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1.
    
The existing global–local multiscale computational methods, using finite element discretization at both the macro‐scale and micro‐scale, are intensive both in terms of computational time and memory requirements and their parallelization using domain decomposition methods incur substantial communication overhead, limiting their application. We are interested in a class of explicit global–local multiscale methods whose architecture significantly reduces this communication overhead on massively parallel machines. However, a naïve task decomposition based on distributing individual macro‐scale integration points to a single group of processors is not optimal and leads to communication overheads and idling of processors. To overcome this problem, we have developed a novel coarse‐grained parallel algorithm in which groups of macro‐scale integration points are distributed to a layer of processors. Each processor in this layer communicates locally with a group of processors that are responsible for the micro‐scale computations. The overlapping groups of processors are shown to achieve optimal concurrency at significantly reduced communication overhead. Several example problems are presented to demonstrate the efficiency of the proposed algorithm. Copyright © 2009 John Wiley & Sons, Ltd.  相似文献   

2.
    
In this paper, we develop a block preconditioner for Jacobian‐free global–local multiscale methods, in which the explicit computation of the Jacobian may be circumvented at the macroscale by using a Newton–Krylov process. Effective preconditioning is necessary for the Krylov subspace iterations (e.g. GMRES) to enhance computational efficiency. This is, however, challenging since no explicit information regarding the Jacobian matrix is available. The block preconditioning technique developed in this paper circumvents this problem by effectively deflating the spectrum of the Jacobian matrix at the current Newton step using information about only the Krylov subspaces corresponding to the Jacobian matrices in the previous Newton steps and their representations on those subspaces. This approach is optimal and results in exponential convergence of the GMRES iterations within each Newton step, thus minimizing expensive microscale computations without requiring explicit Jacobian formation in any step. In terms of both computational cost and storage requirements, the action of a single block of the preconditioner per GMRES step scales linearly as the number of degrees of freedom of the macroscale problem as well as the dimension of the invariant subspace of the preconditioned Jacobian matrix. Copyright © 2011 John Wiley & Sons, Ltd.  相似文献   

3.
For some finite element analyses of stresses in engineering components, low‐order elements can be preferred. This choice, however, results in slow convergence, especially at key stress concentrations. To overcome this difficulty, submodelling of stress concentrators can be employed. With submodelling, a subregion within the original global configuration and centred on the stress concentrator of interest is analysed by itself, with a consequent reduction in computation. The more aggressive the submodelling, the smaller the subregion and the greater the computational savings. To realize such savings in actuality, it is necessary that appropriate boundary conditions be applied to the subregion. Some of these boundary conditions must be drawn from a global analysis of the original configuration: then it is essential to ensure that such boundary conditions are determined sufficiently accurately. This paper describes a procedure for being reasonably certain that such is the case. The procedure is evaluated on a series of test problems and demonstrated on a contact application. Results show that good engineering estimates of peak stresses can be obtained even in regions of unusually high stress gradients. Furthermore, these estimates can be obtained in return for quite moderate levels of computational effort. Copyright © 1999 John Wiley & Sons, Ltd.  相似文献   

4.
There was a tremendous advantage of using the generalized co-ordinate system to express various types of laminate theories. With two layer-dependent terms of both the zeroth- and the first-order of thickness co-ordinate, a generalized zigzag theory was presented in a previous study. Due to its success in laminate analysis, the feasibility of assigning the two high-order terms, i.e. the second- and the third-order terms, of the generalized zigzag theory as layer-dependent variables was of primary interest. It was found that a so-called global–local superposition technique could be used for expressing the laminate theories in an explicit manner, namely recursive equations, to retain the advantage of numerical efficiency. Based on the superposition technique, the fundamental roles of the individual terms are identified. It is concluded that not only the completeness of the terms, but also the inclusion of as many terms as possible, is important to a laminate theory. It then is the goal of this study to look into a laminate theory which can satisfy the requirement of completeness and include all the first-, second- and third-order terms in an assumed displacement field. A special technique, namely hypothesis for double superposition, is presented to achieve the goal. The feasibility of the hypothesis is demonstrated in this study. Although not verified mathematically, the hypothesis seems to be capable of giving accurate and efficient laminate theories. © 1997 by John Wiley & Sons, Ltd.  相似文献   

5.
    
An extended/generalized finite element method (XFEM/GFEM) for simulating quasistatic crack growth based on a phase-field method is presented. The method relies on approximations to solutions associated with two different scales: a global scale, that is, structural and discretized with a coarse mesh, and a local scale encapsulating the fractured region, that is, discretized with a fine mesh. A stable XFEM/GFEM is employed to embed the displacement and damage fields at the global scale. The proposed method accommodates approximation spaces that evolve between load steps, while preserving a fixed background mesh for the structural problem. In addition, a prediction-correction algorithm is employed to facilitate the dynamic evolution of the confined crack regions within a load step. Several numerical examples of benchmark problems in two- and three-dimensional quasistatic fracture are provided to demonstrate the approach.  相似文献   

6.
    
The insulation containment of liquefied natural gas (LNG) carriers is a large‐sized elastic structure made of various metallic and composite materials of complex structural composition to protect the heat invasion and to sustain the hydrodynamic pressure. The goal of the present paper is to present a global–local numerical approach to effectively and accurately compute the local hydroelastic response of a local containment region of interest. The global sloshing flow and hydrodynamic pressure fields of interior LNG are computed by assuming the flexible containment as a rigid container. On the other hand, the local hydroelastic response of the insulation containment is obtained by solving only the local hydroelastic model in which the complex and flexible insulation structure is fully considered and the global analysis results are used as the initial and boundary conditions. The interior incompressible inviscid LNG flow is solved by the first‐order Euler finite volume method, whereas the structural dynamic deformation is solved by the explicit finite element method. The LNG flow and the containment deformation are coupled by the Euler–Lagrange coupling scheme. Copyright © 2008 John Wiley & Sons, Ltd.  相似文献   

7.
    
This paper presents new developments on a weakly intrusive approach for the simplified implementation of space and time multiscale methods within an explicit dynamics software. The ‘substitution’ method proposed in previous works allows to take advantage of a global coarse model, typically used in an industrial context, running separate, refined in space and in time, local analyses only where needed. The proposed technique is iterative, but the explicit character of the method allows to perform the global computation only once per global time step, while a repeated solution is required for the small local problems only. Nevertheless, a desirable goal is to reach convergence with a reduced number of iterations. To this purpose, we propose here a new iterative algorithm based on an improved interface inertia operator. The new operator exploits a combined property of velocity Hermite time interpolation on the interface and of the central difference integration scheme, allowing the consistent upscaling of interface inertia contributions from the lower scale. This property is exploited to construct an improved mass matrix operator for the interface coupling, allowing to significantly enhance the convergence rate. The efficiency and robustness of the procedure are demonstrated through several examples of growing complexity. Copyright © 2014 John Wiley & Sons, Ltd.  相似文献   

8.
To analyze angle-ply laminated composite and sandwich plates coupled bending and extension under thermo-mechanical loading, a refined global–local higher-order theory considering transverse normal strain is presented in this work. Hitherto, present theory for angle-ply laminates has never been reported in the literature, and this theory can satisfy continuity of transverse shear stresses at interfaces. In addition, the number of unknowns in present model is independent of layer numbers of the laminate. Based on this theory as well as methodology of the refined triangular discrete Kirchhoff plate element, a triangular laminated plate element satisfying the requirement of C1 continuity is presented. Numerical results show that the present refined theory can accurately analyze the bending problems of angle-ply composite and sandwich plates as well as thermal expansion problem of cross-ply plates, and the present refined theory is obviously superior to the existing global–local higher-order theory proposed by Li and Liu [Li XY, Liu D. Generalized laminate theories based on double superposition hypothesis. Int J Numer Meth Eng 1997;40:1197–212]. After ascertaining the accuracy of present model, the distributions of displacements and stresses for angle-ply laminated plates under temperature loads are also given in present work. These results can serve as a reference for future investigations.  相似文献   

9.
    
Extensions of a new technique for the finite element modelling of cracks with multiple branches, multiple holes and cracks emanating from holes are presented. This extended finite element method (X‐FEM) allows the representation of crack discontinuities and voids independently of the mesh. A standard displacement‐based approximation is enriched by incorporating discontinuous fields through a partition of unity method. A methodology that constructs the enriched approximation based on the interaction of the discontinuous geometric features with the mesh is developed. Computation of the stress intensity factors (SIF) in different examples involving branched and intersecting cracks as well as cracks emanating from holes are presented to demonstrate the accuracy and the robustness of the proposed technique. Copyright © 2000 John Wiley & Sons, Ltd.  相似文献   

10.
    
This paper presents a new stress recovery technique for the generalized/extended finite element method (G/XFEM) and for the stable generalized FEM (SGFEM). The recovery procedure is based on a locally weighted L2 projection of raw stresses over element patches; the set of elements sharing a node. Such projection leads to a block-diagonal system of equations for the recovered stresses. The recovery procedure can be used with GFEM and SGFEM approximations based on any choice of elements and enrichment functions. Here, the focus is on low-order 2D approximations for linear elastic fracture problems. A procedure for computing recovered stresses at re-entrant corners of any internal angle is also presented. The proposed stress recovery technique is used to define a Zienkiewicz-Zhu (ZZ) a posteriori error estimator for the G/XFEM and the SGFEM. The accuracy, computational cost, and convergence rate of recovered stresses together with the quality of the ZZ estimator, including its effectivity index, are demonstrated in problems with smooth and singular solutions.  相似文献   

11.
    
Several classes of important engineering problems—in this case, problems exhibiting sharp thermal gradients—have solution features spanning multiple spatial scales and, therefore, necessitate advanced hp finite element discretizations. Although hp‐FEM is unavailable off‐the‐shelf in many predominant commercial analysis software packages, the authors herein propose a novel method to introduce these capabilities via a generalized FEM nonintrusively in a standard finite element analysis (FEA) platform. The methodology is demonstrated on two verification problems as well as a representative, industrial‐scale problem. Numerical results show that the techniques utilized allow for accurate resolution of localized thermal features on structural‐scale meshes without hp‐adaptivity or the ability to account for complex and very localized loads in the FEA code itself. This methodology enables the user to take advantage of all the benefits of both hp‐FEM discretizations and the appealing features of many available computer‐aided engineering /FEA software packages to obtain optimal convergence for challenging multiscale problems. Copyright © 2012 John Wiley & Sons, Ltd.  相似文献   

12.
    
A method for the modeling of dislocations and cracks by atomistic/continuum models is described. The methodology combines the extended finite element method with the bridging domain method (BDM). The former is used to model crack surfaces and slip planes in the continuum, whereas the BDM is used to link the atomistic models with the continuum. The BDM is an overlapping domain decomposition method in which the atomistic and continuum energies are blended so that their contributions decay to their boundaries on the overlapping subdomain. Compatibility between the continua and atomistic domains is enforced by a continuous Lagrange multiplier field. The methodology allows for simulations with atomistic resolution near crack fronts and dislocation cores while retaining a continuum model in the remaining part of the domain and so a large reduction in the number of atoms is possible. It is applied to the modeling of cracks and dislocations in graphene sheets. Energies and energy distributions compare very well with direct numerical simulations by strictly atomistic models. Copyright © 2008 John Wiley & Sons, Ltd.  相似文献   

13.
    
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   

14.
A displacement-based variable kinematic global–local finite element model is developed using hierarchical, multiple assumed displacement fields at two different levels: (1) at the element level, and (2) at the mesh level. The displacement field hierarchy contains both a conventional plate expansion (2-D) and a full layerwise (3-D) expansion. Depending on the accuracy desired, the variable kinematic element can use various terms from the composite displacement field, thus creating a hierarchy of different elements having a wide range of kinematic complexity and representing a number of different mathematical models. The VKFE is then combined with the mesh superposition technique to further increase the computational efficiency and robustness of the computational algorithm. These models are used to analyse a number of laminated composite plate problems that contain localized subregions where significant 3-D stress fields exist (e.g. free-edge effects).  相似文献   

15.
    
We present a new multiscale method for crack simulations. This approach is based on a two‐scale decomposition of the displacements and a projection to the coarse scale by using coarse scale test functions. The extended finite element method (XFEM) is used to take into account macrocracks as well as microcracks accurately. The transition of the field variables between the different scales and the role of the microfield in the coarse scale formulation are emphasized. The method is designed so that the fine scale computation can be done independently of the coarse scale computation, which is very efficient and ideal for parallelization. Several examples involving microcracks and macrocracks are given. It is shown that the effect of crack shielding and amplification for crack growth analyses can be captured efficiently. Copyright © 2007 John Wiley & Sons, Ltd.  相似文献   

16.
    
A generalized multiscale finite element method is introduced to address the computationally taxing problem of elastic fracture across scales. Crack propagation is accounted for at the microscale utilizing phase field theory. Both the displacement-based equilibrium equations and phase field state equations at the microscale are mapped on a coarser scale. The latter is defined by a set of multinode coarse elements, where solution of the governing equations is performed. Mapping is achieved by employing a set of numerically derived multiscale shape functions. A set of representative benchmark tests is used to verify the proposed procedure and assess its performance in terms of accuracy and efficiency compared with the standard phase field finite element implementation.  相似文献   

17.
18.
    
New methods for the analysis of failure by multiscale methods that invoke unit cells to obtain the subscale response are described. These methods, called multiscale aggregating discontinuities, are based on the concept of ‘perforated’ unit cells, which exclude subdomains that are unstable, i.e. exhibit loss of material stability. Using this concept, it is possible to compute an equivalent discontinuity at the coarser scale, including both the direction of the discontinuity and the magnitude of the jump. These variables are then passed to the coarse‐scale model along with the stress in the unit cell. The discontinuity is injected at the coarser scale by the extended finite element method. Analysis of the procedure shows that the method is consistent in power and yields a bulk stress–strain response that is stable. Applications of this procedure to crack growth in heterogeneous materials are given. Copyright © 2007 John Wiley & Sons, Ltd.  相似文献   

19.
    
A method for coarse graining of microcrack growth to the macroscale through the multiscale aggregating discontinuity (MAD) method is further developed. Three new features are: (1) methods for treating nucleating cracks, (2) the linking of the micro unit cell with the macroelement by the hourglass mode, and (3) methods for recovering macrocracks with variable crack opening. Unlike in the original MAD method, ellipticity is not retained at the macroscale in the bulk material, but we show that the element stiffness of the bulk material is positive definite. Several examples with comparisons with direct numerical simulations are given to demonstrate the effectiveness of the method. Copyright © 2009 John Wiley & Sons, Ltd.  相似文献   

20.
    
Based on completely three‐dimensional elasticity theory, a refined global–local higher‐order theory is presented as enhanced version of the classical global–local theory proposed by Li and Liu (Int. J. Numer. Meth. Engng. 1997; 40 :1197–1212), in which the effect of transverse normal deformation is enhanced. Compared with the previous higher‐order theory, the refined theory offers some valuable improvements these are able to predict accurately response of laminated plates subjected to thermal loading of uniform temperature. However, the previous higher‐order theory will encounter difficulty for this problem. A refined three‐noded triangular element satisfied the requirement of C1 weak‐continuity conditions in the inter‐element is also presented. The results of numerical examples of moderately thick laminated plates and even thick plates with span/thickness ratios L/h = 2 are given to show that in‐plane stresses and transverse shear stresses can be reasonably predicted by the direct constitutive equation approach without smooth technique. In order to accurately obtain transverse normal stresses, the local equilibrium equation approach in one element is employed herein. Copyright © 2006 John Wiley & Sons, Ltd.  相似文献   

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