摘要:

AbstractThe superposition of a rigid body mode on a body should result in a corresponding change in displacement values but should not affect the stresses. However, in the numerical solution by the boundary element method (BEM) large errors may be obtained for displacements and stresses if a rigid body mode is present in the input data. To eliminate the effects of the rigid body mode on the numerical accuracy of the solution, the fundamental solutions for displacements must be correctly interpreted and used. The rigid body mode may be unknowingly present in the boundary condition data. It may be present because the boundary data are not known accurately. Or it may be present if the displacement values at the support have been computed from a separate analysis. A rigid body mode may arise due to the collocation nature of satisfying the boundary conditions. The point values of the applied load at the collocation point may not satisfy equilibrium. Or the point values of the specified displacements may not satisfy the condition of zero translation and rotation. For bodies under pure traction, we know that the analytical solution can contain an arbitrary amount of rigid body mode. Numerically, however, some unknown value is assigned to this rigid body mode. It might be desirable (for example in limit analysis) to eliminate the rigid body mode from the displacements to obtain deformation of a point with respect to a point on the body. In addition, knowledge and elimination of the rigid body mode is necessary for the implementation of a scheme described by this author in an earlier work. The importance of the earlier work is that it reduced the sensitivity of the BEM to changes and errors in the input data. In this paper the causes, and the effects of the rigid body mode on the BEM, the correct interpretation of the fundamental solution for displacements and an algorithm for determining and accounting for the rigid body mode are discussed. A numerical example validates the ideas in this paper for the indirect version. The algorithm for the direct version is presented without a numerical example in the Appendices.

ISSN:0029-5981    

DOI:10.1002/nme.1620290302

出版商:John Wiley&Sons, Ltd    

年代:1990

数据来源: WILEY

摘要:

AbstractThis paper presents an alternative to the subspace iteration and Lanczos techniques, both of which are now used to solve partial eigenvalues and eigenvectors of large generalized linear first order symmetric matrix systems. It is based on non‐linear optimization of a modified Rayleigh quotient. The elements of the eigenvector are the decision variables. Orthogonality constraints with respect to the two matrices are incorporated in the sequential unconstrained optimization scheme. By imposing normality with respect to one of the matrices, the Hessian matrix reduces to a much simpler form for which the Woodburry transformation may be used. This, in combination with the fact that the banded structure of the matrices is maintained, results in a number of operations of the same order as the two standard methods. Shifting is readily integrated. Numerical comparison with existing techniques demonstrate the practicality of this metho

ISSN:0029-5981    

DOI:10.1002/nme.1620290303

出版商:John Wiley&Sons, Ltd    

年代:1990

数据来源: WILEY

摘要:

AbstractSome constitutive and computational aspects of finite deformation plasticity are discussed. Attention is restricted to multiplicative theories of plasticity, in which the deformation gradients are assumed to be decomposable into elastic and plastic terms. It is shown by way of consistent linearization of momentum balance that geometric terms arise which are associated with the motion of the intermediate configuration and which in general render the tangent operator non‐symmetric even for associated plastic flow. Both explicit (i.e. no equilibrium iteration) and implicit finite element formulations are considered. An assumed strain formulation is used to accommodate the near‐incompressibility associated with fully developed isochoric plastic flow. As an example of explicit integration, the rate tangent modulus method is reviewed in some detail. An implicit scheme is derived for which the consistent tangents, resulting in quadratic convergence of the equilibrium iterations, can be written out in closed form for arbitrary material models. All the geometrical terms associated with the motion of the intermediate configuration and the treatment of incompressibility are given explicitly. Examples of application to void growth and coalescence and to crack tip blunting are developed which illustrate the performance of the implicit met

ISSN:0029-5981    

DOI:10.1002/nme.1620290304

出版商:John Wiley&Sons, Ltd    

年代:1990

数据来源: WILEY

摘要:

AbstractIn this paper the magnetostatic problem is stated in terms of two‐component electric and magnetic vector potentials. An associated numerical method, based on the adoption of edge elements, is proposed. This procedure overcomes the cancellation problems and the complexity of the interface conditions encountered by similar approaches in the presence of magnetic inhomogeneities and discontinuities of currents and magnetic field

ISSN:0029-5981    

DOI:10.1002/nme.1620290305

出版商:John Wiley&Sons, Ltd    

年代:1990

数据来源: WILEY

摘要:

AbstractSimulation of turbulent swirling flows has been carried out to provide insight on streamline curvature effects. Numerical calculations were based on the control‐volume method. Turbulence effects were represented by two‐equation turbulence models. The analysis of steady flow between two concentric rotating cylinders showed that the most promising model which incorporates curvature effects is that based on mixing energy developed by Wilcox and Chambers, as opposed to thead hocmodification to the standardk–ϵ model. This model has also been used to simulate the decay of turbulent swirling flow in a short cylinder. A comparison between calculations and experimental results for such flow fields has been pre

ISSN:0029-5981    

DOI:10.1002/nme.1620290306

出版商:John Wiley&Sons, Ltd    

年代:1990

数据来源: WILEY

摘要:

AbstractA panel method using source and doublet singularity has been proposed to solve for subcritical aerodynamics of a two dimensional steady and unsteady aerofoil. The source singularities are placed on the aerofoil surface. The doublet singularity is distributed by a function along the chordline of the aerofoil; this distribution is further projected downstream into infinity.The aerodynamics of an oscillating aerofoil is investigated. The governing unsteady linearized potential equation has a Hankel function as its fundamental solution, which is a source type function. A combination of source and doublet singularity is therefore used for solving the unsteady compressible problem by means of the panel method, this methodology being an extension of a steady aerofoil formulation. Incremental effects of profile change in aerofoil and wake geometry are accounted for. A surface boundary condition is applied on the stationary mean aerofoil surface with time dependent geometrical changes accounted for. An unsteady Kutta condition of equal pressure across the trailing edge is assumed. Results are presented on the aerodynamic influence of Mach number, oscillating frequency parameter, angle of incidence and change of pivoting point. Results are also compared with linear theory, a subsonic experimental result and a subcritical solution of a transonic model.

ISSN:0029-5981    

DOI:10.1002/nme.1620290307

出版商:John Wiley&Sons, Ltd    

年代:1990

数据来源: WILEY

摘要:

AbstractThe finite element method is used in calculating accurate collapse loads. The behaviour of granular materials is described by the non‐associated Mohr–Coulomb model. The load–displacement path is traced up to and beyond limit points using an accelerated initial stiffness method. The convergence properties of this method are examined, both for associated and non‐associated plasticity.Step sizes in the incremental iterative procedure are adapted during the iteration process, depending on an estimated number of iterations. The automatic step size control thus obtained proves to be robust and particularly appropriate for non‐associated plasticity. Some soil collapse calculations are discussed to demonstrate the practical application of t

ISSN:0029-5981    

DOI:10.1002/nme.1620290308

出版商:John Wiley&Sons, Ltd    

年代:1990

数据来源: WILEY

摘要:

AbstractThis study, dealing with model reduction for thermal diffusion, describes the numerical techniques used: the Eitelberg, Marshall and aggregation methods. The non‐linear model of a heat transmission tube, to which these methods are applied, is then described, pointing out the necessary initial algebraic treatment for reduction. Finally the outputs of the complete model and of several reduced ones are compared for some characteristic variations of the inputs. For this problem, the Eitelberg and Marshall methods, which can be used with a high coefficient of reduction, are well adapte

ISSN:0029-5981    

DOI:10.1002/nme.1620290309

出版商:John Wiley&Sons, Ltd    

年代:1990

数据来源: WILEY

摘要:

AbstractThree parallel iterative schemes to solve banded systems of equations are presented in this study. The techniques are special implementations of the theory of matrix multisplitting. The resulting algorithms are implemented on a Multiple Instruction Multiple Data (MIMD) grid architecture using 16 Transputer processors. Parametric analyses are performed to develop convergence criteria and examine the speed‐up of solution. It is concluded that the algorithms make very efficient use of the parallel computer architecture, especially if this consists of a large number of node

ISSN:0029-5981    

DOI:10.1002/nme.1620290310

出版商:John Wiley&Sons, Ltd    

年代:1990

数据来源: WILEY

摘要:

AbstractA method is presented that may be used to empirically establish the type of relationship that is present between a response variable and its influencing factors, by fitting a mathematical model to three dimensional scattered data. The generated response surface is composed of continuous triangular planes that are fitted to the corresponding data in the least squares sense. The method may be easily implemented. It requires some fairly large number of scattered data, two initial boundary conditions and a desired accuracy for the band‐wise partitioning of the data. The proposed surface fitting technique has been successfully applied to solar radiation modelling for a number of different data combination

ISSN:0029-5981    

DOI:10.1002/nme.1620290311

出版商:John Wiley&Sons, Ltd    

年代:1990

数据来源: WILEY