摘要:

AbstractA number of problems are analysed by the displacement method to assess the stress accuracy at very low compressibilities. ‘Parabolic’ isoparametric elements are used. It is found that the mean stress becomes grossly in error at the centre and edges of each element as the compressibility is reduced whereas the deviatoric stress components do not. All stress components retain good accuracy at the ‘reduced’ integration sampling points (2 × 2 Gauss). ‘Exact’ integration yields a similar stress distribution to ‘reduced’ but the mean stress is grossly in error at the integration points (3 × 3 Gauss). Exceptions, however, occur.These findings are interpreted, and a rule for predetermining whether or not accurate stresses can be obtained at the integrating points is suggested. Thus it is shown that the displacement method is suitable for analysing materials which for practical purposes are incompressible.A procedure is then presented for analysing porous media‐both linear and non‐linear‐by separating the stiffness into ‘effective’ and ‘pore fluid’ components. This allows excess pore pressure to be calculated explicitly. Applications to saturated soils are given which make use of the findings

ISSN:0029-5981    

DOI:10.1002/nme.1620080302

出版商:John Wiley&Sons, Ltd    

年代:1974

数据来源: WILEY

摘要:

AbstractThe concepts and potential advantages of local and global least squares smoothing of discontinuous finite element functions are introduced.The relationship between local smoothing and the ‘reduced’ integration' technique is established.Examples are presented to illustrate the application of the two smoothing techniques to the finite element stresses from several structural analysis problems.The paper concludes with some practical recommendations for discontinuous finite element function smooth

ISSN:0029-5981    

DOI:10.1002/nme.1620080303

出版商:John Wiley&Sons, Ltd    

年代:1974

数据来源: WILEY

摘要:

AbstractA finite element weighted residual process has been used to solve transient linear and non‐linear two‐dimensional heat conduction problems. Rectangular prisms in a space‐time domain were used as the finite elements. The weighting function was equal to the shape function defining the dependent variable approximation. The results are compared in tables with analytical, as well as other numerical data. The finite element method compared favourably with these results. It was found to be stable, convergent to the exact solution, easily programmed, and computationally fast. Finally, the method does not require constant parameters over the entire solution d

ISSN:0029-5981    

DOI:10.1002/nme.1620080304

出版商:John Wiley&Sons, Ltd    

年代:1974

数据来源: WILEY

摘要:

AbstractIn a two‐dimensional space of points on an equilateral triangle grid, a single difference equation holding at each node is found from the finite element formulation of the wave equation for all published polynomial orders of the functional expansion. Assuming homogeneous boundary conditions on any equilateral triangle whose edges and vertices pass through the grid points, the eigensolutions of the difference equation are found exactly and thus provide an excellent test problem for the programmer or engineer. The advantage of the present method over other formulations is that the number of linear operations required to produce the difference equation is minima

ISSN:0029-5981    

DOI:10.1002/nme.1620080305

出版商:John Wiley&Sons, Ltd    

年代:1974

数据来源: WILEY

摘要:

AbstractThis paper deals with solving the two‐dimensional variational problem for plate bending by the Ritz method using bicubic fundamental splines. It is a piecewise polynomial method, very adaptable to practical numerical computation, and can be an alternative for the well‐known Finite Element Meth

ISSN:0029-5981    

DOI:10.1002/nme.1620080306

出版商:John Wiley&Sons, Ltd    

年代:1974

数据来源: WILEY

摘要:

AbstractEdge displacement of assumed‐stress hybrid plate elements are commonly chosen as either linear, quadratic or cubic functions of the edge co‐ordinate. The present paper examines the effect of this choice on the acceptability, accuracy, and possible zero energy modes of elements based on a linear stress field. It is concluded that triangular elements may be preferable to quadrilaterals, and that linear edge displacements are not desira

ISSN:0029-5981    

DOI:10.1002/nme.1620080307

出版商:John Wiley&Sons, Ltd    

年代:1974

数据来源: WILEY

摘要:

AbstractTwo methods are presented for the automatic selection of a cycle basis leading to a sparse flexibility matrix for the analysis of rigid‐jointed skeletal structures.The first method having a local approach forms a maximal set of admissible minimal cycles, while the second having a global approach constructs admissible minimal cycles on the ordered chords of a shortest route tree. A cycle ordering algorithm is also given to reduce the band width of the corresponding flexibility matri

ISSN:0029-5981    

DOI:10.1002/nme.1620080308

出版商:John Wiley&Sons, Ltd    

年代:1974

数据来源: WILEY

摘要:

AbstractThe steady state flow problem known in magnetohydrodynamics as Hartmann's flow is converted into variational formulation and is given an approximate solution by means of the spline blended interpolation technique. The equations of motion consist of two coupled potential flow problems with homogeneous boundary conditions. The spline blended interpolation method is reduced here, because of the shape of the domain, to a cartesian product of cardinal splines with trigonometric or ordinary polynomials. ‘Exact’ boundary conditions are presented by the blending technique. The numerical results indicate that high accuracy is possible with relatively few unkno

ISSN:0029-5981    

DOI:10.1002/nme.1620080309

出版商:John Wiley&Sons, Ltd    

年代:1974

数据来源: WILEY

摘要:

AbstractThe development of a generalized quadrilateral finite element that includes a singular point at a corner node is presented. Inter‐element conformability is maintained so that monotone convergence is preserved. The global‐local concept of finite elements is used to formulate the complete set of equations. Examples of crack tip singularities are gi

ISSN:0029-5981    

DOI:10.1002/nme.1620080310

出版商:John Wiley&Sons, Ltd    

年代:1974

数据来源: WILEY

摘要:

AbstractThe triangular element is one of the most useful finite difference elements for the potential problems because of its versatility in fitting irregular boundary, in connecting one element type to another, and in changing grid fineness. Such triangular elements find many applications in conduction problems in cartesian co‐ordinates. This paper presents a new triangular element for the finite' difference solution of axisymmetric conduction problems in cylindrical co‐ordinates. Thevalidityof the proposed triangular element is analyzed, and itsworkabilityis demonstrated using three selected examples. Also, an industrial application highlights the advantageous characteristics of the triangular element, and gives a comparison with known results obtained by finite element met

ISSN:0029-5981    

DOI:10.1002/nme.1620080311

出版商:John Wiley&Sons, Ltd    

年代:1974

数据来源: WILEY