摘要:

AbstractThe calculation of the response of rotationally periodic structures to transient forces and prescribed motions is considered. The work extends the work previously described by Thomas1in which only the free and harmonic forced vibration problems were considered. It is assumed that the finite element method is to be used, so that the equation of motion of the structure contains a finite number of degrees‐of‐freedom whose responses are governed by mass, stiffness and damping matrices. It is shown that an exact solution to the equation of motion of the idealized full structure can be obtained by solving the equation of motion of a single substructure for a number of different spatial Fourier harmonics of force (and hence response). A modal method of solving this equation is described. a brief description of the implementation of the method in a suite of computer programs, and the application of the programs to a practical problems, is also gi

ISSN:0029-5981    

DOI:10.1002/nme.1620170703

出版商:John Wiley&Sons, Ltd    

年代:1981

数据来源: WILEY

摘要:

AbstractFamilies of difference schemes are developed for both the linear and nonlinear inviscid Burger's equation and a system of shallow water equations. Single‐step and two‐step (Lax–Wendroff type) families are described and comparisons are made with other difference schemes.The schemes are developed using a very limited portion of a space–time continua, coupled with Galerkin's method applied over a few triangular elements. The elements are geometrically flexible as a function of a geometry factor α, creating the idea of difference families.Stability is commented on, including the continuous relationship between stability and the families of schemes as a function of α. Numerical results are presented and commented on for the system of shallow water equations and the inviscid Burger's equation. Several areas for future research are

ISSN:0029-5981    

DOI:10.1002/nme.1620170704

出版商:John Wiley&Sons, Ltd    

年代:1981

数据来源: WILEY

摘要:

AbstractThe application of the mixed finite element method to two‐dimensional elastic contact problems is investigated. Since in the mixed method, both displacements and stresses are retained as variables, it is found that all the contact conditions—displacement as well as stress—can be approximated directly. A significant novelty is that some of the displacement variables are treated as natural boundary conditions in the contact region. In cases where the contact region is independent of the applied loading, an iterative procedure is used to establish the sliding and adhering portions of the contact region. In cases where the contact region is a function of the applied loading, for example progressive contact, an incremental formulation is employed to describe the discretized contact stages before invoking the former iterations. Several numerical examples are presented and the results are compared with those from the conventional potential energy or displacement finite element m

ISSN:0029-5981    

DOI:10.1002/nme.1620170705

出版商:John Wiley&Sons, Ltd    

年代:1981

数据来源: WILEY

摘要:

AbstractFinite element preprocessor programs have been developed in recent years in order to expedite the task of data preparation. A key decision in the design of these programs is the choice of a method for automated mesh generation. Three popular methods (Laplacian, isoparametric and transfinite mappings) are compared. Transfinite mappings with boundary information represented in discrete form are found to possess distinct advantages for the task of mesh generation.A two‐dimensional preprocessor program utilizing the discrete transfinite mappings is described. Interactive computer graphics techniques are used extensively to facilitate data preparation and display. The geometry‐generating routines are general, and may be used in any finite element application. A specialized graphical ‘attribute editor’ for structural mechanics problems is also described. This editor provides an efficient method of specifying boundary conditions, material properties, loa

ISSN:0029-5981    

DOI:10.1002/nme.1620170706

出版商:John Wiley&Sons, Ltd    

年代:1981

数据来源: WILEY

摘要:

AbstractThe singularity mapping elementology based on the constant and semi‐radial field conditions is presented in an originally quadrilateral finite element. With the complete evaluations of singularities in the stress and strain as well as of the strain energy finiteness, it is demonstrated that this singularity element family is highly versatile. Differences and some identities between the semi‐radial mapping and the so‐called quarter‐point mapping are also e

ISSN:0029-5981    

DOI:10.1002/nme.1620170707

出版商:John Wiley&Sons, Ltd    

年代:1981

数据来源: WILEY

摘要:

AbstractThis paper presents a series summation computation method for calculating temperatures arising from some geometries which commonly occur in microelectronics. The method, which is suitable for use with pocket calculators, involves an exchange of terms with those of a known series. At each stage of the summation a state of convergence (SOC) is calculated in terms of the maximum possible error, thus enabling the calculation to be terminated as soon as the required accuracy has been obtained.

ISSN:0029-5981    

DOI:10.1002/nme.1620170708

出版商:John Wiley&Sons, Ltd    

年代:1981

数据来源: WILEY

摘要:

AbstractA numerical analysis of the critical conditions of thermal ignition for a two‐dimensional cylindrical reactor with flow field occurrence was carried out. The critical conditions of thermal ignition were defined as bifurcation points of the limit type. The dependence of the bifurcation points on aerodynamics was analysed by a sequential variation of the Peclet number. The flow field in the reactor was generated previously by a numerical solution of the Navier‐Stokes equations.The nonlinear parabolic equation of heat balance and linear eigenvalue boundary problems occurring in the proposed non‐stationary method for calculating the bifurcation points was solved numerically using the finite difference technique.It was shown that the critical points of thermal ignition form a surface bounded by the line of ‘limit of criticality’ in the parameter space. For large values of the Peclet number, the dependence of the critical parameter of ignition on Peclet number becom

ISSN:0029-5981    

DOI:10.1002/nme.1620170709

出版商:John Wiley&Sons, Ltd    

年代:1981

数据来源: WILEY

摘要:

AbstractThe upwinded finite element method was introduced for the solution of conduction–convection problems by considering the model problem,u″‐Ku′=0,K>0, subject to the boundary conditionsu(0)=1,u(1)=0. In this paper we consider the solution of this problem by the collocation method using piecewise cubic Hermite polynomials and a uniform grid. We consider the collocation points to be arbitrary parameters which enable us to express the collocation points in terms of the upwinding parameter of the upwinded finite element method. Various choices of the collocation points, including values which lead to complete accuracy in the nodal function values as well as the nodal values of the derivatives are discussed. Finally, we discuss the application of these points to slightly more general problems. Numerical results illustrating the behaviour of these points ar

ISSN:0029-5981    

DOI:10.1002/nme.1620170710

出版商:John Wiley&Sons, Ltd    

年代:1981

数据来源: WILEY

摘要:

AbstractThis paper presents an algorithm and corresponding FORTRAN program for the solution of unsymmetric banded linear equation systems. The algorithm is based on the Crout method. A special technique, called double windowing, enables the solution of very large equation systems with a total equation number reaching 30,000 and a full bandwidth in excess of 1,000. Special attention was devoted to minimization of peripheral processor time (communication with backing disc memory). An appendix lists the complete program for Cyber series computers (CDC).

ISSN:0029-5981    

DOI:10.1002/nme.1620170711

出版商:John Wiley&Sons, Ltd    

年代:1981

数据来源: WILEY

ISSN:0029-5981    

DOI:10.1002/nme.1620170712

出版商:John Wiley&Sons, Ltd    

年代:1981

数据来源: WILEY