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1.
B. Boroomand F. Mossaiby 《International journal for numerical methods in engineering》2005,64(4):461-502
In this part of the paper we shall use the formulation given in the first part to assess the quality of recovery‐based error estimators using two recovery methods, i.e. superconvergent patch recovery (SPR) and recovery by equilibrium in patches (REP). The recovery methods have been shown to be asymptotically robust and superconvergent when applied to two‐dimensional problems. In this study we shall examine the behaviour of the recovery methods on several three‐dimensional mesh patterns for patches located either inside or at boundaries. This is performed by first finding an asymptotic finite element solution, irrespective of boundary conditions at far ends of the domain, and then applying the recovery methods. The test procedure near kinked boundaries is explained in a step‐by‐step manner. The results are given in a series of tables and figures for various cases of three‐dimensional mesh patterns. It has been experienced that the full superconvergent property is generally lost due to presence of boundary layer solution and the definition of the recoveries near boundaries though the results of the robustness test is still within an acceptable range. Copyright © 2005 John Wiley & Sons, Ltd. 相似文献
2.
B. Boroomand M. Ghaffarian O. C. Zienkiewicz 《International journal for numerical methods in engineering》2004,61(10):1644-1673
In this paper a study is performed on application of two recovery methods, i.e. superconvergent patch recovery (SPR) and the recovery by equilibrium of patches (REP), to plate problems. The two recovery methods have been recognized to give similar results in adaptive solutions of two dimensional stress problems. While the former applies a least square fit over a set of values at the so called superconvergent points, the latter does not need any knowledge of such points and thus has a wider application especially in non‐linear problems. The formulation of REP is extended to Reissner–Mindlin plate problems. The convergence rates of the recovered fields of the gradients obtained from application of the two methods are compared using series of regular triangular and rectangular meshes for thick and thin plate solution cases. Assumed strain formulation based elements, i.e. the elements formulated by mixed interpolation of tensorial components, as well as conventional from of elements based on selective integration schemes are employed for the study. In order to investigate the possibility of any improvement in the results by adding equilibrium constraints to SPR, as some authors suggest for simple two‐dimensional problems, some weighted forms of such conditions are designed and added to the formulation. Comprehensive study has been given first by varying the weight terms to obtain the best enhanced results and then using the optimal values to investigate the effects of the constraints on the rate of convergence. It is observed that despite of the cost of this approach, due to the coupling of the gradient terms, no significant improvement is achieved. Copyright © 2004 John Wiley & Sons, Ltd. 相似文献
3.
Radek Tezaur Antonini Macedo Charbel Farhat Rabia Djellouli 《International journal for numerical methods in engineering》2002,53(6):1461-1476
We report on a generalization of the Bayliss–Gunzburger–Turkel non‐reflecting boundary conditions to arbitrarily shaped convex artificial boundaries. For elongated scatterers such as submarines, we show that this generalization can improve significantly the computational efficiency of finite element methods applied to the solution of three‐dimensional acoustic scattering problems. Copyright © 2001 John Wiley & Sons, Ltd. 相似文献
4.
J. J. Ródenas M. Tur F. J. Fuenmayor A. Vercher 《International journal for numerical methods in engineering》2007,70(6):705-727
The superconvergent patch recovery (SPR) technique is widely used in the evaluation of a recovered stress field σ * from the finite element solution σ fe. Several modifications of the original SPR technique have been proposed. A new improvement of the SPR technique, called SPR‐C technique (Constrained SPR), is presented in this paper. This new technique proposes the use of the appropriate constraint equations in order to obtain stress interpolation polynomials in the patch σ that locally satisfy the equations that should be satisfied by the exact solution. As a result the evaluated expressions for σ will satisfy the internal equilibrium and compatibility equations in the whole patch and the boundary equilibrium equation at least in vertex boundary nodes and, under certain circumstances, along the whole boundary of the patch coinciding with the boundary of the domain. The results show that the use of this technique considerably improves the accuracy of the recovered stress field σ * and therefore the local effectivity of the ZZ error estimator. Copyright © 2006 John Wiley & Sons, Ltd. 相似文献
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用三坐标仪检测两圆柱轴线定向误差 总被引：2，自引：0，他引：2
三坐标测量仪通用测量软件可对两圆柱轴线定向误差进行检测,是一种新研制的快捷精确的测量方法,可广泛用于各类工件两圆柱轴线的平行度、垂直度及倾斜度误差检测,工件可任意摆放,对大型工件测量显得更方便。 相似文献
7.
TAEOH LEE HOON C. PARK SUNG W. LEE 《International journal for numerical methods in engineering》1997,40(6):1139-1160
A stress recovery technique is developed to extract more accurate nodal stress values from the raw stress values obtained directly from the finite element analysis. In the present method a stress field is assumed over a patch of elements, and a least-squares functional is formed using the discrete stress errors at the superconvergent stress points and the residual of the equilibrium equation expressed in the virtual work form. The results of numerical tests conducted on one-dimensional and two-dimensional example problems demonstrate the validity and effectiveness of the present method. The introduction of an equilibrium constraint allows a patch stress field of higher order than is possible without the equilibrium constraint and this leads to a recovered stress field of higher accuracy. Because the residual of equilibrium is expressed in the virtual work form, the proposed method can easily be applied to arbitrarily curved shell structures. © 1997 by John Wiley & Sons, Ltd. 相似文献
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Andrew J. Deeks John P. Wolf 《International journal for numerical methods in engineering》2002,54(4):557-583
The scaled boundary finite‐element method is a novel semi‐analytical technique, combining the advantages of the finite element and the boundary element methods with unique properties of its own. This paper develops a stress recovery procedure based on a modal interpretation of the scaled boundary finite‐element method solution process, using the superconvergent patch recovery technique. The recovered stresses are superconvergent, and are used to calculate a recovery‐type error estimator. A key feature of the procedure is the compatibility of the error estimator with the standard recovery‐type finite element estimator, allowing the scaled boundary finite‐element method to be compared directly with the finite element method for the first time. A plane strain problem for which an exact solution is available is presented, both to establish the accuracy of the proposed procedures, and to demonstrate the effectiveness of the scaled boundary finite‐element method. The scaled boundary finite‐element estimator is shown to predict the true error more closely than the equivalent finite element error estimator. Unlike their finite element counterparts, the stress recovery and error estimation techniques work well with unbounded domains and stress singularities. Copyright © 2002 John Wiley & Sons, Ltd. 相似文献
10.
M. Newman A. Safjan P. Popov D. C. Lagoudas 《International journal for numerical methods in engineering》2005,62(15):2053-2085
In this paper a new technique is introduced and applied in solving one‐dimensional linear and non‐linear wave‐type equations on an unbounded spatial domain. This new technique referred to as the non‐reflecting layer method (NRLM) extends the computational domain with an artificial layer on which a one‐way wave equation is solved. The method will be applied to compute stress waves in long rods consisting of NiTi shape memory alloy material subjected to impact loading and undergoing detwinning and pseudo‐elastic material responses. The NRLM has been tested on model problems and it has been found that the computed solutions agree well with the exact solutions, i.e. normalized error levels are in ranges acceptable for engineering computations. Copyright © 2005 John Wiley & Sons, Ltd. 相似文献
11.
J. J. Ródenas O. A. González‐Estrada J. E. Tarancón F. J. Fuenmayor 《International journal for numerical methods in engineering》2008,76(4):545-571
A new stress recovery procedure that provides accurate estimations of the discretization error for linear elastic fracture mechanic problems analyzed with the extended finite element method (XFEM) is presented. The procedure is an adaptation of the superconvergent patch recovery (SPR) technique for the XFEM framework. It is based on three fundamental aspects: (a) the use of a singular+smooth stress field decomposition technique involving the use of different recovery methods for each field: standard SPR for the smooth field and reconstruction of the recovered singular field using the stress intensity factor K for the singular field; (b) direct calculation of smoothed stresses at integration points using conjoint polynomial enhancement; and (c) assembly of patches with elements intersected by the crack using different stress interpolation polynomials at each side of the crack. The method was validated by testing it on problems with an exact solution in mode I, mode II, and mixed mode and on a problem without analytical solution. The results obtained showed the accuracy of the proposed error estimator. Copyright © 2008 John Wiley & Sons, Ltd. 相似文献
12.
C.-K. CHOI N.-H. LEE 《International journal for numerical methods in engineering》1996,39(9):1585-1606
An automated three-dimensional adaptive h-refinement strategy using the solid transition elements with variable midside nodes at edges and faces of the element is presented. The basic behaviour of these transition elements were improved by addition of associated non-conforming modes. By introducing these transition elements, some difficulties associated with imposing displacement constraints on irregular nodes to enforce interelement compatibility in the conventional adaptive h-refinement are easily overcome. A superconvergent patch recovery technique is also extended to three-dimensional problem. Numerical examples show the effectiveness of the proposed adaptive mesh refinement scheme using transition elements. 相似文献
13.
José M. Navarro-Jiménez Héctor Navarro-García Manuel Tur Juan J. Ródenas 《International journal for numerical methods in engineering》2020,121(6):1297-1313
The superconvergent patch recovery technique with constraints (SPR-C) consists in improving the accuracy of the recovered stresses obtained with the original SPR technique by considering known information about the exact solution, like the internal equilibrium equation, the compatibility equation or the Neumann boundary conditions, during the recovery process. In this paper the SPR-C is extended to consider the equilibrium around the contact area when solving contact problems with the Cartesian grid Finite Element Method. In the proposed method, the Finite Element stress fields of both bodies in contact are considered during the recovery process and the equilibrium is enforced by means of the continuity of tractions along the contact surface. 相似文献
14.
The performance of three different stress recovery procedures, namely, the superconvergent patch recovery technique (SPR), the recovery by equilibrium in patches (REP) and a combined method known as the LP procedure is reviewed. Different order of polynomials and various patch formation strategies have been employed in the numerical studies for the construction of smoothed stress fields. Two 2-D elastostatic problems of different characteristics are used to assess the behaviour of the stress recovery procedures. The numerical results obtained indicate that when the order of polynomial used in the recovery procedure is equal to that of the finite element analysis, the behaviours of all three recovery procedures are very similar and all of them are adequate to provide a reliable recovered stress field for error estimation. In case that the order of polynomial of the recovered stress is increased, the LP procedure seems to give a more stable recovery matrix and a more reliable recovered stress field than the REP procedure. © 1998 John Wiley & Sons, Ltd. 相似文献
15.
Isaac Harari Paul E. Barbone Michael Slavutin Rami Shalom 《International journal for numerical methods in engineering》1998,41(6):1105-1131
A novel approach to the development of infinite element formulations for exterior problems of time-harmonic acoustics is presented. This approach is based on a functional which provides a general framework for domain-based computation of exterior problems. Special cases include non-reflecting boundary conditions (such as the DtN method). A prominent feature of this formulation is the lack of integration over the unbounded domain, simplifying the task of discretization. The original formulation is generalized to account for derivative discontinuities across infinite element boundaries, typical of standard infinite element approximations. Continuity between finite elements and infinite elements is enforced weakly, precluding compatibility requirements. Various infinite element approximations for two-dimensional configurations with circular interfaces are presented. Implementation requirements are relatively simple. Numerical results demonstrate the good performance of this scheme. © 1998 John Wiley & Sons, Ltd. 相似文献
16.
Hoon Cheol Park Sahng‐Hoon Shin Sung W. Lee 《International journal for numerical methods in engineering》1999,45(9):1227-1242
An element‐base superconvergent stress recovery technique is developed for accurate boundary stress extraction. In the present method, higher‐order stress fields are assumed for all stress components and higher order elements are used for the construction of necessary matrices. Unknown coefficients for the assumed stress field are obtained by minimizing the sum of the stress errors and two equilibrium residuals in the least squares sense. The two residuals are derived based on the principle of virtual work. Numerical examples including a three‐dimensional problem have demonstrated that the present method can stably extract very accurate boundary stresses even for coarse meshes. Copyright © 1999 John Wiley & Sons, Ltd. 相似文献
17.
K. M. Liew S. Rajendran 《International journal for numerical methods in engineering》2002,54(8):1103-1130
The Gaussian quadrature points, which are generally observed to be the same as the Barlow points for lower order elements, have so far been used as the sampling points for the superconvergent patch recovery (SPR). Recent developments on the best‐fit method to calculate the optimal sampling points suggest that, for higher order elements, Barlow points need not be the optimal sampling points and also need not be the same as the Gaussian quadrature points. In this paper the best‐fit method is extended to predict the optimal points of the 8‐node serendipity rectangular element, and it is observed that best‐fit points do not exist. Next, a novel method is proposed, in which, the expressions for stress‐error based on the best‐fit are used in the least‐square fit of the patch recovery, and thereby the superconvergent points are obtained more directly. Application of this method to the 8‐node serendipity element reveals the existence of two sets of superconvergent points for patch recovery, one of which is the well‐known Gaussian points, ( ), and the other is the set of four points given by , the existence of which has not been known before. A detailed numerical study on the patch recovery of stresses for two demonstrative problems reveals that there indeed exist two sets of superconvergent points as predicted by the proposed method. The comparative performance of the two sets of points is tested for typical demonstrative problems and the results are discussed. Copyright © 2002 John Wiley & Sons, Ltd. 相似文献
18.
If the photoelastic model has a line of symmetry and is made from a stress frozen sheet, then it is shown how the isoclinics can be obtained from isochromatic measurements only. The accuracy is investigated with experimental examples. The method should have applications in transient problems and where the sandwich method is used. 相似文献
19.
Marc Duflot Stéphane Bordas 《International journal for numerical methods in engineering》2008,76(8):1123-1138
This contribution presents an extended global derivative recovery for enriched finite element methods (FEMs), such as the extended FEM along with an associated error indicator. Owing to its simplicity, the proposed scheme is ideally suited to industrial applications. The procedure is based on global minimization of the L2 norm of the difference between the raw strain field (C?1) and the recovered (C0) strain field. The methodology engineered in this paper extends the ideas of Oden and Brauchli (Int. J. Numer. Meth. Engng 1971; 3 ) and Hinton and Campbell (Int. J. Numer. Meth. Engng 1974; 8 ) by enriching the approximation used for the construction of the recovered derivatives (strains) with the gradients of the functions employed to enrich the approximation employed for the primal unknown (displacements). We show linear elastic fracture mechanics examples, both in simple two‐dimensional settings, and for a three‐dimensional structure. Numerically, we show that the effectivity index of the proposed indicator converges to unity upon mesh refinement. Consequently, the approximate error converges to the exact error, indicating that the error indicator is valid. Additionally, the numerical examples suggest a novel adaptive strategy for enriched approximations in which the dimensions of the enrichment zone are first increased, before standard h‐ and p‐adaptivities are applied; we suggest to coin this methodology e‐adaptivity. Copyright © 2008 John Wiley & Sons, Ltd. 相似文献
20.
David A. Field 《International journal for numerical methods in engineering》2000,47(4):887-906
This paper reviews geometric measures used to assess the shape of finite elements in two‐ and three‐dimensional meshes. Measures have been normalized and made scale invariant whenever possible. This paper also introduces a Universal Similarity Region that enhances comparisons of triangles and their measures. As a byproduct, the USR provides a dynamic way to compare improved triangular meshes. Copyright © 2000 John Wiley & Sons, Ltd. 相似文献