摘要:

AbstractA variation of the Petrov–Galerkin method of solution of a partial differential equation is presented in which the weight function applied to the time derivative term of the transient convection–diffusion equation is different from the weight function applied to the special derivatives. This allows for the formulation of fourth‐order explicit and centred difference schemes. Comparison with analytic solutions show that these methods are able to capture steep wave fronts. The ability of the explicit method to capture wave fronts increases as the amount of convective transport incr

ISSN:0029-5981    

DOI:10.1002/nme.1620380202

出版商:John Wiley&Sons, Ltd    

年代:1995

数据来源: WILEY

摘要:

AbstractA computational procedure is presented for evaluating the sensitivity coefficients of the viscoplastic response of structures subjected to dynamic loading. A state of plane stress is assumed to exist in the structure, a velocity strain‐Cauchy stress formulation is used, and the geometric non‐linearities arising from large strains are incorporated. The Jaumann rate is used as a frame indifferent stress rate. The material model is chosen to be isothermal viscoplasticity, and an associated flow rule is used with a von Mises effective stress. The equations of motion emanating from a finite element semi‐discretization are integrated using an explicit central difference scheme with an implicit stress update. The sensitivity coefficients are evaluated using a direct differentiation approach. Since the domain of integration is the current configuration, the sensitivity coefficients of the spatial derivatives of the shape functions must be included. Numerical results are presented for a thin plate with a central circular cutout subjected to an in‐plane compressive loading. The sensitivity coefficients are generated by evaluating the derivatives of the response quantities with respect to Young's modulus, and two of the material parameters characterizing the viscoplastic response. Time histories of the response and sensitivity coefficients, and spatial distributions at selected times are pr

ISSN:0029-5981    

DOI:10.1002/nme.1620380203

出版商:John Wiley&Sons, Ltd    

年代:1995

数据来源: WILEY

摘要:

AbstractThis paper starts a sequence of three articles that follow an unconventional approach in finite element research. The ultimate objective is to construct high‐performance elements and element‐level error estimators for those elements. The approach takes off from our previous work in high‐performance elements and culminates with the development of finite element templates. The present paper concentrates on the patch test and evolved versions of the test that have played a key role in this research. Following a brief review of the historical roots, we present the Individual Element Test (IET) of Bergan and Hanssen in an expanded context that encompasses several important classes of new elements. The relationship of the IET to the multielement formsA,BandCof the patch test and to the single‐element test are investigated. An important consequence of the IET application is that the element stiffness equations decompose naturally into basic and higher‐order parts. The application of this decomposition to the “sanitization” of the non‐convergent BCIZ element is described and verified with numerical experiments. Two sequel papers in preparation are subtitled ‘the algebraic approach’ and ‘element‐level error estimation’. These apply the fundamental decomposition to the derivation of templates for specific mechanical elements and to the construction of element‐level err

ISSN:0029-5981    

DOI:10.1002/nme.1620380204

出版商:John Wiley&Sons, Ltd    

年代:1995

数据来源: WILEY

摘要:

AbstractChebyshev collocation techniques are developed in this paper to compute the eigenvalues of the Laplacian based on a boundary integral formulation for two‐dimensional domains with piecewise smooth boundaries. Unlike the traditional domain methods (for example, the finite element method) which discretizes the eigenfunctions on the two‐dimensional domain, only a one‐dimensional function defined on the boundary is discretized. Global expansions in terms of Chebyshev polynomials are used in each smooth piece of the boundary to solve the integral equation. Comparing with the boundary element method, this method obtains higher accuracy for a smaller discretized matrix. Finally, an efficient algorithm for generating the discretized matrix (say,n×n) is developed that requires onlyO(n2logn) oper

ISSN:0029-5981    

DOI:10.1002/nme.1620380205

出版商:John Wiley&Sons, Ltd    

年代:1995

数据来源: WILEY

摘要:

AbstractHierarchal elements are finite elements which have the useful property that elements with different polynomial orders can be used together in the same mesh without causing discontinuities. This paper introduces a new hierarchal triangular element in which the basis functions are constructed from orthogonal polynomials—Jacobi polynomials. The resulting element is shown to be better conditioned than the earlier hierarchal element of Rossow and Katz.1Recursive formulas allow the complete set of basis functions for an element to be efficiently evaluated at a given point. In addition, the formulas can be used to generate pre‐computed (universal) matrices. Examples are given of universal matrices, up to order 4, for the generalized Helmholtz equation. An electromagnetic problem involving a length of transmission line is used to show the usefulness of the new eleme

ISSN:0029-5981    

DOI:10.1002/nme.1620380206

出版商:John Wiley&Sons, Ltd    

年代:1995

数据来源: WILEY

摘要:

AbstractA computational methodology combining overlapping grid techniques with multigrid methods has been developed for three‐dimensional flow calculations in or around complex geometries. The computational accuracy, efficiency and capability of the present approach are investigated in this paper. The incompressible Navier–Stokes equations are discretized using a finite volume method on a semi‐staggered grid. The discrete problem is solved by a multigrid algorithm. Some numerical examples are chosen for evaluating numerical accuracy: (a) a straight pipe for which the exact solution is known; (b) curved pipes where previous experimental and numerical data are available; (c) an axisymmetric sudden expansion. The performance of the multigrid method on overlapping grids is assessed. Several cases of flows in stationary and time‐dependent complex geometries are given to demonstrate the capability and the potential of the methods that we

ISSN:0029-5981    

DOI:10.1002/nme.1620380207

出版商:John Wiley&Sons, Ltd    

年代:1995

数据来源: WILEY

摘要:

AbstractBased on a new generalized variational principle, a refined direct stiffness method (RDSM) which can be directly used to improve non‐conforming elements is proposed. The formulation is similar to that of the direct stiffness method (DSM), but the constraint condition of interelement continuity is satisfied in an average sense and as a result convergence and high accuracy are insured. The well‐known BCIZ nine‐parameter triangular thin plate bending element is refined by the RDSM to yield a new nine‐parameter thin plate bending element RT9. Numerical examples are presented to show that the present model passes the patch test and possesses high a

ISSN:0029-5981    

DOI:10.1002/nme.1620380208

出版商:John Wiley&Sons, Ltd    

年代:1995

数据来源: WILEY

摘要:

AbstractAn algorithm for optimal design of non‐linear shell structures is presented. The algorithm uses numerical optimization techniques and nonlinear finite element analysis to find a minimum weight structure subject to equilibrium conditions, stability constraints and displacement constraints. A barrier transformation is used to treat an apparent non‐smoothness arising from posing the stability constraints in terms of the eigenvalues of the Hessian of the potential energy of the structure. A sequential quadratic programming strategy is used to solve the resulting non‐linear optimization problem. Matrix sparsity in the constraint Jacobian is exploited because of the large number of variables. The usefulness of the proposed algorithm is demonstrated by minimizing the weight of a number of stiffened thin shell struc

ISSN:0029-5981    

DOI:10.1002/nme.1620380209

出版商:John Wiley&Sons, Ltd    

年代:1995

数据来源: WILEY

摘要:

AbstractIn this paper the extension of the dual boundary element method (DBEM) to the analysis of elastoplastic fracture mechanics (EPFM) problems is presented. The dual equations of the method are the displacement and the traction boundary integral equations. When the displacement equation is applied on one of the crack surfaces and the traction equation on the other, general mixed‐mode crack problems can be solved with a single‐region formulation. In order to avoid collocation at crack tips, crack kinks and crack‐edge corners, both crack surfaces are discretized with discontinuous quadratic boundary elements. The elastoplastic behaviour is modelled through the use of an approximation for the plastic component of the strain tensor on the region expected to yield. This region is discretized with internal quadratic, quadrilateral and/or triangular cells. This formulation was implemented for two‐dimensional domains only, although there is no theoretical or numerical limitation to its application to three‐dimensional ones. A centre‐cracked plate and a slant edge‐cracked plate subjected to tensile load are analysed and the results are compared with others available in the literature.J‐type integrals

ISSN:0029-5981    

DOI:10.1002/nme.1620380210

出版商:John Wiley&Sons, Ltd    

年代:1995

数据来源: WILEY

摘要:

AbstractThermocapillary‐induced and buoyancy‐driven convective flows that commonly occur in crystal growth are numerically simulated using Galerkin finite element method. The physical domain comprises of a open cavity with aspect ratio one and differentially heated vertical walls. The top gas–melt interface is free to deform subject to 90° contact angle boundary conditions at the two vertical walls. The unsteady two‐dimensional Navier–Stokes equations are discretized in time using Chorin‐type splitting scheme and pressure is determined from the Poisson's equation. The free surface is taken to be resting on vertical spines and its evolution in time is determined from the kinematic free surface equation. The governing equations for heat and momentum are solved in the Arbitrary Lagrangian Eulerian frame of reference to handle the moving boundary. The influence of Grashof number, Marangoni number, Bond number, Ohnesorge number and Prandtl number on the flow field and heat transfer is

ISSN:0029-5981    

DOI:10.1002/nme.1620380211

出版商:John Wiley&Sons, Ltd    

年代:1995

数据来源: WILEY