摘要:

AbstractA numerical technique for solving unsteady gas dynamic equations is presented. The technique is based onleast squares finite elementconcepts with elements that are constructed in both space and time. Both linear and quadratic interpolation is used on individual elements. The technique is tested against a problem whose solution is known so that numerical accuracy can be ascertained.

ISSN:0029-5981    

DOI:10.1002/nme.1620120102

出版商:John Wiley&Sons, Ltd    

年代:1978

数据来源: WILEY

摘要:

AbstractThe discretization of the media at all spatial co‐ordinates but one is presented here. This partial discretization leads to continuous finite elements as opposed to fully discrete ones and the problem resolves, for the cases presented here, into a set of linear differential equations rather than algebraic equations. The general problem of first derivative functionals in elastostatics is considered and it is shown, in general, how the continuous finite elements required for the solution may be obtained. Plane states, axisymmetric and three‐dimensional continuous elements are obtained to illustrate application to particular cases.Different methods of solution for the set of differential equations are discussed and it is shown that several existing and widely used finite element related techniques are particular cases of this local partial discretization. Three numerical examples are solved to demonstrate the good comparison obtained between the numerical and the exact solutions. The semi‐infinite examples included also illustrate the treatment of these types of problems without the use of fictitious bound

ISSN:0029-5981    

DOI:10.1002/nme.1620120103

出版商:John Wiley&Sons, Ltd    

年代:1978

数据来源: WILEY

摘要:

AbstractFormulation of a transition element is presented. Such an element makes it possible to match one element with two elements side‐by‐side. A modified quadrature formula is used to numerically integrate discontinuous functions in the expression of the stiffness matrix. Numerical examples show the applicability of the elem

ISSN:0029-5981    

DOI:10.1002/nme.1620120104

出版商:John Wiley&Sons, Ltd    

年代:1978

数据来源: WILEY

摘要:

AbstractA viscous approximation for steady creeping flow is extended to include the effect of elastic strains. Two examples are presented which illustrate both the method and the need for including elastic strains in the analysis of steady‐state visco‐plastic fl

ISSN:0029-5981    

DOI:10.1002/nme.1620120105

出版商:John Wiley&Sons, Ltd    

年代:1978

数据来源: WILEY

摘要:

AbstractThis note presents the closed form equations for the stiffness terms in the elastic‐plastic stiffness matrix for axisymmetric finite elements. The element considered is a triangular ring element characterized by linear displacement relationships and an averaged state of stress. The physical law is modelled by the incremental theory of plasticity utilizing the Prandtl‐Reuss flow rule and von‐Mises Yield Criterion. Results are presented comparing stiffness terms as computed by numerical integration to those computed from the closed form equations. Significant errors in stiffness terms arising from numerical integration are observed for axisymmetric elements located near the line of axial symmetry as a result of the logarithmic nature of some of the stiffness

ISSN:0029-5981    

DOI:10.1002/nme.1620120106

出版商:John Wiley&Sons, Ltd    

年代:1978

数据来源: WILEY

摘要:

AbstractFor a wide calss of finite element matrices integrated numerically rather than exactly, a definable number of sampling points is found to be sufficient for keeping their theoretical properties unchanged. A systematic criterion limiting the number of possible point configurations for numerical quadrature formulas on triangles is established. Some new high order formulas are presented. Tables containing optional formulas with respect to minimum number of sampling points and required degrees of accuracy are given. They are arranged so as to assist with selection of suitable quadrature formulas for finite element computer programming.

ISSN:0029-5981    

DOI:10.1002/nme.1620120107

出版商:John Wiley&Sons, Ltd    

年代:1978

数据来源: WILEY

摘要:

AbstractBlending function interpolants on rectangular elements are used to construct an overall interpolant which exactly matches function and normal derivative on the perimeter of a rectangular region. This overall interpolant is incorporated into the Ritz‐Galerkin version of the finite element method and a test problem involving the biharmonic equation is solved. The numerical results obtained demonstrate the considerable increase in accuracy of the exact boundary methods as compared with the usual method using interpolated boundary conditions. A similar investigation of second order elliptic problems with Dirichlet boundary conditions where the rectangular region is divided up into triangular elements yields the perhaps surprising result that blended interpolants on triangular elements do not necessarily improve the accuracy of the Ritz‐Galekin version of the Finite Element Met

ISSN:0029-5981    

DOI:10.1002/nme.1620120108

出版商:John Wiley&Sons, Ltd    

年代:1978

数据来源: WILEY

摘要:

AbstractThe compressible potential flow on a blade‐to‐blade surface of a turbomachine is analysed using the Thomas algorithm. The numerical properties of resulting non‐linear simultaneous equations are studied with respect to grid aspect ratios and convergence. The heuristic approach has established which are the important factors that affect the flow solution in typical blade‐to‐blade confi

ISSN:0029-5981    

DOI:10.1002/nme.1620120109

出版商:John Wiley&Sons, Ltd    

年代:1978

数据来源: WILEY

摘要:

AbstractThis note describes improvements to the Suhara‐Fukuda method for generating a triangular finite element network. These are based on the use of a node generation procedure which distributes nodes is a regular pattern across the network area and is sufficiently flexible to permit any variation in element density. Because of the regular node distribution, poorly shaped elements will not arise and so the procedure for connecting the nodes to form elements can be simplified. Examples of networks generaed in this way are give

ISSN:0029-5981    

DOI:10.1002/nme.1620120110

出版商:John Wiley&Sons, Ltd    

年代:1978

数据来源: WILEY

摘要:

AbstractA finite element formulation for large elasto‐plastic deformation of polycrystalline materials is proposed in incremental form. The effect of rotation of crystal axes besides usual element rotaion is taken into account. Some numerical considerations on polycrystalline plasticity (i.e. stress‐strain curves for several proportional loadings, effect of change of loading path on stress‐strain curve, subsequent yield loci for uniaxial and equi‐biaxial loadings and so forth) are given for the case of small deformation by using a plate model which consists of 121 square FCC c

ISSN:0029-5981    

DOI:10.1002/nme.1620120111

出版商:John Wiley&Sons, Ltd    

年代:1978

数据来源: WILEY