共查询到20条相似文献，搜索用时 15 毫秒
1.
L. Gendre O. Allix P. Gosselet 《International journal for numerical methods in engineering》2011,87(9):889-905
This paper presents a two‐scale approximation of the Schur complement of a subdomain's stiffness matrix, obtained by combining local (i.e. element strips) and global (i.e. homogenized) contributions. This approximation is used in the context of a coupling strategy that is designed to embed local plasticity and geometric details into a small region of a large linear elastic structure; the strategy consists in creating a local model that contains the desired features of the concerned region and then substituting it into the global problem by the means of a non‐intrusive solver coupling technique adapted from domain decomposition methods. Using the two‐scale approximation of the Schur complement as a Robin condition on the local model enables to reach high efficiency. Examples include a large 3D problem provided by our industrial partner Snecma. Copyright © 2011 John Wiley & Sons, Ltd. 相似文献
2.
Jinyou Xiao Chuanzeng Zhang Tsung‐Ming Huang Tetsuya Sakurai 《International journal for numerical methods in engineering》2017,110(8):776-800
Numerical solution of nonlinear eigenvalue problems (NEPs) is frequently encountered in computational science and engineering. The applicability of most existing methods is limited by the matrix structures, properties of the eigen‐solutions, sizes of the problems, etc. This paper aims to remove those limitations and develop robust and universal NEP solvers for large‐scale engineering applications. The novelty lies in two aspects. First, a rational interpolation approach (RIA) is proposed based on the Keldysh theorem for holomorphic matrix functions. Comparing with the existing contour integral approach, the RIA provides the possibility to select sampling points in more general regions and has advantages in improving the accuracy and reducing the computational cost. Second, a resolvent sampling scheme using the RIA is proposed to construct reliable search spaces for the Rayleigh–Ritz procedure, based on which a robust eigen‐solver, called resolvent sampling based Rayleigh–Ritz method (RSRR), is developed for solving general NEPs. The RSRR can be easily implemented and parallelized. The advantages of the RIA and the performance of the RSRR are demonstrated by a variety of benchmark and application examples. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
3.
J. Wong E. Kuhl E. Darve 《International journal for numerical methods in engineering》2015,102(12):1784-1814
Recently, graphics processing units (GPUs) have been increasingly leveraged in a variety of scientific computing applications. However, architectural differences between CPUs and GPUs necessitate the development of algorithms that take advantage of GPU hardware. As sparse matrix vector (SPMV) multiplication operations are commonly used in finite element analysis, a new SPMV algorithm and several variations are developed for unstructured finite element meshes on GPUs. The effective bandwidth of current GPU algorithms and the newly proposed algorithms are measured and analyzed for 15 sparse matrices of varying sizes and varying sparsity structures. The effects of optimization and differences between the new GPU algorithm and its variants are then subsequently studied. Lastly, both new and current SPMV GPU algorithms are utilized in the GPU CG solver in GPU finite element simulations of the heart. These results are then compared against parallel PETSc finite element implementation results. The effective bandwidth tests indicate that the new algorithms compare very favorably with current algorithms for a wide variety of sparse matrices and can yield very notable benefits. GPU finite element simulation results demonstrate the benefit of using GPUs for finite element analysis and also show that the proposed algorithms can yield speedup factors up to 12‐fold for real finite element applications. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
4.
《International journal for numerical methods in engineering》2018,113(9):1531-1539
Dynamic relaxation is an iterative method to solve nonlinear systems of equations, which is frequently used for form finding and analysis of structures that undergo large displacements. It is based on the solution of a fictitious dynamic problem where the vibrations of the structure are traced by means of a time integration scheme until a static equilibrium is reached. Fictitious values are used for the mass and damping parameters. Heuristic rules exist to determine these values in such a way that the time integration procedure converges rapidly without becoming unstable. Central to these heuristic rules is the assumption that the highest convergence rate is achieved when the ratio of the highest and lowest eigenfrequency of the structure is minimal. This short communication shows that all eigenfrequencies become identical when a fictitious mass matrix proportional to the stiffness matrix is used. If, in addition, specific values are used for the fictitious damping parameters and the time integration step, the dynamic relaxation method becomes completely equivalent to the Newton‐Raphson method. The Newton‐Raphson method can therefore be regarded as a specific form of dynamic relaxation. This insight may help to interpret and improve nonlinear solvers based on dynamic relaxation and/or the Newton‐Raphson method. 相似文献
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Roman Vetter Norbert Stoop Thomas Jenni Falk K. Wittel Hans J. Herrmann 《International journal for numerical methods in engineering》2013,95(9):791-810
A thin shell finite element approach based on Loop's subdivision surfaces is proposed, capable of dealing with large deformations and anisotropic growth. To this end, the Kirchhoff–Love theory of thin shells is derived and extended to allow for arbitrary in‐plane growth. The simplicity and computational efficiency of the subdivision thin shell elements is outstanding, which is demonstrated on a few standard loading benchmarks. With this powerful tool at hand, we demonstrate the broad range of possible applications by numerical solution of several growth scenarios, ranging from the uniform growth of a sphere, to boundary instabilities induced by large anisotropic growth. Finally, it is shown that the problem of a slowly and uniformly growing sheet confined in a fixed hollow sphere is equivalent to the inverse process where a sheet of fixed size is slowly crumpled in a shrinking hollow sphere in the frictionless, quasistatic, elastic limit. Copyright © 2013 John Wiley & Sons, Ltd. 相似文献
6.
Andrew S. Wixom J. Gregory McDaniel 《International journal for numerical methods in engineering》2017,109(4):533-554
This paper develops and demonstrates a strategy for identifying the lack of dynamic interaction, or coupling, between potential design modifications to a vibrating base structure. Such decoupling may be exploited to efficiently compare the performance of competing engineering designs. In particular, it is shown how different design modifications may be represented as the addition or removal of substructures. When these substructures are uncoupled according to the metric developed here, the computational cost of determining the optimal system design can be greatly reduced. For example, if a designer considers seven possible modifications and wishes to examine all possible combinations of the modifications, 128 possible structures must be analyzed. However, if all modifications are dynamically uncoupled, significant computational effort need only be spent on eight of the possible structures in order to generate the responses for all remaining designs. Example problems demonstrate this cost reduction and illustrate cases where dynamic uncoupling occurs. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
7.
Long‐Sun Chao Hsiun‐Chang Peng 《International journal for numerical methods in engineering》2009,79(10):1245-1263
Adaptive time step methods provide a computationally efficient means of simulating transient problems with a high degree of numerical accuracy. However, choosing appropriate time steps to model the transient characteristics of solidification processes is difficult. The Gresho–Lee–Sani predictor–corrector strategy, one of the most commonly applied adaptive time step methods, fails to accurately model the latent heat release associated with phase change due to its exaggerated time steps while the apparent heat capacity method is applied. Accordingly, the current study develops a modified local time truncation error‐based strategy designed to adaptively adjust the size of the time step during the simulated solidification procedure in such a way that the effects of latent heat release are more accurately modeled and the precision of the computational solutions correspondingly improved. The computational accuracy and efficiency of the proposed method are demonstrated via the simulation of several one‐dimensional and two‐dimensional thermal problems characterized by different phase change phenomena and boundary conditions. The feasibility of the proposed method for the modeling of solidification processes is further verified via its applications to the enthalpy method. Copyright © 2009 John Wiley & Sons, Ltd. 相似文献
8.
找形分析是膜结构设计中的关键环节,但在数学上,膜结构的极小曲面找形分析是一个高度非线性问题,一般无法求得其解析解,因此数值方法成为重要工具。近年来,基于单元能量投影法（EEP法）的一维非线性有限元的自适应分析已经取得成功,基于EEP法的二维线性有限元自适应分析也被证实是有效、可靠的。在此基础上,该文提出一种基于EEP法的二维非线性有限元自适应方法,并成功将之应用于膜结构的找形分析。其主要思想是,通过将非线性问题用Newton法线性化,引入现有的二维线性问题的自适应求解技术,进而实现二维有限元自适应分析技术从线性到非线性的跨越,将非线性有限元的自适应分析求解从一维问题拓展到二维问题。该方法兼顾求解的精度和效率,对网格自适应地进行调整,最终得到优化的网格,其解答可按最大模度量逐点满足用户设定的误差限。该文综述介绍了这一进展,并给出数值算例用以表明该方法的可行性和可靠性。 相似文献
9.
The edge‐based smoothed finite element method (ES‐FEM) was proposed recently in Liu, Nguyen‐Thoi, and Lam to improve the accuracy of the FEM for 2D problems. This method belongs to the wider family of the smoothed FEM for which smoothing cells are defined to perform the numerical integration over the domain. Later, the face‐based smoothed FEM (FS‐FEM) was proposed to generalize the ES‐FEM to 3D problems. According to this method, the smoothing cells are centered along the faces of the tetrahedrons of the mesh. In the present paper, an alternative method for the extension of the ES‐FEM to 3D is investigated. This method is based on an underlying mesh composed of tetrahedrons, and the approximation of the field variables is associated with the tetrahedral elements; however, in contrast to the FS‐FEM, the smoothing cells of the proposed ES‐FEM are centered along the edges of the tetrahedrons of the mesh. From selected numerical benchmark problems, it is observed that the ES‐FEM is characterized by a higher accuracy and improved computational efficiency as compared with linear tetrahedral elements and to the FS‐FEM for a given number of degrees of freedom. Copyright © 2013 John Wiley & Sons, Ltd. 相似文献
10.
J. Marchais L. Chamoin C. Rey 《International journal for numerical methods in engineering》2017,110(8):745-775
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Paul R. Heyliger 《International journal for numerical methods in engineering》2017,112(13):2174-2182
Finite element approximations are developed for three‐dimensional domains naturally represented in either cylindrical or spherical coordinates. Lines of constant radius, axial length, or angle are used to represent the domain and cast approximations that are natural for these geometries. As opposed to general isoparametric three‐dimensional elements generated in conventional parent space, these elements can be evaluated analytically and do not generate geometric discretization error. They also allow for anisotropic material coefficients that are frequently aligned in either cylindrical or spherical coordinates. Several examples are provided that show convergence properties and comparison with analytical solutions of the Poisson equation. 相似文献
13.
Carsten Carstensen Antonio Orlando Jan Valdman 《International journal for numerical methods in engineering》2006,67(13):1851-1887
The boundary value problem representing one time step of the primal formulation of elastoplasticity with positive hardening leads to a variational inequality of the second kind with some nondifferentiable functional. This paper establishes an adaptive finite element algorithm for the solution of this variational inequality that yields the energy reduction and, up to higher order terms, the R‐linear convergence of the stresses with respect to the number of loops. Applications include several plasticity models: linear isotropic‐kinematic hardening, linear kinematic hardening, and multisurface plasticity as model for nonlinear hardening laws. For perfect plasticity, the adaptive algorithm yields strong convergence of the stresses. Numerical examples confirm an improved linear convergence rate and study the performance of the algorithm in comparison with the more frequently applied maximum refinement rule. Copyright © 2006 John Wiley & Sons, Ltd. 相似文献
14.
Mark Adams 《International journal for numerical methods in engineering》2002,55(5):519-534
Multigrid has been a popular solver method for finite element and finite difference problems with regular grids for over 20 years. The application of multigrid to unstructured grid problems, in which it is often difficult or impossible for the application to provide coarse grids, is not as well understood. In particular, methods that are designed to require only data that are easily available in most finite element applications (i.e. fine grid data), constructing the grid transfer operators and coarse grid operators internally, are of practical interest. We investigate three unstructured multigrid methods that show promise for challenging problems in 3D elasticity: (1) non‐nested geometric multigrid, (2) smoothed aggregation, and (3) plain aggregation algebraic multigrid. This paper evaluates the effectiveness of these three methods on several unstructured grid problems in 3D elasticity with up to 76 million degrees of freedom. Published in 2002 by John Wiley & Sons, Ltd. 相似文献
15.
A.G. Buchan C.C. Pain A.P. Umpleby R.P. Smedley‐Stevenson 《International journal for numerical methods in engineering》2012,92(3):318-342
This article describes a new element agglomeration multigrid method for solving partial differential equations discretised through a sub‐grid scale finite element formulation. The sub‐grid scale discretisation resolves solution variables through their separate coarse and fine scales, and these are mapped between the multigrid levels using a dual set of transfer operators. The sub‐grid scale multigrid method forms coarse linear systems, possessing the same sub‐grid scale structure as the original discretisation, that can be resolved without them being stored in memory. This is necessary for the application of this article in resolving the Boltzmann transport equation as the linear systems become extremely large. The novelty of this article is therefore a matrix‐free multigrid scheme that is integrated within its own sub‐grid scale discretisation using dual transfer operators and applied to the Boltzmann transport equation. The numerical examples presented are designed to show the method's preconditioning capabilities for a Krylov space‐based solver. The problems range in difficulty, geometry and discretisation type, and comparisons made with established methods show this new approach to perform consistently well. Smoothing operators are also analysed and this includes using the generalized minimal residual method. Here, it is shown that an adaptation to the preconditioned Krylov space is necessary for it to work efficiently. Copyright © 2012 John Wiley & Sons, Ltd. 相似文献
16.
In previous work, the nonlinear localization was first presented and studied in the case of large displacements but only for globally stable structural responses. In this paper, the influence of the local error criterion on the performance of the strategy is investigated in structures exhibiting more complex behaviour, such as snap-through and snap-back. Second, a path following method is implemented in the domain decomposition framework of the strategy in order to track the solution around a critical point (snap-through and snap-back). 相似文献
17.
G. Garcea G. A. Trunfio R. Casciaro 《International journal for numerical methods in engineering》2002,55(1):73-100
A path‐following non‐linear elastic analysis for structures composed of assemblages of flat slender elastic panels is presented. The proposed path‐following method employs FEM technology and a kinematical model to analyse these structures using a Koiter asymptotic approach. As a result it is possible to verify the accuracy achieved by the asymptotic method. The proposed mixed path‐following formulation is both efficient and robust with regards to the locking extrapolation phenomenon that strongly affects compatible formulations. The use of an HC finite element makes it possible to avoid the problem of the finite rotations in the space, maintaining a high degree of continuity and making the numeric formulation simple and efficient. Copyright © 2002 John Wiley & Sons, Ltd. 相似文献
18.
本文提出了相对刚度参数及其衍生参数的概念,它们可以揭示和反映杆系结构全过程跟踪分析中结构刚度的变化规律。根据这两个参数的特性,文中提出了确定自动荷载增量参数的新方法,较好地解决了稳定分析中全过程跟踪技术中的疑难问题。文中通过实例来说明相对刚度参数的确定和应用,表明本文分析方法是正确的和有效的。 相似文献
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Isaac Fried 《International journal for numerical methods in engineering》2016,106(9):760-770
A universal, practical, a priori, numerical procedure is presented by which to realistically bind the spectral condition number of the global stiffness matrix generated by the finite element least‐squares method. The procedure is then applied to second and fourth‐order problems in one and two dimensions to show that the condition of the global stiffness matrix thus generated is, in all instances, proportional to but the diameter of the element squared. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献