摘要:

AbstractSimple mixed models are developed for the geometrically nonlinear analysis of shells. A total Lagrangian description of the shell deformation is used, and the analytical formulation is based on a form of the nonlinear shallow shell theory with the effects of transverse shear deformation and bending‐extensional coupling included. The fundamental unknowns consist of eight stress resultants and five generalized displacements of the shell, and the element characteristic arrays are obtained by using the Hellinger‐Reissner mixed variational principle. The polynomial interpolation (or shape) functions used in approximating the stress resultants are, in general, of different degree than those used for approximating the generalized displacements. The stress resultants are discontinuous at the element boundaries and are eliminated on the element level.The equivalence and ‘near‐equivalence’ between the mixed models developed herein and displacement models based on reduced/selective integration of both transverse shear and extensional energy terms is discussed. The use of reduction methods in conjunction with the mixed models is outlined and the advantages of mixed models over displacement models are delineated. Analytic expressions are derived for the rigid‐body and spurious (or zero energy) models for the various mixed models and their equivalent displacement models. Also, the advantages of mixed models over equivalent displacement models are outlined. Numerical results are presented to demonstrate the high accuracy and effectiveness of the mixed models developed, and to compare their performance with other mixed models reported in the

ISSN:0029-5981    

DOI:10.1002/nme.1620181002

出版商:John Wiley&Sons, Ltd    

年代:1982

数据来源: WILEY

摘要:

AbstractHybrid stress elements are known to provide accurate results for analyses of plate bending; in particular, for the prediction of moment distribution. The construction of hybrid stiffness matrix requires numerical inversion of a moment matrix, evaluation of some relatively complicated boundary integrals and several matrix transformations. Each of these operations can be time‐consuming, and the matrix inversion can result in a loss of numerical accuracy.This paper devises methods to explicitly invert the moment matrices. We find that for triangular elements the inverse is independent of the element shape and is only inversely proportional to its size. We also use a novel set of displacement variables, which greatly simplifies the boundary integration. The displacement variables are chosen in a hierarchical form so that lower order elements can be determined by straightforward reduction of excess terms in a higher order element. Except for the nodal displacements at the vertices, the present approach involves only variables at the midpoints of the sides of an elemen

ISSN:0029-5981    

DOI:10.1002/nme.1620181003

出版商:John Wiley&Sons, Ltd    

年代:1982

数据来源: WILEY

摘要:

AbstractIt is known that the matrix force method has certain advantages over the displacement method for a class of structural problems. It is also known that the force method, when carried out by the conventional Gauss‐Jordan procedure, tends to fill in the problem data, making the method unattractive for large size, sparse problems. This poor fill‐in property, however, is not necessarily inherent to the method, and the sparsity may be maintained if one uses what we call the Turn‐BackLUProcedure. The purpose of this paper is two‐fold. First, it is shown that there exist some close relationships between the force method and the least squares problem, and that many existing algebraic procedures to perform the force method can be regarded as applications/extensions of certain well‐known matrix factorization schemes for the least squares problem. Secondly, it is demonstrated that these algebraic procedures for the force method can be unified form the matrix factorization viewpoint. Included in this unification is the Turn‐BackLUProcedure, which was originally proposed by Topçu in his thesis.8It is explained why this procedure tends to produce sparse and banded ‘self‐stress’ and flexibility matrices with small band width. Some computational results are presented to demonstrate the superiority of the Turn‐BackLUProcedure over the other schemes cons

ISSN:0029-5981    

DOI:10.1002/nme.1620181004

出版商:John Wiley&Sons, Ltd    

年代:1982

数据来源: WILEY

摘要:

AbstractA hybrid integral equation method is formulated to study the diffraction of oblique waves by an infinite cylinder. The water depth and the geometry of the floating cylinder are assumed to be uniform in they‐direction (one of the horizontal axes). Numerical discretization and integrations are performed in the vertical plane. Analytical solutions are used in far fields such that radiation boundary conditions are satisfied. Numerical results are obtained for the case of wave scattering by a floating rectangular cylinder in a constant water depth. The accuracy and efficiency of present method are compared with those obtained by other numerical technique

ISSN:0029-5981    

DOI:10.1002/nme.1620181005

出版商:John Wiley&Sons, Ltd    

年代:1982

数据来源: WILEY

摘要:

AbstractThe present paper deals with the theoretical and numerical treatment of dynamic unilateral problems. The governing equations are formulated as an equivalent variational inequality expressing D' Alembert's principle in its inequality form. The discretization with respect to time and space leads to a static nonlinear programming problem which is solved by an appropriate algorithm. Some properties of dynamic unilateral problems are outlined and the influence of several parameters on the solution is investigated by means of numerical examples.

ISSN:0029-5981    

DOI:10.1002/nme.1620181006

出版商:John Wiley&Sons, Ltd    

年代:1982

数据来源: WILEY

摘要:

AbstractThe eigenvalue economization process is an efficient way of reducing the size of eigenvalue problems to manageable proportions, at the expense of introducing approximations. The use of automatic criteria for selecting the slave variables to be eliminated has considerably eased the use of this technique recently. However, it is necessary to ensure that unacceptable errors are not introduced by the condensation process. Until recently, there has been little available to guide the user in estimating errors except past experience. In this paper, the errors introduced in the condensation process are considered theoretically, using an algebraic approach. This enables an absolute error bound to be stated, together with an approximate bound which can be very easily evaluated. Examples are given of the use of the approximate bound.

ISSN:0029-5981    

DOI:10.1002/nme.1620181007

出版商:John Wiley&Sons, Ltd    

年代:1982

数据来源: WILEY

摘要:

AbstractThe finite element solution of various partial differential equations leads to large linear equation systems, which may have a DBBF (double bounded band form) coefficient matrix, if periodicity conditions are taken into account. An efficient Fortran program solving such equation systems, developed for Control Data computers from the Cyber 70/170 series, utilizes the original block‐indexed approach to reduce input‐output time in communication with disc memory. Program performance is presented in some detail and quantitative comparison with other possible algorithms is carried out. An appendix lists the complete prog

ISSN:0029-5981    

DOI:10.1002/nme.1620181008

出版商:John Wiley&Sons, Ltd    

年代:1982

数据来源: WILEY

摘要:

AbstractThe problem of steady, two‐dimensional seepage from a nonsymmetric channel through a homogeneous porous medium underlain at a finite depth by a drain, is solved using the Baiocchi transformation and method. Because of the nonsymmetry in the problem, both free surfaces must be included in the solution domain of the problem. Thus, several interesting complexities are introduced into the solution of the problem. First, there are the two solution domain extensions (one across each free surface) and then the formulation of the new dependent variable throughout the extended solution domain. Secondly, the projection operator has two bounds in the numerical scheme. Finally, there are two compatibility conditions—one for the flowrate and one for the value of the new dependent variable at the left‐hand side free surface‐channel intersection. A secant method for the solution of two simultaneous nonlinear equations was used to obtain the values of these parameters. Results from the proposed method compared favourably with what few results were available in the lit

ISSN:0029-5981    

DOI:10.1002/nme.1620181009

出版商:John Wiley&Sons, Ltd    

年代:1982

数据来源: WILEY

摘要:

AbstractThe use of warping displacement functions for the torsional stiffness representation of beams with rectangular cross‐sections is studied. These functions can directly be employed in the displacement‐based formulation of Hermitian and isoparametric three‐dimensional beam elements for linear, elastic‐plastic or large displacement/large rotation analysis. the results of some studies are given to demonstrate the applicability and use of the proposed fu

ISSN:0029-5981    

DOI:10.1002/nme.1620181010

出版商:John Wiley&Sons, Ltd    

年代:1982

数据来源: WILEY

摘要:

AbstractWe report on a very effective program for uniform approximation of functions (or discrete data) by generalized rational functions of any number of variables over point sets so large that conventional methods are inapplicable. The points need not be arranged in a regular pattern, but if they are, the number of points is normally limited only by the computer time available. The program extends the differential correction algorithm discussed in an earlier article in this journal by combining it with a first Remes‐type exchange procedure, while retaining the flexibility and robustness of differential correction. Furthermore, this algorithm is guaranteed to converge in theory. Testing has shown that, even when the point set is small enough for differential correction to be applied directly, this algorithm is usually faster. We discuss the algorithm and program along with several numerical examples, one of which involves more than three million data points. A FORTRAN listing with illustrative output can be obtained from the first autho

ISSN:0029-5981    

DOI:10.1002/nme.1620181011

出版商:John Wiley&Sons, Ltd    

年代:1982

数据来源: WILEY