共查询到20条相似文献，搜索用时 15 毫秒
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A high‐order discontinuous Galerkin method for calculations of complex dispersion relations of two‐dimensional photonic crystals is presented. The medium is characterized by a complex‐valued permittivity and we relate for this absorptive system the spectral parameter to the time frequency. We transform the non‐linear eigenvalue problem for a Lorentz material in air into a non‐Hermitian linear eigenvalue problem and uses a Krylov space method to compute approximate eigenvalues. Moreover, we study the impact of the penalty term numerically and illustrate the high convergence rate of the method. Copyright © 2010 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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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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Pedro Ribeiro 《International journal for numerical methods in engineering》2004,61(15):2696-2715
A p‐version, hierarchical finite element for curved, moderately thick, elastic and isotropic beams is introduced. The convergence properties of the element are analysed and some results are compared with results published elsewhere or calculated using a commercial finite element package. It is verified that, with the proposed element, shear locking does not affect the computation of the natural frequencies and that low dimensional, accurate models are obtainable. Geometrically non‐linear vibrations due to finite deformations, which occur for harmonic excitations with frequencies close to the first three natural frequencies of vibration, are investigated using Newmark's method. The influence of the thickness, longitudinal inertia and curvature radius on the dynamic behaviour of curved beams are studied. Copyright © 2004 John Wiley & Sons, Ltd. 相似文献
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Z. Yue D. H. Robbins Jr 《International journal for numerical methods in engineering》2007,72(9):1063-1094
An s‐adaptive finite element procedure is developed for the transient analysis of 2‐D solid mechanics problems with material non‐linearity due to progressive damage. The resulting adaptive method simultaneously estimates and controls both the spatial error and temporal error within user‐specified tolerances. The spatial error is quantified by the Zienkiewicz–Zhu error estimator and computed via superconvergent patch recovery, while the estimation of temporal error is based on the assumption of a linearly varying third‐order time derivatives of the displacement field in conjunction with direct numerical time integration. The distinguishing characteristic of the s‐adaptive procedure is the use of finite element mesh superposition (s‐refinement) to provide spatial adaptivity. Mesh superposition proves to be particularly advantageous in computationally demanding non‐linear transient problems since it is faster, simpler and more efficient than traditional h‐refinement schemes. Numerical examples are provided to demonstrate the performance characteristics of the s‐adaptive method for quasi‐static and transient problems with material non‐linearity. Copyright © 2007 John Wiley & Sons, Ltd. 相似文献
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I. Romero F. Armero 《International journal for numerical methods in engineering》2002,54(7):1043-1086
This paper presents a new family of time‐stepping algorithms for the integration of the dynamics of non‐linear shells. We consider the geometrically exact shell theory involving an inextensible director field (the so‐called five‐parameter shell model). The main characteristic of this model is the presence of the group of finite rotations in the configuration manifold describing the deformation of the solid. In this context, we develop time‐stepping algorithms whose discrete solutions exhibit the same conservation laws of linear and angular momenta as the underlying physical system, and allow the introduction of a controllable non‐negative energy dissipation to handle the high numerical stiffness characteristic of these problems. A series of algorithmic parameters for the different components of the deformation of the shell (i.e. membrane, bending and transverse shear) fully control this numerical dissipation, recovering existing energy‐momentum schemes as a particular choice of these algorithmic parameters. We present rigorous proofs of the numerical properties of the resulting algorithms in the full non‐linear range. Furthermore, it is argued that the numerical dissipation is introduced in the high‐frequency range by considering the proposed algorithm in the context of a linear problem. The finite element implementation of the resulting methods is described in detail as well as considered in the final arguments proving the aforementioned conservation/dissipation properties. We present several representative numerical simulations illustrating the performance of the newly proposed methods. The robustness gained over existing methods in these stiff problems is confirmed in particular. Copyright © 2002 John Wiley & Sons, Ltd. 相似文献
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Gye‐Hee Lee Heung‐Jin Chung Chang‐Koon Choi 《International journal for numerical methods in engineering》2003,56(3):331-350
In this paper, an adaptive analysis of crack propagation based on the error estimation by the element‐free Galerkin (EFG) method is presented. The adaptivity analysis in quasi‐static crack propagation is achieved by adding and/or removing the nodes along the background integration cells, those are refined or recovered according to the estimated errors. These errors are obtained basically by calculating the difference between the values of the projected stresses and original EFG stresses. To evaluate the performance of the proposed adaptive procedure, the crack propagation behaviour is investigated for several examples. The results of these examples show the efficiency and accuracy of the proposed scheme in crack propagation analysis. Copyright © 2002 John Wiley & Sons, Ltd. 相似文献
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S. A. Hosseini Kordkheili R. Naghdabadi 《International journal for numerical methods in engineering》2007,72(8):964-986
A finite element formulation governing the geometrically non‐linear thermoelastic behaviour of plates and shells made of functionally graded materials is derived in this paper using the updated Lagrangian approach. Derivation of the formulation is based on rewriting the Green–Lagrange strain as well as the 2nd Piola–Kirchhoff stress as two second‐order functions in terms of a through‐the‐thickness parameter. Material properties are assumed to vary through the thickness according to the commonly used power law distribution of the volume fraction of the constituents. Within a non‐linear finite element analysis framework, the main focus of the paper is the proposal of a formulation to account for non‐linear stress distribution in FG plates and shells, particularly, near the inner and outer surfaces for small and large values of the grading index parameter. The non‐linear heat transfer equation is also solved for thermal distribution through the thickness by the Rayleigh–Ritz method. Advantages of the proposed approach are assessed and comparisons with available solutions are presented. Copyright © 2007 John Wiley & Sons, Ltd. 相似文献
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L. Noels R. Radovitzky 《International journal for numerical methods in engineering》2008,74(9):1393-1420
An explicit‐dynamics spatially discontinuous Galerkin (DG) formulation for non‐linear solid dynamics is proposed and implemented for parallel computation. DG methods have particular appeal in problems involving complex material response, e.g. non‐local behavior and failure, as, even in the presence of discontinuities, they provide a rigorous means of ensuring both consistency and stability. In the proposed method, these are guaranteed: the former by the use of average numerical fluxes and the latter by the introduction of appropriate quadratic terms in the weak formulation. The semi‐discrete system of ordinary differential equations is integrated in time using a conventional second‐order central‐difference explicit scheme. A stability criterion for the time integration algorithm, accounting for the influence of the DG discretization stability, is derived for the equivalent linearized system. This approach naturally lends itself to efficient parallel implementation. The resulting DG computational framework is implemented in three dimensions via specialized interface elements. The versatility, robustness and scalability of the overall computational approach are all demonstrated in problems involving stress‐wave propagation and large plastic deformations. Copyright © 2007 John Wiley & Sons, Ltd. 相似文献
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Stefano de Miranda Massimo Mancuso Francesco Ubertini 《International journal for numerical methods in engineering》2010,83(3):323-346
In this paper a new time discontinuous Galerkin (TDG) formulation for non‐linear elastodynamics is presented. The new formulation embeds an energy correction which ensures truly energy decaying, thus allowing to achieve unconditional stability that, as shown in the paper, is not guaranteed by the classical TDG formulation. The resulting method is simple and easily implementable into existing finite element codes. Moreover, it inherits the desirable higher‐order accuracy and high‐frequency dissipation properties of the classical formulation. Numerical results illustrate the very good performance of the proposed formulation. Copyright © 2010 John Wiley & Sons, Ltd. 相似文献
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Jari Mäkinen 《International journal for numerical methods in engineering》2007,70(9):1009-1048
In this paper, we introduce a new Reissner's geometrically exact beam element, which is based on a total Lagrangian updating procedure. The element has the rotation vector as the dependent variable and the singularity problems at the rotation angle 2π and its multiples are passed by the change of parametrization on the rotation manifold. The beam formulation has several benefits such as all the unknown vectors belong to the same tangential vector space, no need for secondary storage variables, the path‐independence in the static case, any standard time‐integration algorithm may be used, and the symmetric stiffness. Copyright © 2006 John Wiley & Sons, Ltd. 相似文献
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This paper presents an enriched meshless method for fracture analysis of cracks in homogeneous, isotropic, non‐linear‐elastic, two‐dimensional solids, subject to mode‐I loading conditions. The method involves an element‐free Galerkin formulation and two new enriched basis functions (Types I and II) to capture the Hutchinson–Rice–Rosengren singularity field in non‐linear fracture mechanics. The Type I enriched basis function can be viewed as a generalized enriched basis function, which degenerates to the linear‐elastic basis function when the material hardening exponent is unity. The Type II enriched basis function entails further improvements of the Type I basis function by adding trigonometric functions. Four numerical examples are presented to illustrate the proposed method. The boundary layer analysis indicates that the crack‐tip field predicted by using the proposed basis functions matches with the theoretical solution very well in the whole region considered, whether for the near‐tip asymptotic field or for the far‐tip elastic field. Numerical analyses of standard fracture specimens by the proposed meshless method also yield accurate estimates of the J‐integral for the applied load intensities and material properties considered. Also, the crack‐mouth opening displacement evaluated by the proposed meshless method is in good agreement with finite element results. Furthermore, the meshless results show excellent agreement with the experimental measurements, indicating that the new basis functions are also capable of capturing elastic–plastic deformations at a stress concentration effectively. Copyright © 2003 John Wiley & Sons, Ltd. 相似文献
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Mohamed S. Ebeida Roger L. Davis Roland W. Freund 《International journal for numerical methods in engineering》2010,84(3):305-329
This paper describes a new fast hybrid adaptive grid generation technique for arbitrary two‐dimensional domains. This technique is based on a Cartesian background grid with square elements and quadtree decomposition. A new algorithm is introduced for the distribution of boundary points based on the curvature of the domain boundaries. The quadtree decomposition is governed either by the distribution of the boundary points or by a size function when a solution‐based adaptive grid is desired. The resulting grid is quaddominant and ready for the application of finite element, multi‐grid, or line‐relaxation methods. All the internal angles in the final grid have a lower bound of 45° and an upper bound of 135°. Although our main interest is in grid generation for unsteady flow simulations, the technique presented in this paper can be employed in many other fields. Several application examples are provided to illustrate the main features of this new approach. Copyright © 2010 John Wiley & Sons, Ltd. 相似文献
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Anthony Gravouil Alain Combescure 《International journal for numerical methods in engineering》2001,50(1):199-225
We present a method with domain decomposition to solve time‐dependent non‐linear problems. This method enables arbitrary numeric schemes of the Newmark family to be coupled with different time steps in each subdomain: this coupling is achieved by prescribing continuity of velocities at the interface. We are more specifically interested in the coupling of implicit/explicit numeric schemes taking into account material and geometric non‐linearities. The interfaces are modelled using a dual Schur formulation where the Lagrange multipliers represent the interfacial forces. Unlike the continuous formulation, the discretized formulation of the dynamic problem is unable to verify simultaneously the continuity of displacements, velocities and accelerations at the interfaces. We show that, within the framework of the Newmark family of numeric schemes, continuity of velocities at the interfaces enables the definition of an algorithm which is stable for all cases envisaged. To prove this stability, we use an energy method, i.e. a global method over the whole time interval, in order to verify the algorithms properties. Then, we propose to extend this to non‐linear situations in the following cases: implicit linear/explicit non‐linear, explicit non‐linear/explicit non‐linear and implicit non‐linear/explicit non‐linear. Finally, we present some examples showing the feasibility of the method. Copyright © 2001 John Wiley & Sons, Ltd. 相似文献
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Abstract This paper presents the utilization of boundary element method (BEM) to analyze the elasto‐plastic deformation of upsetting problems. Method of successive elastic solutions is used in the nonlinear analysis; both the linear strain hardening and the power law relation are used as constitutive equations of the material. For the later model the slope of strain hardening at each step is modified to a more correct prediction to make the deformation step larger and to obtain better convergence. The result may verify the stress‐strain curve as it does, and verify the similar pattern of the plastic zone propagation as Roll's result by finite element method. It is shown that various frictional conditions and width‐height ratios of the workpiece also influence the propagation behavior of plastic zones. 相似文献
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This paper presents the formulation and a partial analysis of a class of discontinuous Galerkin methods for quasistatic non‐linear elasticity problems. These methods are endowed with several salient features. The equations that define the numerical scheme are the Euler–Lagrange equations of a one‐field variational principle, a trait that provides an elegant and simple derivation of the method. In consonance with general discontinuous Galerkin formulations, it is possible within this framework to choose different numerical fluxes. Numerical evidence suggests the absence of locking at near‐incompressible conditions in the finite deformations regime when piecewise linear elements are adopted. Finally, a conceivable surprising characteristic is that, as demonstrated with numerical examples, these methods provide a given accuracy level for a comparable, and often lower, computational cost than conforming formulations. Stabilization is occasionally needed for discontinuous Galerkin methods in linear elliptic problems. In this paper we propose a sufficient condition for the stability of each linearized non‐linear elastic problem that naturally includes material and geometric parameters; the latter needed to account for buckling. We then prove that when a similar condition is satisfied by the discrete problem, the method provides stable linearized deformed configurations upon the addition of a standard stabilization term. We conclude by discussing the complexity of the implementation, and propose a computationally efficient approach that avoids looping over both elements and element faces. Several numerical examples are then presented in two and three dimensions that illustrate the performance of a selected discontinuous Galerkin method within the class. Copyright © 2006 John Wiley & Sons, Ltd. 相似文献
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A. Portela 《International journal for numerical methods in engineering》2011,86(12):1457-1480
This paper is concerned with the effective numerical implementation of the adaptive dual boundary‐element method (DBEM), for two‐dimensional potential problems. Two boundary integral equations, which are the potential and the flux equations, are applied for collocation along regular and degenerate boundaries, leading always to a single‐region analysis. Taking advantage on the use of non‐conforming parametric boundary‐elements, the method introduces a simple error estimator, based on the discontinuity of the solution across the boundaries between adjacent elements and implements the p, h and mixed versions of the adaptive mesh refinement. Examples of several geometries, which include degenerate boundaries, are analyzed with this new formulation to solve regular and singular problems. The accuracy and efficiency of the implementation described herein make this a reliable formulation of the adaptive DBEM. Copyright © 2011 John Wiley & Sons, Ltd. 相似文献