摘要:

AbstractThe analysis of axisymmetric structures in which geometric and material properties are independent of the circumferential co‐ordinate, but for which loading may be dependent on this co‐ordinate, is considered. The analysis is performed by expressing the field variables in a Fourier series and results in the solutions of a series of two‐dimensional problems. The assumed‐stress hybrid model is used and the element matrices for each harmonic are derived. To assess the procedure, two‐4 node elements, differing in the form of the assumed stress field, are developed; both elements are shown to possess the correct rank. A series of example problems are considered, and the better of the two elements is i

ISSN:0029-5981    

DOI:10.1002/nme.1620170602

出版商:John Wiley&Sons, Ltd    

年代:1981

数据来源: WILEY

摘要:

AbstractThis paper is concerned with the large‐deflection (bending and free vibration)analysis of thin elastic curved beams by conventional and mixed finite element methods. The conventional finite element method is based on the total potential energy expression, whereas the mixed method is based on a Reissner‐type variational statement and involves the bending moments and deflections as primary dependent variables. Incremental and direct formulations are presented for both methods. The nonlinearity is included in the numerical method via an iterative procedure (i.e. the in‐plane force due to the large deflection is not treated as constant but included under the integral in the energy expression). In the case of vibrations, the transverse shear and rotary inertia effects are also included. A number of numerical examples of beams with various edge conditions are analysed for deflections and natural frequencies, and the results are compared with those reported in the liter

ISSN:0029-5981    

DOI:10.1002/nme.1620170603

出版商:John Wiley&Sons, Ltd    

年代:1981

数据来源: WILEY

摘要:

AbstractThe stability of plane Poiseuille flow and circular Couette flow are examined with respect to linear azimuthally periodic disturbances by the finite element method. In the case of Couette motion, solutions are obtained for a narrow gap, a wide gap and a dilute polymer solution with an elongational viscosity in the narrow gap limit when both cylinders rotate at almost equal speed in the same direction. Results are in good agreement with previous calculations by other numerical methods.

ISSN:0029-5981    

DOI:10.1002/nme.1620170604

出版商:John Wiley&Sons, Ltd    

年代:1981

数据来源: WILEY

摘要:

AbstractThis paper considers some consequences of the common implementation of the finite element method in which element integrals are evaluated numerically by Gaussian quadrature. It shows that if the order of the Gauss scheme is less than the number of basis functions on an element, then the numerically evaluated capacity matrix for that element is singular. The capacity matrix of an assembly of such elements is also considered and is shown to be singular under certain conditions.

ISSN:0029-5981    

DOI:10.1002/nme.1620170605

出版商:John Wiley&Sons, Ltd    

年代:1981

数据来源: WILEY

摘要:

AbstractA curved triangular element for plate bending is developed, using the displacement method of formulation. The element has one outwardly curved side and conforms on an arbitrary quadratic boundary.To the user, the element appears as a single curved triangle. Internally, however, the element is subdivided into a straight‐sided triangle and a ‘curved segment’. The straight‐sided triangle is extensively documented in the literature2‐5and is referred to in the paper as the Cowper triangle. The curved segment is a two‐noded element with 12 degrees‐of‐freedom. It has one straight side and one curved side.Independent expansions are assumed in each domain and explicit shape functions derived. The theoretical solution to a few practical problems is contained in each of the two expansions. In such cases, the curved triangle produces perfect results. Otherwise, the accuracy is of the same order as that obtained in similar problems with straight boundaries.The method is easily extended to elements

ISSN:0029-5981    

DOI:10.1002/nme.1620170606

出版商:John Wiley&Sons, Ltd    

年代:1981

数据来源: WILEY

摘要:

AbstractA finite element formulation for the solution of time‐dependent inelastic deformation problems for metallic structures, in the presence of transient thermal stresses, is presented in this paper. A rate formulation of the equations is used and any of a number of recently proposed combined creep‐plasticity constitutive models with state variables can be adopted to describe material behaviour. The computer program developed can solve planar (plane strain and stress) and axisymmetric problems. Using one of the above‐mentioned constitutive models, numerical results are presented for several illustrative problems, and comparisons of results, using either the quasi‐steady or the unsteady diffusion equation for the determination of the temperature field, are carr

ISSN:0029-5981    

DOI:10.1002/nme.1620170607

出版商:John Wiley&Sons, Ltd    

年代:1981

数据来源: WILEY

摘要:

AbstractThis paper presented an efficient computational algorithm for the eigensolution for real symmetric positive definite matrices. The algorithm is based on the Cholesky decomposition and will be referred to as theCholesky algorithm. The efficiency of the algorithm is due to the combination of several iteration cycles into one, as well as to a judicious choice of shifts. The latter is accomplished by combining an approach based on Sturm's theorem for the initial stages of the process with another approach based on Gersch‐gorin's theorem for the subsequent and final stages of the process. The efficiency of the proposed algorithm was tested against that of theQLmethod and was found to be superior. Moreover, its superiority increases with an increase in the order of the eigenvalue problem. For an eigenvalue problem of order 100, the proposed algorithm produced a solution in about one‐half the time required by theQLmet

ISSN:0029-5981    

DOI:10.1002/nme.1620170608

出版商:John Wiley&Sons, Ltd    

年代:1981

数据来源: WILEY

摘要:

AbstractThe use of the finite element concept in the time domain has resulted in a reinterpretation of many previously recorded recurrence formulae and the discovery of new ones. An important new feature common to all such schemes is the fact that a weighted forcing term is used. This precludes the application of unrealistic forcing terms resulting in a direct finite difference derivation and ‘smooths’ oscillation due to sudden changes of boundary condition. This problem is discussed in the context of various two‐ and three‐level time

ISSN:0029-5981    

DOI:10.1002/nme.1620170609

出版商:John Wiley&Sons, Ltd    

年代:1981

数据来源: WILEY

摘要:

AbstractFinite element methods are formulated and investigated for the effectiveness factor problem for heat and mass transfer with chemical reactions in catalyst pellet models. A Galerkin finite element method is compared with a previousC1collocation method7. A scheme that is conceptually intermediate between these two methods and accordingly has been termed collocation‐Galerkin is formulated and numerical experiments considered. Of particular interest here are superconvergence results at the Gauss and Jacobi points, respectively. Numerical studies of superconvergence in the presence of a nonlinear reaction‐rate term are presented. An integral formula is devised and used to compute the flux at the pellet surface to optimal accuracy. Numerical experiments are conducted to demonstrate the improvement in computed flu

ISSN:0029-5981    

DOI:10.1002/nme.1620170610

出版商:John Wiley&Sons, Ltd    

年代:1981

数据来源: WILEY

ISSN:0029-5981    

DOI:10.1002/nme.1620170611

出版商:John Wiley&Sons, Ltd    

年代:1981

数据来源: WILEY