摘要:

AbstractThis is the first of two papers concerning superconvergent recovery techniques anda posteriorierror estimation. In this paper, a general recovery technique is developed for determining the derivatives (stresses) of the finite element solutions at nodes. The implementation of the recovery technique is simple and cost effective. The technique has been tested for a group of widely used linear, quadratic and cubic elements for both one and two dimensional problems. Numerical experiments demonstrate that the recovered nodal values of the derivatives with linear and cubic elements are superconvergent. One order higher accuracy is achieved by the procedure with linear and cubic elements but two order higher accuracy is achieved for the derivatives with quadratic elements. In particular, anO(h4) convergence of the nodal values of the derivatives for a quadratic triangular element is reported for the first time. The performance of the proposed technique is compared with the widely used smoothing procedure of globalL2projection and other methods. It is found that the derivatives recovered at interelement nodes, by usingL2projection, are also superconvergent for linear elements but not for quadratic elements. Numerical experiments on the convergence of the recovered solutions in the energy norm are also presented. Higher rates of convergence are again observed. The results presented in this part of the paper indicate clearly that a new, powerful and economical process is now available which should supersede the currently used post‐processing procedures applied in most code

ISSN:0029-5981    

DOI:10.1002/nme.1620330702

出版商:John Wiley&Sons, Ltd    

年代:1992

数据来源: WILEY

摘要:

AbstractIn this second part of the paper, the issue of a posteriori error estimation is discussed. In particular, we derive a theorem showing the dependence of the effectivity index for the Zienkiewicz–Zhu error estimator on the convergence rate of the recovered solution. This shows that with superconvergent recovery the effectivity index tends asymptotically to unity. The superconvergent recovery technique developed in the first part of the paper1is the used in the computation of the Zienkiewicz–Zhu error estimator to demonstrate accurate estimation of the exact error attainable. Numerical tests are shown for various element types illustrating the excellent effectivity of the error estimator in the energy norm and pointwise gradient (stress) error estimation. Several examples of the performance of the error estimator in adaptive mesh refinement are also presen

ISSN:0029-5981    

DOI:10.1002/nme.1620330703

出版商:John Wiley&Sons, Ltd    

年代:1992

数据来源: WILEY

摘要:

AbstractThe natural frequencies of simultaneously skewed and twisted cantilevered parallelepipeds are determined using the Ritz method. The present work is the first known three‐dimensional study of the problem. Assumed displacement functions are in the form of algebraic polynomials which satisfy the fixed face conditions exactly, and which are mathematically complete. Reasonably accurate natural frequencies are calculated for low aspect ratio, thick parallelepipeds having arbitrary degrees of twist and skewness. Detailed numerical studies show that a three‐dimensional analysis is essential in monitoring complicated coupled‐mode sensitivities in the variation of non‐dimensional natural frequencies with increasing skew and twist angles and thickness ratio. Results obtained using the present method are compared with those obtained in a detailed three‐dimensional finite element analysis, where the suitability and limitations of s‐version solid element discretizations are clearly

ISSN:0029-5981    

DOI:10.1002/nme.1620330704

出版商:John Wiley&Sons, Ltd    

年代:1992

数据来源: WILEY

摘要:

AbstractA class of ‘assumed strain’ mixed finite element methods for fully non‐linear problems in solid mechanics is presented which, when restricted to geometrically linear problems, encompasses the classical method of incompatible modes as a particular case. The method relies crucially on alocalmultiplicative decomposition of the deformation gradient into aconforming and an enhanced part, formulated in the context of a three‐field variational formulation. The resulting class of mixed methods provides a possible extension to the non‐linear regime of well‐known incompatible mode formulations. In addition, this class of methods includes non‐linear generalizations of recently proposed enhanced strain interpolations for axisymmetric problems whichcannot be interpretedas incompatible modes elements. The good performance of the proposed methodology is illustrated in a number of simulations including 2‐D, 3‐D and axisymmetric finite deformation problems in elasticity and elastoplasticity. Remarkably, these methods appear to be specially well suited for problems involving localization of the deformation, as illustrated in several n

ISSN:0029-5981    

DOI:10.1002/nme.1620330705

出版商:John Wiley&Sons, Ltd    

年代:1992

数据来源: WILEY

摘要:

AbstractNumerical analysis with the Boundary Element Method (BEM) has been used more and more in various engineering fields in recent years. In numerical techniques, however, there are some problems which have not been fully solved even now. The most essential one is the drop in the accuracy of results for internal points near the boundary of the structure, where the singularity of integrands in the boundary integral equation is too strong to be evaluated with the normal numerical method. For the boundary integral equation of stress, this problem became more serious, and the accuracy can be improved only partly, even though very refined boundary elements are used.In this paper, the boundary integral equation is newly formulated using a relative quantity of displacement. In this way, the singularity of boundary integrals is reduced by the order of 1/r, and the accuracy of solution is improved significantly. Furthermore, in order to integrate it more accurately, two kinds of numerical integral methods are newly developed. By using these methods, both displacement and stress can be obtained with excellent accuracy at almost any point in the structure without any numerical difficulty, although the discretization may be comparatively coarse. The generality and practicability of the present formulation and integral methods are confirmed through some examples of three dimensional elastic problems.

ISSN:0029-5981    

DOI:10.1002/nme.1620330706

出版商:John Wiley&Sons, Ltd    

年代:1992

数据来源: WILEY

摘要:

AbstractThe performance of three iterative methods, local SOR, preconditioned generalized conjugate gradient methods such as ORTHOMIN(1) and the GCG–LS method with preconditioning matrices derived by incomplete (modified and unmodified) pointwise factorizations of the matrix corresponding to implicit finite difference schemes for the 2‐D Navier–Stokes equations, is compared. The relative merits of these methods in terms of CPU time, average number of iterations with respect to the Reynolds number and discretization parameters are empha

ISSN:0029-5981    

DOI:10.1002/nme.1620330707

出版商:John Wiley&Sons, Ltd    

年代:1992

数据来源: WILEY

摘要:

AbstractThis paper presents the derivation of the non‐singular integral representation of stresses in two‐ and three‐dimensional elastostatics. In contrast to the strongly singular and weakly singular integral representations, the numerical computation of the nearly singular integrals is eliminated because all the integrands are made finite in this new formulation even if the internal point approaches the boundary. Thus the method gives accurate numerical results even in that portion of a solid which is very close to a discretized boundary. Three test problems are analysed in which we present a comparison of the accuracies achieved by the numerical computations based on the use of strongly singular, weakly singular and non‐singular integral representations of s

ISSN:0029-5981    

DOI:10.1002/nme.1620330708

出版商:John Wiley&Sons, Ltd    

年代:1992

数据来源: WILEY

摘要:

AbstractFlow and pressure transients in single‐phase liquid‐filled closed pipes (i.e. waterhammer) are described by quasi‐linear hyperbolic partial differential equations for which the preferred solution technique is the Method of Characteristics. However, this is not appropriate for control and stability analyses where a lumped‐parameter single independent variable (i.e. time) model is preferred, using, intentionally or otherwise, the Method of Lines (or partial discretization). By empirical comparison of this with Method of Characteristics time‐domain simulation, it has been found that certain implementations introduce avoidable numerical errors or even instabilities. Four aspects have been investigated:(i)the dependent variables have often been taken as the original primitive variables but Riemann or Allievi characteristic variables are preferable;(ii)for the waterhammer hyperbolic equations at least, a first‐order discrete space interpolating polynomial represents the underlying physics better than higher‐order approximations;(iii)terms in which finite‐differences are used to represent quantities which are integrals rather than derivatives, in particular pipe friction, may introduce numerical instability and require particular care;(iv)for time‐domain simulation, first‐order Euler integration is more accurate than higher‐order methods which introduce errors by violating the hyperbolic equation

ISSN:0029-5981    

DOI:10.1002/nme.1620330709

出版商:John Wiley&Sons, Ltd    

年代:1992

数据来源: WILEY

摘要:

AbstractA boundary integral equation formulation for the analysis of two‐dimensional elastic contact problems with friction is developed. In this formulation, the contact equations are written explicitly with both tractions and displacements retained as unknowns. These equations are arranged such that a blocked coefficient matrix results. An incremental and iterative procedure is discussed which, in the case of proportional loading, modifies only the equations in the potential contact zon

ISSN:0029-5981    

DOI:10.1002/nme.1620330710

出版商:John Wiley&Sons, Ltd    

年代:1992

数据来源: WILEY

摘要:

AbstractThis paper gives solutions to various frictionless and frictional contact problems using the boundary integral formulation developed in Part 1. A range of problems is considered in order to demonstrate the applicability of the approach. In most cases equal size linear elements are found to give best results. In the case of frictional problems the arrangement of strick‐slip zones is affected by the node locations and a relatively large number of elements may be required to produce satisfactory results. In all cases, the boundary integral equation method yields numerical solutions that are in very good agreement with the analytical solutions to which they are compare

ISSN:0029-5981    

DOI:10.1002/nme.1620330711

出版商:John Wiley&Sons, Ltd    

年代:1992

数据来源: WILEY