摘要:

AbstractA method for determining the optimum step‐size in numerical differentiation of a tabulated function is described. In test cases it gives an average error of about four times the error in the data; thus, it is more than twice as accurate as previously published methods. A Fortran program is presente

ISSN:0029-5981    

DOI:10.1002/nme.1620210702

出版商:John Wiley&Sons, Ltd    

年代:1985

数据来源: WILEY

摘要:

AbstractA modification to a conventional critical state model is described which introduces some plasticity in the stress region which is normally fully elastic. The effect is to blur the otherwise sharp distinction between elastic and yielding states. The modification is conceptually simple and does not require any additional material parameters. The model was developed for the dual purpose of providing a more robust constitutive law for finite element applications and to provide a more realistic representation of the soil. Its potential is demonstrated by simulating the response of a plane strain sample tested over a range of loading and unloading stress paths. The results are in accordance with expectations from physical tests. Further, they show that the model has some potential for at least the first few cycles of cyclic loading. A finite element boundary value analysis of an excavation is also described. This shows how the model copes with the severe test of stress paths which unload while yielding. Finally, the model is used to match stress‐strain curves obtained from large‐scale laboratory tests on a compacted clay. Close agreement with three of the five tests was obtained using a single set of material paramet

ISSN:0029-5981    

DOI:10.1002/nme.1620210703

出版商:John Wiley&Sons, Ltd    

年代:1985

数据来源: WILEY

摘要:

AbstractA uniform beam element of open thin‐walled cross‐section is studied under stationary harmonic end excitation. An exact dynamic (transcendentally frequency‐dependent) 14 × 14 element stiffness matrix is derived from Vlasov's coupled differential equations. Special attention is paid to the computational problems arising when coefficients vanish in these equations because of symmetric cross‐section, zero warping stiffness, etc. The dynamic element stiffness matrix is established via a generalized linear eigenvalue problem and a system of linear algebraic equations with complex matrices. A static stiffness matrix is also derived and the associated consistent mass and geometric stiffness matrices are given. Modal masses are evaluated. A FORTRAN program and a numerical example are

ISSN:0029-5981    

DOI:10.1002/nme.1620210704

出版商:John Wiley&Sons, Ltd    

年代:1985

数据来源: WILEY

摘要:

AbstractRecently, a new type of infinite elements which usesr−1decay was proposed. They were applied to exterior wave problems and good results were obtained. In two‐dimensional problems, however, it was necessary to move the origin of ther−1decay in order to model the outgoing wave more accurately, because it decays roughly asr−1/2. In this paper, the mapped infinite elements withr−1/2decay and the necessary numerical integration procedure are presented. These elements do not require any artificial movement of the origin. Several example problems are solved. The results show that the infinite elements withr−1/2decay here give much more accurate values than the infinite elements with exponential decay and any damp

ISSN:0029-5981    

DOI:10.1002/nme.1620210705

出版商:John Wiley&Sons, Ltd    

年代:1985

数据来源: WILEY

摘要:

AbstractBased on the size variable‐independence of the equilibrium equations in matrix format, a rational reduced basis reanalysis and an approximate reanalysis method are presented. Because the redundancy of structures is often low, and the decomposed coefficient matrix is known, these techniques can be advantageous in the structural optimization process. Several truss structures are studied for the purpose of numerical illustratio

ISSN:0029-5981    

DOI:10.1002/nme.1620210706

出版商:John Wiley&Sons, Ltd    

年代:1985

数据来源: WILEY

摘要:

AbstractFinite elements with ‘Special’ basis functions have been proposed to develop better approximations for problems where the behaviour is known to be non‐polynomial. This paper discusses extension of Gaussian quadrature integration procedures of non‐conventional form to the evaluation of the finite element matrices for ‘Special’ elements. Algorithms for general ‘Special’ elements are discussed. The techniques are applied to ‘Special’ one‐ and two‐dimensional elements for spherically symmetric potential flow. The accuracy of the new ‘Special’ element is shown to be superior to linear and quadratic elements for spherically symmet

ISSN:0029-5981    

DOI:10.1002/nme.1620210707

出版商:John Wiley&Sons, Ltd    

年代:1985

数据来源: WILEY

摘要:

AbstractThis paper reviews and evaluates two methods for processing nonlinear constraints. Both are based on the Lagrange multiplier technique. However, one of them, the constraint forces method, is often more efficient than the commonly used method of elimination. The two methods are evaluated by applying them to an example problem and comparing corresponding solution times. Guidelines are given for selecting the more efficient method for a given constraint problem.

ISSN:0029-5981    

DOI:10.1002/nme.1620210708

出版商:John Wiley&Sons, Ltd    

年代:1985

数据来源: WILEY

摘要:

AbstractThe stiffness matrix for the DKT plate‐bending element is formulated explicitly in a global co‐ordinate system. This approach avoids transformations of stiffness, and elasticity properties for anisotropic materials, from local to global co‐ordinates, which were required in previous formulations. A FORTRAN listing of the algorithm is appended for potential

ISSN:0029-5981    

DOI:10.1002/nme.1620210709

出版商:John Wiley&Sons, Ltd    

年代:1985

数据来源: WILEY

摘要:

AbstractThree formulations of the boundary element method (BEM) and one of the Galerkin finite element method (FEM) are compared according to accuracy and efficiency for the spatial discretization of two‐dimensional, moving‐boundary problems based on Laplace's equation. The same Euler‐predictor, trapezoid‐corrector scheme for time integration is used for all four methods. The model problems are on either a bounded or a semi‐infinite strip and are formulated so that closed‐form solutions are known. Infinite elements are used with both the BEM and FEM techniques for the unbounded domain. For problems with the bounded region, the BEM using the free‐space Green's function and piecewise quadratic interpolating functions (QBEM) is more accurate and efficient than the BEM with linear interpolation. However, the FEM with biquadratic basis functions is more efficient for a given accuracy requirement than the QBEM, except when very high accuracy is demanded. For the unbounded domain, the preferred method is the BEM based on a Green's function that satisfies the lateral symmetry conditions and which leads to discretization of the potential only along the moving surface. This last formulation is the only one that reliably satisfies the far‐field bou

ISSN:0029-5981    

DOI:10.1002/nme.1620210710

出版商:John Wiley&Sons, Ltd    

年代:1985

数据来源: WILEY

摘要:

AbstractWe present the results of a numerical study of the preconditioned conjugate gradient algorithm, the minimal residual algorithm, the biconjugate gradient algorithm and the bi‐minimal residual algorithm using both simple test matrices and more realistic test matrices derived from physical problems. The application of the methods to unsymmetric matrices is considered. We emphasize the importance of a good preconditioning, look at various methods including ICGG(n) and incomplete block factorization, and make some practical recommendations. Some of the folk‐lore surrounding the semi‐iterative methods is disp

ISSN:0029-5981    

DOI:10.1002/nme.1620210711

出版商:John Wiley&Sons, Ltd    

年代:1985

数据来源: WILEY