ISSN:0029-5981    

DOI:10.1002/nme.1620120802

出版商:John Wiley&Sons, Ltd    

年代:1978

数据来源: WILEY

摘要:

AbstractA direct variational method has been considered for solving mixed boundary value problems for linear elliptical equations. The main idea of the method consists in searching the unknown solution in a class of functions satisfying the differential equation and some of the boundary conditions. The functional to be minimized may be expressed in terms of the boundary values of the unknown solution, and thus the dimension of the variational problem is reduced. Reduction of the functional defined on the domain to a functional on its boundary corresponds to the common in the elsaticity theory of application of Clapeyron's theorem for the transformation of functionals of minimum elastic potential energy and complementary work. The reduced problem may be solved by the Ritz direct method. Some examples from the elasticity and seepage theories have been given to demonstrate the effectiveness of the method. Among the problems that have been solved by the method we may mention the plane elastic problem for a crack in a strip, three‐dimensional elastic problems for a plane rectangular crack in an infinite elastic medium and the problem of a rectangular die in sliding contact with an elastic half‐space (numerical solutions exhibit correct asymptotic behaviour in the neighbourhood of corners of cracks or die), and the plane and axisymmetric seepage probl

ISSN:0029-5981    

DOI:10.1002/nme.1620120803

出版商:John Wiley&Sons, Ltd    

年代:1978

数据来源: WILEY

摘要:

AbstractThe node Admittance matrices for Water Networks are normally sparse and symmetrical. Advantage may be taken of these properties to reduce the amount of computational time and memory required to solve them. Two node reordering algorithms and an economic system of storing input data are described. The node reordering algorithms minimize the number of fill‐ins which would occur in the solution of the node admittance matrix. Only non‐zero elements are stored and operated on. Subroutines for the node reordering algorithms and storge of input data, written in FORTRAN IV are inclu

ISSN:0029-5981    

DOI:10.1002/nme.1620120804

出版商:John Wiley&Sons, Ltd    

年代:1978

数据来源: WILEY

摘要:

AbstractA computer program for Water Network analysis has been developed usingy sparse matrix techniques for solution. The method used is the successive linearization method where the set of equations [Q]=[Y][H] is solved. In the process, two subroutines for node reordering to preserve sparsity of the Jacobian matrix and a subroutine for solving the matrix by the Doolittle method are included. The method is user oriented and requires a minimum amount of input data and effort. Networks of up to 200 nodes and 300 pipes may be analysed on an IBM 1130 computer with 16K words of memory.

ISSN:0029-5981    

DOI:10.1002/nme.1620120805

出版商:John Wiley&Sons, Ltd    

年代:1978

数据来源: WILEY

摘要:

AbstractA new procedure is presented for the analysis of geometrically non‐linear frame structures. It assumes small strains and uses ‘fictitious forces’ based on the rotation from the initial configuration. The procedure also uses total displacements rather than incremental displacements. The procedure is valid for rotation up to 180 degrees and converges in a relatively small number of itera

ISSN:0029-5981    

DOI:10.1002/nme.1620120806

出版商:John Wiley&Sons, Ltd    

年代:1978

数据来源: WILEY

摘要:

AbstractA superposition method, in which analytical and finite element solutions are combined through the variational principle, is presented for determining the three‐dimensional stress intensity factors of the through‐wall crack. Cumbersome volume integral due to the singular terms at the crack tip is carried on by applying the least squares methods to the results obtained by the Legendre‐Gauss quadrature. Several numerical calculations are made based on the present method, showing that the three‐dimensional effects cannot be neglected especially for the cases of larger Poisson's raito. The comparison of the present method with the other finite element methods proposed for determining the three‐dimensional stress intensity factors indicates that the former has the obvious superiority to the latters in respect to the numbers of elements and nodal points necessary to obtain reasonabl

ISSN:0029-5981    

DOI:10.1002/nme.1620120807

出版商:John Wiley&Sons, Ltd    

年代:1978

数据来源: WILEY

摘要:

AbstractThe paper develops an efficient free‐vibration analysis procedure of two‐dimensional structures. This is achieved by employing a discretization technique based on a recently developed concept of finite dynamic elements, involving higher order dynamic correction terms in the associated stiffness and inertia matrices. A plane rectangular dynamic element is developed in detail. Numerical solution results of free‐vibration analysis presented herein clearly indicate that these dynamic element combined with a suitable quadratic matrix eigenproblem solution technique effect a most economical and efficient solution for such an analysis when compared with the usual finite element m

ISSN:0029-5981    

DOI:10.1002/nme.1620120808

出版商:John Wiley&Sons, Ltd    

年代:1978

数据来源: WILEY

摘要:

AbstractSucessive Overrlaxation and Conjugate Gradients are used to solve the linear algebraic system set up with finite elements for the discretization of a plane, linear, head conducting problem. It is numerically shown that even with the optimal overrelaxation factor SOR is hardly superior to CG which is decisively simpler to program.

ISSN:0029-5981    

DOI:10.1002/nme.1620120809

出版商:John Wiley&Sons, Ltd    

年代:1978

数据来源: WILEY

摘要:

AbstractRecently1−3alternative methods of constructing triangular elements that reproduce strain singularities at crack‐tips have been suggested. The differences and similarities between the approaches are considered in this n

ISSN:0029-5981    

DOI:10.1002/nme.1620120810

出版商:John Wiley&Sons, Ltd    

年代:1978

数据来源: WILEY

摘要:

AbstractA finite difference perturbation scheme is developed which allows a simple solution to a wide class of non‐linear difurcation problems. The analysis shows that in order to determine the inital post bucking behaviour accurately, it is not necessary to solve more than the linear eigenvalue difference equation with similar accurac

ISSN:0029-5981    

DOI:10.1002/nme.1620120811

出版商:John Wiley&Sons, Ltd    

年代:1978

数据来源: WILEY