共查询到20条相似文献，搜索用时 15 毫秒
1.
R. Rumpler P. Göransson H.J. Rice 《International journal for numerical methods in engineering》2014,100(9):689-710
Most engineering applications involving solutions by numerical methods are dependent on several parameters, whose impact on the solution may significantly vary from one to the other. At times an evaluation of these multivariate solutions may be required at the expense of a prohibitively high computational cost. In the present paper, an adaptive approach is proposed as a way to estimate the solution of such multivariate finite element problems. It is based upon the integration of so‐called nested Padé approximants within the finite element procedure. This procedure includes an effective control of the approximation error, which enables adaptive refinements of the converged intervals upon reconstruction of the solution. The main advantages lie in a potential reduction of the computational effort and the fact that the level of a priori knowledge required about the solution in order to have an accurate, efficient, and well‐sampled estimate of the solution is low. The approach is introduced for bivariate problems, for which it is validated on elasto‐poro‐acoustic problems of both academic and more industrial scale. It is argued that the methodology in general holds for more than two variables, and a discussion is opened about the truncation refinements required in order to generalize the results accordingly. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
2.
To increase the robustness of a Padé‐based approximation of parametric solutions to finite element problems, an a priori estimate of the poles is proposed. The resulting original approach is shown to allow for a straightforward, efficient, subsequent Padé‐based expansion of the solution vector components, overcoming some of the current convergence and robustness limitations. In particular, this enables for the intervals of approximation to be chosen a priori in direct connection with a given choice of Padé approximants. The choice of these approximants, as shown in the present work, is theoretically supported by the Montessus de Ballore theorem, concerning the convergence of a series of approximants with fixed denominator degrees. Key features and originality of the proposed approach are (1) a component‐wise expansion which allows to specifically target subsets of the solution field and (2) the a priori, simultaneous choice of the Padé approximants and their associated interval of convergence for an effective and more robust approximation. An academic acoustic case study, a structural‐acoustic application, and a larger acoustic problem are presented to demonstrate the potential of the approach proposed. 相似文献
3.
J. P. Pereira C. A. Duarte D. Guoy X. Jiao 《International journal for numerical methods in engineering》2009,77(5):601-633
A high‐order generalized finite element method (GFEM) for non‐planar three‐dimensional crack surfaces is presented. Discontinuous p‐hierarchical enrichment functions are applied to strongly graded tetrahedral meshes automatically created around crack fronts. The GFEM is able to model a crack arbitrarily located within a finite element (FE) mesh and thus the proposed method allows fully automated fracture analysis using an existing FE discretization without cracks. We also propose a crack surface representation that is independent of the underlying GFEM discretization and controlled only by the physics of the problem. The representation preserves continuity of the crack surface while being able to represent non‐planar, non‐smooth, crack surfaces inside of elements of any size. The proposed representation also provides support for the implementation of accurate, robust, and computationally efficient numerical integration of the weak form over elements cut by the crack surface. Numerical simulations using the proposed GFEM show high convergence rates of extracted stress intensity factors along non‐planar curved crack fronts and the robustness of the method. Copyright © 2008 John Wiley & Sons, Ltd. 相似文献
4.
E. H. Boutyour H. Zahrouni M. Potier‐Ferry M. Boudi 《International journal for numerical methods in engineering》2004,60(12):1987-2012
The aim of this work is to develop a reliable and fast algorithm to compute bifurcation points and bifurcated branches. It is based upon the asymptotic numerical method (ANM) and Padé approximants. The bifurcation point is detected by analysing the poles of Padé approximants or by evaluating, along the computed solution branch, a bifurcation indicator well adapted to ANM. Several examples are presented to assess the effectiveness of the proposed method, that emanate from buckling problems of thin elastic shells. Especially problems involving large rotations are discussed. Copyright © 2004 John Wiley & Sons, Ltd. 相似文献
5.
T. C. Fung Z. L. Chen 《International journal for numerical methods in engineering》2006,68(11):1115-1136
An efficient precise time‐step integration (PTI) algorithm to solve large‐scale transient problems is presented in this paper. The Krylov subspace method and the Padé approximations are applied to modify the original PTI algorithm in order to improve the computational efficiency. Both the stability and accuracy characteristics of the resultant algorithms are investigated. The efficiency can be further improved by expanding the dimension to avoid the computation of the particular solutions. The present algorithm can also be extended to tackle nonlinear problems without difficulty. Two numerical examples are given to illustrate the highly accurate and efficient algorithm. Copyright © 2006 John Wiley & Sons, Ltd. 相似文献
6.
Chongmin Song Mohammad Hossein Bazyar 《International journal for numerical methods in engineering》2007,69(11):2330-2358
A boundary condition satisfying the radiation condition at infinity is frequently required in the numerical simulation of wave propagation in an unbounded domain. In a frequency domain analysis using finite elements, this boundary condition can be represented by the dynamic stiffness matrix of the unbounded domain defined on its boundary. A method for determining a Padé series of the dynamic stiffness matrix is proposed in this paper. This method starts from the scaled boundary finite‐element equation, which is a system of ordinary differential equations obtained by discretizing the boundary only. The coefficients of the Padé series are obtained directly from the ordinary differential equations, which are not actually solved for the dynamic stiffness matrix. The high rate of convergence of the Padé series with increasing order is demonstrated numerically. This technique is applicable to scalar waves and elastic vector waves propagating in anisotropic unbounded domains of irregular geometry. It can be combined seamlessly with standard finite elements. Copyright © 2006 John Wiley & Sons, Ltd. 相似文献
7.
James P. Tuck‐Lee Peter M. Pinsky 《International journal for numerical methods in engineering》2008,73(5):728-746
For many problems in structural acoustics, it is desired to obtain solutions at many frequencies over a large range in the frequency domain. A reduced‐order multifrequency algorithm based on matrix Padé approximation, using the matrix Padé‐via‐Lanczos (MPVL) connection, has been previously used to solve both exterior and interior acoustic problems. However, the method is not guaranteed to give the correct solution across the entire frequency region of interest, but only locally around a reference frequency. An adaptive frequency windowing scheme is introduced to address this shortcoming for practical application of this method. The application of this algorithm to tightly coupled problems in interior structural acoustics is presented. Copyright © 2007 John Wiley & Sons, Ltd. 相似文献
8.
S.‐A. Papanicolopulos A. Zervos I. Vardoulakis 《International journal for numerical methods in engineering》2009,77(10):1396-1415
In gradient elasticity strain gradient terms appear in the expression of virtual work, leading to the need for C1 continuous interpolation in finite element discretizations of the displacement field only. Employing such interpolation is generally avoided in favour of the alternative methods that interpolate other quantities as well as displacement, due to the scarcity of C1 finite elements and their perceived computational cost. In this context, the lack of three‐dimensional C1 elements is of particular concern. In this paper we present a new C1 hexahedral element which, to the best of our knowledge, is the first three‐dimensional C1 element ever constructed. It is shown to pass the single element and patch tests, and to give excellent rates of convergence in benchmark boundary value problems of gradient elasticity. It is further shown that C1 elements are not necessarily more computationally expensive than alternative approaches, and it is argued that they may be more efficient in providing good‐quality solutions. Copyright © 2008 John Wiley & Sons, Ltd. 相似文献
9.
Vasco Varduhn Ming‐Chen Hsu Martin Ruess Dominik Schillinger 《International journal for numerical methods in engineering》2016,107(12):1054-1079
The finite cell method (FCM) is an immersed domain finite element method that combines higher‐order non‐boundary‐fitted meshes, weak enforcement of Dirichlet boundary conditions, and adaptive quadrature based on recursive subdivision. Because of its ability to improve the geometric resolution of intersected elements, it can be characterized as an immersogeometric method. In this paper, we extend the FCM, so far only used with Cartesian hexahedral elements, to higher‐order non‐boundary‐fitted tetrahedral meshes, based on a reformulation of the octree‐based subdivision algorithm for tetrahedral elements. We show that the resulting TetFCM scheme is fully accurate in an immersogeometric sense, that is, the solution fields achieve optimal and exponential rates of convergence for h‐refinement and p‐refinement, if the immersed geometry is resolved with sufficient accuracy. TetFCM can leverage the natural ability of tetrahedral elements for local mesh refinement in three dimensions. Its suitability for problems with sharp gradients and highly localized features is illustrated by the immersogeometric phase‐field fracture analysis of a human femur bone. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
10.
E. P. Kasper R. L. Taylor 《International journal for numerical methods in engineering》2002,53(9):2061-2086
A four‐noded quadrilateral axisymmetric formulation in the context of a mixed‐enhanced method is presented. The strain field is represented by two sets of element parameters, which results in enhanced performance and coarse mesh accuracy in bending dominated problems and locking‐free response in the near incompressible limit. The mixed fields presented are such that variational stress recovery is permissible. In addition, the formulation is cast such that the mixed parameters are obtained explicitly yielding finite element arrays with the proper rank using standard order quadrature. In this paper our attention is restricted to the area of geometrically linear problems in solid mechanics. Representative simulations show favourable performance of the formulation. Copyright © 2002 John Wiley & Sons, Ltd. 相似文献
11.
&#x;ukasz Kaczmarczyk Chris J. Pearce Nenad Bi&#x;ani&#x; 《International journal for numerical methods in engineering》2008,74(3):506-522
Formulation of the scale transition equations coupling the microscopic and macroscopic variables in the second‐order computational homogenization of heterogeneous materials and the enforcement of generalized boundary conditions for the representative volume element (RVE) are considered. The proposed formulation builds on current approaches by allowing any type of RVE boundary conditions (e.g. displacement, traction, periodic) and arbitrary shapes of RVE to be applied in a unified manner. The formulation offers a useful geometric interpretation for the assumptions associated with the microstructural displacement fluctuation field within the RVE, which is here extended to second‐order computational homogenization. A unified approach to the enforcement of the boundary conditions has been undertaken using multiple constraint projection matrices. The results of an illustrative shear layer model problem indicate that the displacement and traction RVE boundary conditions provide the upper and lower bounds of the response determined via second‐order computational homogenization, and the solution associated with the periodic RVE boundary conditions lies between them. Copyright © 2007 John Wiley & Sons, Ltd. 相似文献
12.
M. Mancuso F. Ubertini 《International journal for numerical methods in engineering》2003,56(13):1883-1912
This work presents a methodology which generates efficient higher‐order methods for linear dynamics by improving the accuracy properties of Nørsett methods towards those of Padé methods. The methodology is based on a simple and low‐cost iterative procedure which is used to implement a set of higher‐order methods with controllable dissipation. A sequence of improved solutions is obtained which correspond to algorithms offering an effective compromise between the efficiency of Nørsett methods and the accuracy of Padé methods. Moreover, a direct control over high‐frequency dissipation is possible by means of an algorithmic parameter. Numerical tests are reported which confirm that this set of algorithms is really attractive for linear dynamic analysis. Copyright © 2003 John Wiley & Sons, Ltd. 相似文献
13.
Chongmin Song 《International journal for numerical methods in engineering》2009,77(8):1139-1171
The scaled boundary finite element method is extended to solve problems of structural dynamics. The dynamic stiffness matrix of a bounded (finite) domain is obtained as a continued fraction solution for the scaled boundary finite element equation. The inertial effect at high frequencies is modeled by high‐order terms of the continued fraction without introducing an internal mesh. By using this solution and introducing auxiliary variables, the equation of motion of the bounded domain is expressed in high‐order static stiffness and mass matrices. Standard procedures in structural dynamics can be applied to perform modal analyses and transient response analyses directly in the time domain. Numerical examples for modal and direct time‐domain analyses are presented. Rapid convergence is observed as the order of continued fraction increases. A guideline for selecting the order of continued fraction is proposed and validated. High computational efficiency is demonstrated for problems with stress singularity. Copyright © 2008 John Wiley & Sons, Ltd. 相似文献
14.
Yalin Akz Fethi Kadiolu 《International journal for numerical methods in engineering》1999,44(12):1909-1932
The quasi‐static and dynamic responses of a linear viscoelastic Timoshenko beam on Winkler foundation are studied numerically by using the hybrid Laplace–Carson and finite element method. In this analysis the field equation for viscoelastic material is used. In the transformed Laplace–Carson space two new functionals have been constructed for viscoelastic Timoshenko beams through a systematic procedure based on the Gâteaux differential. These functionals have six and two independent variables respectively. Two mixed finite element formulations are obtained; TB12 and TB4. For the inverse transform Schapery and Fourier methods are used. The numerical results for quasi‐static and dynamic responses of several visco‐elastic models are presented. Copyright © 1999 John Wiley & Sons, Ltd. 相似文献
15.
R. Rumpler P. Göransson J.‐F. Deü 《International journal for numerical methods in engineering》2014,97(10):759-784
In this work, a solution strategy is investigated for the resolution of multi‐frequency structural‐acoustic problems including 3D modeling of poroelastic materials. The finite element method is used, together with a combination of a modal‐based reduction of the poroelastic domain and a Padé‐based reconstruction approach. It thus takes advantage of the reduced‐size of the problem while further improving the computational efficiency by limiting the number of frequency resolutions of the full‐sized problem. An adaptive procedure is proposed for the discretization of the frequency range into frequency intervals of reconstructed solution. The validation is presented on a 3D poro‐acoustic example. Copyright © 2013 John Wiley & Sons, Ltd. 相似文献
16.
A discontinuous Galerkin formulation of the boundary value problem of finite‐deformation elasticity is presented. The primary purpose is to establish a discontinuous Galerkin framework for large deformations of solids in the context of statics and simple material behaviour with a view toward further developments involving behaviour or models where the DG concept can show its superiority compared to the continuous formulation. The method is based on a general Hu–Washizu–de Veubeke functional allowing for displacement and stress discontinuities in the domain interior. It is shown that this approach naturally leads to the formulation of average stress fluxes at interelement boundaries in a finite element implementation. The consistency and linearized stability of the method in the non‐linear range as well as its convergence rate are proven. An implementation in three dimensions is developed, showing that the proposed method can be integrated into conventional finite element codes in a straightforward manner. In order to demonstrate the versatility, accuracy and robustness of the method examples of application and convergence studies in three dimensions are provided. Copyright © 2006 John Wiley & Sons, Ltd. 相似文献
17.
18.
Shanlong Yao Michele Zappalorto Changzheng Cheng Zhongrong Niu Jingchuan Li 《Fatigue & Fracture of Engineering Materials & Structures》2020,43(7):1384-1398
In this paper, the singular behavior for anisotropic multimaterial V‐notched plates is investigated under antiplane shear loading condition. Firstly, the elastic governing equations are transformed into eigen ordinary differential equations through introducing the asymptotic expansions of displacements near the notch tip. The stress singularity exponents, including the higher‐order terms, and the corresponding eigen angular functions are then obtained by solving the established equations by using the interpolating matrix method. Thus, using the combination of the results from finite element analyses and the derived asymptotic expansion, an overdeterministic method is employed to calculate the amplitudes of the coefficients in the asymptotic expansions. Finally, the stress and displacement fields in the vicinity of the notch tip, consisting of both singular terms and higher‐order terms, are determined. The effects of material properties and geometry characteristic on the singular behaviour of the notch tip are discussed in detail. 相似文献
19.
P.L. George H. Borouchaki 《International journal for numerical methods in engineering》2014,99(8):611-632
Finite elements of degree two or more are needed to solve various PDE problems. This paper discusses a method to validate such meshes for the case of quadrilateral elements of degree 2. The first section of this paper comes back to Bézier curve and Bézier quadrilateral patches of degree 2. The way in which a Bézier quad patch and a Q2 finite element quad are related is introduced. The two possible quads are discussed, the 9‐node (or complete) quad together with the 8‐node (or Serendipity) quad. A validity condition, the positivity of the Jacobian, is exhibited for these two elements. The discussion continues with a rational Bézier quad patch that can be used as a finite element. Extension to arbitrary degrees is given. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
20.
W. Aggoune H. Zahrouni M. Potier‐Ferry 《International journal for numerical methods in engineering》2006,68(6):605-631
New algorithms based upon the asymptotic numerical method (ANM) are proposed to solve unilateral contact problems. ANM leads to a representation of a solution path in terms of series or Padé approximants. To get a smooth solution path, a hyperbolic relation between contact forces and clearance is introduced. Three key points are discussed: the influence of the regularization of the contact law, the discretization of the contact force by Lagrange multipliers and prediction–correction algorithms. Simple benchmarks are considered to evaluate the relevance of the proposed algorithms. Copyright © 2006 John Wiley & Sons, Ltd. 相似文献