摘要:

AbstractA new numerical technique has been developed for the analysis of two‐dimensional transient solidification processes in the presence of time‐dependent natural convection in the melt. The method can cope with irregular, transient morphologies of the solid—liquid interface using a new Galerkin formulation for the energy balance on the solid—liquid interface. The finite element solution to the Galerkin formulation yields the displacement of individual nodes on the solid—liquid interface. The displacement of the nodes is expressed by uncoupled components in thexandydirections.The fluid flow problem was solved using a ‘penalty’ formulation. Numerical experiments were performed for Rayleigh numbers as high as 106to demonstrate the method and to indicate the effect of natural convection on the solid—liquid inter

ISSN:0029-5981    

DOI:10.1002/nme.1620231002

出版商:John Wiley&Sons, Ltd    

年代:1986

数据来源: WILEY

摘要:

AbstractThe accuracies of the computed temperatures of a liquid in a corner region under freezing conditions are compared for various fixed‐grid finite element techniques using the analytical solution for this problem as a reference.In the finite element formulation of the problem different time‐stepping schemes are compared: the implicit Euler‐backward algorithm combined with an iterative scheme and two three‐time‐level methods—the Lees algorithm and a Dupont algorithm, which are both applied as non‐iterative schemes.Furthermore, different methods for handling the evolution of latent heat are examined: an approximation method suggested by Lemmon and one suggested by Del Giudice, both using the enthalpy formulation as well as a fictitious heat‐flow method presented by Rolph and Bathe.Results of calculations performed with the consistent heat‐capacity matrix are compared with those performed with a lumped hea

ISSN:0029-5981    

DOI:10.1002/nme.1620231003

出版商:John Wiley&Sons, Ltd    

年代:1986

数据来源: WILEY

摘要:

AbstractThe probabilistic finite element method (PFEM) is formulated for linear and non‐linear continua with inhomogeneous random fields. Analogous to the discretization of the displacement field in finite element methods, the random field is also discretized. The formulation is simplified by transforming the correlated variables to a set of uncorrelated variables through an eigenvalue orthogonalization. Furthermore, it is shown that a reduced set of the uncorrelated variables is sufficient for the second‐moment analysis. Based on the linear formulation of the PFEM, the method is then extended to transient analysis in non‐linear continua.The accuracy and efficiency of the method is demonstrated by application to a one‐dimensional, elastic/plastic wave propagation problem and a two‐dimensional plane‐stress beam bending problem. The moments calculated compare favourably with those obtained by Monte Carlo simulation. Also, the procedure is amenable to implementation in deterministic FEM based comput

ISSN:0029-5981    

DOI:10.1002/nme.1620231004

出版商:John Wiley&Sons, Ltd    

年代:1986

数据来源: WILEY

摘要:

AbstractElastic—plastic anti‐plane strain problems can be solved by using FEM programs developed for plane stress. The technique does not involve any manipulations with the FEM code, but is merely a matter of specialization and of translation of notation. Two analytically solvable cases are chosen for demonstrat

ISSN:0029-5981    

DOI:10.1002/nme.1620231005

出版商:John Wiley&Sons, Ltd    

年代:1986

数据来源: WILEY

摘要:

AbstractIn this paper Kron's primitive composite system matrix is shown to be reducible to a symmetric indefinite matrix. This matrix, although never formed explicitly, can then be transformed to a tridiagonal matrix of reduced order by the Lanczos algorithm. Eigenvalue solutions of this partially tridiagonalized matrix give very good approximations to the eigenvalues of the composite system. The method has multiplication counts which are over 90 per cent lower than when the (condensed) Kron matrix is solved by the Newton‐Raphson iteration applied to the Kron scalar equation. Numerical examples illustrating the Kron‐Lanczos method when solving for the natural frequencies of frames with large numbers of degrees of freedom are presen

ISSN:0029-5981    

DOI:10.1002/nme.1620231006

出版商:John Wiley&Sons, Ltd    

年代:1986

数据来源: WILEY

摘要:

AbstractThis paper presents a simple extension of the patch test to mixed formulations to provide the necessary and sufficient conditions for convergence. The general algebraic conditions of Babuska and Brezzi are given a simple form and a conceptual application of the patch tests serves to point out the instability of several well known formulations for incompressible problems. The test is also applied to mixed displacement—strain formulations of elasticity, and limiting formulations are note

ISSN:0029-5981    

DOI:10.1002/nme.1620231007

出版商:John Wiley&Sons, Ltd    

年代:1986

数据来源: WILEY

摘要:

AbstractIn this work, we present a critical comparison of two basic ways of implementing the boundary element method in three‐dimensional elastostatics. The first way is by using non‐conforming elements, i.e. elements which have the collocation nodes removed from their perimeter. The number of nodes used for the collocation of the boundary tractions and displacements need not coincide with the number of nodes placed along the perimeter of the element for the purpose of describing the geometry. The second way is by placing the collocation nodes along the perimeter of the element, usually in coincidence with the geometry nodes. Thus, interelement continuity of the displacements is obtained. The basic reasons for the use of non‐conforming elements in the boundary element method are twofold. First, simplification in the assembly and solution of the system equations and, secondly, easy computation of the ‘free’ and Cauchy principal value terms appearing in the integral equations. The state of the art in the boundary element method, however, has advanced in the last decade to the point where both of the aforementioned reasons are no longer problematic. As will be shown in what follows, conforming elements are able to produce more accurate results than non‐conforming ones with substantial economy in the final size of the syste

ISSN:0029-5981    

DOI:10.1002/nme.1620231008

出版商:John Wiley&Sons, Ltd    

年代:1986

数据来源: WILEY

摘要:

AbstractA frontwidth reduction algorithm is presented with an execution time which may be traded against its primary memory requirement, making it possible to optimize the performance of the algorithm on a particular computer. With an amount of primary memoryO(E1/2), whereEis the number of elements, the execution time of the algorithm isO(E3/2), in two or three dimensions. The algorithm has two parts: first, new node‐based data structures are derived from the conventional element list, then these structures are used to reorder the elements for reduced frontwidt

ISSN:0029-5981    

DOI:10.1002/nme.1620231009

出版商:John Wiley&Sons, Ltd    

年代:1986

数据来源: WILEY

摘要:

AbstractFinite element and boundary element methods are described for predicting high‐frequency electromagnetic heating of tissue as a cancer therapy. For the class of clinical problems of interest, the patient is electrically inhomogeneous and best discretized by finite elements, but the unbounded nature of practical source configurations calls for a boundary element approach. A hybrid is introduced which couples the two methods and is superior in algebraic requirements to either method alone. The formulation is three‐dimensional and allows exact satisfaction of the electromagnetic jump conditions at interfaces separating distinct tissue types. Test cases show its validity for transverse magnetic and electric situations with known solutions. Examples of clinical applications are sh

ISSN:0029-5981    

DOI:10.1002/nme.1620231010

出版商:John Wiley&Sons, Ltd    

年代:1986

数据来源: WILEY

摘要:

AbstractThis paper introduces a general theory for the derivation of the shape functions for the quadrilateral family of finite elements. The first section deals with the Lagrangian shape functions for the cases of uniform and boundary‐described elements. Two basic procedures are introduced; the first by linear combinations of side‐interpolations and the second by superposition. The remainder of the paper introduces a theory for the general uniform Hermitian element of any order. Details for quadrilateral elements, with first order derivatives are explained. All of the shape functions presented here were derived in the interval [0,1].The shape functions, developed by such an engineering approach, have been used successfully in the ABSEA Finite Element System of Cranfield Institute of Technol

ISSN:0029-5981    

DOI:10.1002/nme.1620231011

出版商:John Wiley&Sons, Ltd    

年代:1986

数据来源: WILEY