摘要:

AbstractThe object of this paper is to describe a new algorithm for the semi‐automatic triangulation of arbitrary, multiply connected planar domains. The strategy is based upon a modification of a finite element mesh genration algorithm recently developed.1The scheme is designed for maximum flexibility and is capable of generating meshes of triangular elements for the decomposition of virtually any multiply connected planar domain. Moreover, the desired density of elements in various regions of the problem domain is specified by the user, thus allowing him to obtain a mesh decomposition appropriate to the physical loading and/or boundary conditions of the particular problem at hand. Several examples are presented to illustrate the applicability of the algorithm. An extension of the algorithm to the triangulation of shell structures is indicate

ISSN:0029-5981    

DOI:10.1002/nme.1620080402

出版商:John Wiley&Sons, Ltd    

年代:1974

数据来源: WILEY

摘要:

AbstractIt is shown how the elasticity equations can be formulated in terms of a general procedure of abstract analysis, called the projective method, for constructing an approximate solution. This allows the many studies of convergence and uniqueness of solutions which have been made in modern mathematics to be applied to the elasticity problem. The abstract formulation also suggests an organizational scheme for generating a computer code. A computer code for hollow or solid cylinders of arbitrary cross section was developed and several numerical examples are presented. The procedure is computationally advantageous for the class of problems under consideration because of the relatively small number of equations that must be solved as compared to the finite element method. The results presented demonstrate the accuracy of the method.

ISSN:0029-5981    

DOI:10.1002/nme.1620080403

出版商:John Wiley&Sons, Ltd    

年代:1974

数据来源: WILEY

摘要:

AbstractA characteristic feature of the variational functionals for several boundary value problems in polar co‐ordinates is the fact that one independent variable occurs explicitly in the denominator. Therefore, the coefficients of the finite element equations for sectors of circular ring shaped elements are not constants but functions of the distance of the elements from the origin of co‐ordinates.1We name them coefficient functions. In order to show the particular aspects of the calculations in terms of polar co‐ordinates we deal here with the solution of the torsion problem by bilinear and bicubic Hermitian interpolation.The finite element equations are arranged according to Schaefer2in the form of block which can easily be transformed into ‘stars’3or molecules4,5similar to those used in finite difference methods. The origin of co‐ordinates requires a special consideration, firstly because of the coincidence of several nodes at that point and secondly because of the divergent behaviour of some coefficient functions. It turns out to be advantageous for the numerical calculations to expand the coefficient functions in power series. Besides, the expansions are required to deduce the equations for rectangular elements by limiting processes. The twisting moments and shearing stresses calculated for several cross sections illustrate the numerical suitability of the method. The finite element values are compared partly with exact solutions and partly with experimental results obtained by a moiré method using Prandtl's soap film analogy.6Finally it is shown how the accuracy of the finite element values can be improved by the Richardson ex

ISSN:0029-5981    

DOI:10.1002/nme.1620080404

出版商:John Wiley&Sons, Ltd    

年代:1974

数据来源: WILEY

摘要:

AbstractA polynomial shape function of triangular elements for finite element analysis of general deformation of sheet metals with or without orthotropic anisotropy is proposed. And general formulation for large deformation and large strain analysis with non‐linearity of material property, say plasticity, is given. Some numerical examples are examined with respect to hydraulic bulgin

ISSN:0029-5981    

DOI:10.1002/nme.1620080405

出版商:John Wiley&Sons, Ltd    

年代:1974

数据来源: WILEY

摘要:

AbstractThediscrete (Legendre) orthogonal polynomials, (DLOP's) are useful for approximation purposes. This set ofmth degree polynomials {Pm(K,N)} are orthogonal with unity weight over a uniform discrete interval and are completely determined by the normalizationPm(O,N) = 1. The authors are employing these polynomials as assumed modes in engineering applications of weighted residual methods. Since extensive material on these discrete orthogonal polynomials, and their properties, is not readily available, this paper is designed to unify and summarize the presently available information on the DLOP's and related polynomials. In so doing, many new properties have been derived. These properties, along with sketches of their derivation, are included. Also presented are a representation of the DLOP's as a product of vectors and matrices, and an efficient computational scheme for generating these polynomials.

ISSN:0029-5981    

DOI:10.1002/nme.1620080406

出版商:John Wiley&Sons, Ltd    

年代:1974

数据来源: WILEY

摘要:

AbstractThe steady two‐dimensional, viscous, electrically conducting flow around a circular cylinder is investigated. The flow and magnetic field are uniform and parallel at large distances from the cylinder. The equations and boundary conditions are derived for arbitrary values ofR,Rmand β, whereRis the Reynolds number,Rmthe magnetic Reynolds number and β, the ratio of the square of the Alfvén speed to the square of the main stream speed. Because of the large number of parameters involved, the numerical solution is restricted toR= 40,Rm= 1 and infinity and 0 ⩽ β ⩽ 4. Also the cylinder is taken to be a perfect conductor, this avoids having to compute the magnetic field within the cylinder.The numerical computations for the non‐magnetic case, i.e. β = 0, are presented and are found to be in good agreement with existing results. The effect of increasing the strength of the magnetic field (i.e. increasing β) on the drag coefficient, the size and position of the standing vortex and the increasing effect of the upstream propagation of disturbances

ISSN:0029-5981    

DOI:10.1002/nme.1620080407

出版商:John Wiley&Sons, Ltd    

年代:1974

数据来源: WILEY

摘要:

AbstractThe patch test is shown to be contained in the variational formulations of the finite element methods at the assembling level, all of which require the vanishing of the virtual work of interface connection loads. By a systematic introduction of stress generating functions, attention is drawn to the fact that any given finite element model can be assembled in two different ways: either by identification of a set of boundary displacements (leading to the direct stiffness method), or by identification of a set of local stress function values (leading to the dual direct flexibility method). Looking at any conjugate couple (generalized displacement‐generalized surface traction) at an interface, one is strongly transmitted, the other weakly. Discretization of the zero virtual work condition at an interface of plate bending models, by means of Legendre polynomial expansions, allows a systematic construction of so‐called ‘non‐conforming’ elements that pass the patch test. They are in fact identified with weakly conforming, but strongly diffusive, hybrids, and the lowest degree element (quadratic) is in fact the Morley constant‐moment element. Examples are given for higher degree displacement fields.The case of plate stretching elements can be handled by duality, the difficulties being here associated with the requirements for diffusivity. Non‐diffusive elements that pass the zero interface virtual work test can be constructed systematically and are identifiable with weakly diffusive, but strongly conforming, hybrids of the type first proposed by

ISSN:0029-5981    

DOI:10.1002/nme.1620080408

出版商:John Wiley&Sons, Ltd    

年代:1974

数据来源: WILEY

摘要:

AbstractThe elastoplastic deformation of spherical shells of uniform thickness acted upon by external pressure is investigated in this paper. A deformation theory of plasticity is combined with the classical elasticity equations and a solution is obtained by the method of successive elastic solutions. A logarithmic effective stress‐effective plastic strain diagram is used to determine the volume change for thick polypropylene spheres under the action of external pressure. These results are compared with previously published experimental volume changes in polypropylene spheres. This comparison shows that the predicted volume changes are similar to the experimental result

ISSN:0029-5981    

DOI:10.1002/nme.1620080409

出版商:John Wiley&Sons, Ltd    

年代:1974

数据来源: WILEY

摘要:

AbstractWe describe a finite element method for the one‐dimensional Stefan problem. The elements are quadrilaterals of the space‐time plane which are determined at each time‐step in relation with the position of the free boundary. The method appears as a generalization of the classical Crank‐Nicolson scheme, since it is identical to this scheme in the case of rectangular elements; it has the advantage of providing a simple and accurate determination of the free boundary. Numerical experiments show that the order of accuracy is equ

ISSN:0029-5981    

DOI:10.1002/nme.1620080410

出版商:John Wiley&Sons, Ltd    

年代:1974

数据来源: WILEY

摘要:

AbstractThe visco‐plastic model of material behaviour is of much practical interest in its own right and initial strain techniques for its solution have been developed and proved efficient. More important however is the fact that the visco‐plastic model can be used to generate plasticity solutions in a simple manner when stationary conditions are reached and, at the other extreme, can reproduce standard creep phenomena. Used in this sense it allows the treatment of non‐associated plasticity and strain softening situations which present difficulties in conventional plasticity approaches. A standard programme thus allows the treatment of a wide range of materially non‐linear problems.The paper discusses various applications of the new general formulation and introduces certain numerical information on solution st

ISSN:0029-5981    

DOI:10.1002/nme.1620080411

出版商:John Wiley&Sons, Ltd    

年代:1974

数据来源: WILEY