摘要:

AbstractA boundary‐location method is developed for finite element simulation of steady, two‐dimensional flows of Newtonian liquid with free boundaries. In the method, boundary shape and position and the velocity and pressure fields are determined simultaneously. Inertial, viscous, gravitational, and surface tension effects are included in the development. The complete set of nonlinear finite element equations is solved by a modified frontal method combined with Newton‐Raphson iteration to speed convergence. The finite element used to illustrate the method approximates the pressure as a piecewise constant function and the velocity and free boundaries as piecewise linear functions. Example calculations for flow from a slit show that the method can be effe

ISSN:0029-5981    

DOI:10.1002/nme.1620150502

出版商:John Wiley&Sons, Ltd    

年代:1980

数据来源: WILEY

摘要:

AbstractA plasticity theory for porous metals is proposed. A simple model of a porous materials is analysed by the finite element method. Small strain elastic–plastic analysis provides stress–strain curves, yield stressed and incremental plastic strain vectors for different void ratios. An assessment is made of an existing yield criterion for porous metals. A modified yield criterion and plastic potential function and, consequently, different plasticity equations are given. Reasonable agreement is obtained between the present numerical results and previous results in the literat

ISSN:0029-5981    

DOI:10.1002/nme.1620150503

出版商:John Wiley&Sons, Ltd    

年代:1980

数据来源: WILEY

摘要:

AbstractA modification (Irons;6Concuset al.1) to the conjugate gradient (CG) method by Hestenes and Stiefel5has recently renewed the interest in this elegant technique which appears to be extraordinarily promising for large sparse systemsAx = b, whereAis a symmetric positive definite matrix. A good approximationK−1for the inverse ofAis needed in the modified algorithm. For finite difference sets of equations, Meijerink and van der Vorst9and Kershaw7have experienced a very fast convergence with a matrixK−1determined by the incomplete Cholesky decomposition ofA.A further acceleration of the iteration may be achieved by preliminarily processing the initial guessed solution by the Newton iterative scheme before using the modified conjugate gradient (MCG) method. The initial Newton iterations (NI) have the useful property of significantly reducing the components of the residualr0along the eigenvectors ofAK−1associated with the eigenvalues lying in the vicinity of 1. The latter are expected to include the vast majority of the eigenvalues ofAK−1. As a result the MCG method is left with a smaller number ofr0components to set to zero in a reduced dimensional eigenvector space and hence the solution is arrived at in fewer iterations. Depending on the desired final accuracy, up to 50 per cent of the MCG iterations may be equivalently replaced by an equal number of NI which are computationally faster.This approach has been applied to the solution of finite element sets of linear equations arising from the arbitrarily irregular triangle discretization of groundwater flow domains in both steady and unsteady conditions. For diagonally dominant matrices the results emphasize the excellent performance of the MCG method which proved much faster than the first‐degree Chebyshev iteration (CHI) and required a number of iterations an order of magnitude smaller than the successive over‐relaxation technique (SOR) with optimum over‐rela

ISSN:0029-5981    

DOI:10.1002/nme.1620150504

出版商:John Wiley&Sons, Ltd    

年代:1980

数据来源: WILEY

ISSN:0029-5981    

DOI:10.1002/nme.1620150505

出版商:John Wiley&Sons, Ltd    

年代:1980

数据来源: WILEY

摘要:

AbstractThe choice on an efficient direct integration procedure for linear structural dynamic equations of motion is discussed. It is suggested that as accuracy parameter the truncation error on the exponential terms contained in the modal contributions of the exact solution be assumed. This error does not always coincide with the local truncation error. These considerations were used to design an unconditionally stable one‐step method whose accuracy is 0(h4). Numerical comparisons with some well‐known integration schemes showed the efficiency of the proposed met

ISSN:0029-5981    

DOI:10.1002/nme.1620150506

出版商:John Wiley&Sons, Ltd    

年代:1980

数据来源: WILEY

摘要:

AbstractThe method of data transfer from the peripheral storage unit to the central processor unit, when dealing with large solution systems, is of greater importance, as each access of peripheral stored data interrupts the active flow of arithmetic operation in the central processor core. When solving a large number of symmetrical positive‐definite equations this generally leads to difficulties in channel interaction and priority, possibly even to the breakdown of the computer system or to uneconomical computing times. The problem increases when considering the iterative approximation of nonlinear problems; further still, when using the frontal solution method. It will be shown that this difficulty can be avoided by inserting two different types of buffers—a micro‐buffer and a macro‐buffer—into the data transfer between the central memory and an arbitrary peripheral storage unit. This method should primarily be used in those finite element (FE) programs which are based on the ‘slow’ BACKSPACE‐READ‐BACKSPACE commands, but even in the case of peripheral storage units such as magnetic discs (random access) or magnetic tape machines (working in one or two directions) the computing time and channel control can successfully be improved. A second achievement of this procedure is the possibility of applying a FE program economically, not only to large element systems and elements of a ‘higher order’ but also with good results for small element systems, e.g. when investigating nonlinear material behaviour with simple element types and geometrical structure. Another purpose of this text is to recommend the FORTRAN subroutine in the Appendix, whose novel features make it a useful supplement to

ISSN:0029-5981    

DOI:10.1002/nme.1620150507

出版商:John Wiley&Sons, Ltd    

年代:1980

数据来源: WILEY

摘要:

AbstractThis paper presents a generalized method which generates linear, triangular, quadrilateral and pentahedral elements for the finite element method. Depending on geometrical and material variations, the region to be discretized is manually divided into blocks such as lines, triangles, quadrilaterals, pentahedrons and hexahedrons in several appropriate co‐ordinate systems. However, no connectivity information of the adjacent blocks is required by the user as input. The continuity of the generated nodal co‐ordinates and element configurations at the block interface are automatically maintained to describe the geometry of structures, no matter how these five types of blocks are connected. Furthermore, a mesh grading algorithm which generates reliable mesh grade distributions in the interior of the triangular and quadrilateral blocks is established corresponding to the arbitrarily defined subdivision numbers for each edge line of blocks. This algorithm is extended to the mesh grading in the interior of the hexahedral and pentahedral blocks. Element numbers are also renumbered in this scheme, in addition to node numbers, in order to increase the computational efficiency of the global matrix assembly. Additional facilities, i.e. loading data generation, boundary condition data generation and so on, are also discussed. An illustrative and a practical example are given to demonstrate the capabilities of this sch

ISSN:0029-5981    

DOI:10.1002/nme.1620150508

出版商:John Wiley&Sons, Ltd    

年代:1980

数据来源: WILEY

摘要:

AbstractA concise and efficient algorithm is presented for deriving finite element shape functions from an arbitrary set of independent functions. Based on special one‐dimensional interpolatory schemes derived via the algorithm, a variety of two‐ and three‐dimensional interpolatory schemes are developed which are useful for modelling singular behaviour. The methodology presented is general and may be fruitfully applied to the development of ‘special’ finite element shape functions for a variety of other s

ISSN:0029-5981    

DOI:10.1002/nme.1620150509

出版商:John Wiley&Sons, Ltd    

年代:1980

数据来源: WILEY

摘要:

AbstractThis paper evaluates the relative merits of the band‐schemes over the frontal‐routines in the solution of the linearized algebraic equations resulting from a nonlinear structural analysis. Through examples it is shown that the use of the former in the nonlinear analysis programs results in considerable savings in computer time. This is especially so when the structure under consideration is subject to dynamic loads due to earthquakes or simulated ground moti

ISSN:0029-5981    

DOI:10.1002/nme.1620150510

出版商:John Wiley&Sons, Ltd    

年代:1980

数据来源: WILEY

摘要:

AbstractA variational principle is presented which represents steady ideal flow with a free surface under gravity in terms of the stream function with Dirichlet boundary conditions. A different principle of Ikegawa and Washizu is shown to require restricted variations not consistent with the mass flow specification. The new principle is a special case of the of O'Carroll and Harrison in terms of enthalpy discontinuity between two streams. It is also reciprocal to a velocity potential functional. Finite element procedures and the determination of critical flow are discussed.

ISSN:0029-5981    

DOI:10.1002/nme.1620150511

出版商:John Wiley&Sons, Ltd    

年代:1980

数据来源: WILEY