementation issues are discussed with reference to the special structure of the common lower bound load optimization problem, and finally the efficiency and accuracy of the method is demonstrated by means of examples of plate and slab structures obeying different non‐linear yield criteria. Copyright © 2002 John Wiley & Sons, Ltd. 相似文献