摘要:

AbstractWhen large, progressive, deformation occurs under plastic or visco‐plastic conditions, elastic deformations are negligible and the material flows in a viscous manner. The flow is non‐Newtonian and the viscosity is a function of the current strain rates. An effective numerical treatment of such non‐Newtonian flow by the finite element method is indicated here and is illustrated by examples of an extrusion process for which approximate slip line solutions are known.The methodology is extended to the solution of transient, quasi‐static situations and coupling with thermodynamic equations is discussed.A stream function formulation of the problem

ISSN:0029-5981    

DOI:10.1002/nme.1620080102

出版商:John Wiley&Sons, Ltd    

年代:1974

数据来源: WILEY

摘要:

AbstractThree variational statements for the slow time‐independent flow of a Navier‐Poisson fluid are derived. All of these statements are suitable as the bases of finite elements. The first statement is applied successfully to several flow situati

ISSN:0029-5981    

DOI:10.1002/nme.1620080103

出版商:John Wiley&Sons, Ltd    

年代:1974

数据来源: WILEY

摘要:

AbstractBody oriented co‐ordinates are defined for three‐dimensional regions bounded by six surfaces. From this definition of body oriented co‐ordinates, two transformations are derived:1Body oriented surface co‐ordinates to the Cartesian co‐ordinates, and2Body oriented co‐ordinates for a three‐dimensional region to Cartesian co‐ordinates.With these transformations a mesh generator is developed based on the principle that the mesh required to describe a region will be calculated according to the placement of the discrete points that describe the boundary edges. This is accomplished with two versions of the mesh generator: the surface generator and the volume generator. The surface generator maps the four boundaries of the surface onto the four boundaries of a unit square. Next, the interior points for the surface mesh are established in the mapped space. Then, using the first transformation, the co‐ordinates for the surface nodal points are calculated. Similarly, the volume generator maps the six surfaces of the body onto the surfaces of a unit cube, establishes the interior nodal points in the mapped space, and using the second transformation, calculates the co‐ordinates for the in

ISSN:0029-5981    

DOI:10.1002/nme.1620080104

出版商:John Wiley&Sons, Ltd    

年代:1974

数据来源: WILEY

摘要:

AbstractThis paper deals with a finite element formulation and solution of the boundary value problem of a concentrated force acting on a semi‐infinite micropolar solid. A stiffness matrix is derived for a flat micropolar rectangular element in a plane state and use is made of this element to solve the case of the semi‐infinite micropolar solid both in a state of plane stress and plane strain. An immediate application of the plane strain case is the important practical problem of a long line load acting on a soil mass which may be simulated as a micropolar b

ISSN:0029-5981    

DOI:10.1002/nme.1620080105

出版商:John Wiley&Sons, Ltd    

年代:1974

数据来源: WILEY

摘要:

AbstractThe finite element method is applied to dynamic linear viscoelastic analysis. The arising system of differential equations is integrated by means of the Laplace transformation. The direct numerical evaluation of the inversion integral seems to be appropriate in case of vibrational problems. The method is applied to examples of transient vibrations of elastic bodies. Initial conditions and arbitrary damping matrices can be considered.

ISSN:0029-5981    

DOI:10.1002/nme.1620080106

出版商:John Wiley&Sons, Ltd    

年代:1974

数据来源: WILEY

摘要:

AbstractBy use of the least squares error criterion, an alternate finite element formulation is presented. The method is based on the discrete or element‐wise minimization of square and weighted differential equation residuals which are expressed in terms of element nodal quantities. In order to overcome the stringent inter‐element continuity requirement, a major stumbling block, on the element trial functions two practical schemes are proposed. One is the reduction of the original governing differential equation to a system of equivalent first order differential equations; the other is a method of smoothing discontinous trial functions. The latter essentially relaxes the continuity requirement and yields efficient non‐conforming finite elements. This paper also demonstrates the use of constant weights which significantly improves the rates of convergence. Several numerical examples illustrate the proposed method. From these examples, it may be concluded that the use of constant weights and the relaxation of the inter‐element continuity requirement are two indispensable features of the weighted discrete least square

ISSN:0029-5981    

DOI:10.1002/nme.1620080107

出版商:John Wiley&Sons, Ltd    

年代:1974

数据来源: WILEY

摘要:

AbstractThis paper deals with the numerical solution of wave propagation problems in general although the primary area of interest is elastodynamics. The work is applicable to a variety of wave propagation phenomena of classical physics. Explicit schemes of Strang type are used, which allow many simplifications over existing methods. The Strang schemes allow in a very real but perhaps unexpected way the splitting of the elasticity operator.

ISSN:0029-5981    

DOI:10.1002/nme.1620080108

出版商:John Wiley&Sons, Ltd    

年代:1974

数据来源: WILEY

摘要:

AbstractThis paper discusses three numerical integration schemes connected with a finite element solution to the transient heat‐conduction equation. The main emphasis is on the achievable accuracy. A simple recurrence relation derived from the Galerkin process is suggested for the treatment of fast‐varying boundary conditions as being significantly better than the usual Crank‐Nicholson scheme in matters of short‐time a

ISSN:0029-5981    

DOI:10.1002/nme.1620080109

出版商:John Wiley&Sons, Ltd    

年代:1974

数据来源: WILEY

摘要:

AbstractThis paper presents an extension to the Matrix Transfer Method which gives quadratic convergence to a natural frequency from within a range on either side.The method is described and illustrated by application to:1A torsional vibration problem, and2A lumped mass beam vibration problem.

ISSN:0029-5981    

DOI:10.1002/nme.1620080110

出版商:John Wiley&Sons, Ltd    

年代:1974

数据来源: WILEY

摘要:

AbstractA direct method is described for the evaluation of the critical loads on deep circular arches having various forms of end support. The method is applicable to arches of non‐uniform flexural rigidity and may cater for arbitrary forms of applied load distribution. The results calculated for two examples are given, and compared with those obtained analytically and experimentally by other investigators. A complete listing of a computer program for one of the examples is provided in the Appendice

ISSN:0029-5981    

DOI:10.1002/nme.1620080111

出版商:John Wiley&Sons, Ltd    

年代:1974

数据来源: WILEY