摘要:

AbstractThe present paper further develops the boundary element singularity subtraction technique, to provide an efficient and accurate method of analysing the general mixed‐mode deformation of two‐dimensional linear elastic structures containing sharp notches. The elastic field around sharp notches is singular. Because of the convergence difficulties that arise in numerical modelling of elastostatic problems with singular fields, these singularities are subtracted out of the original elastic field, using the first term of the Williams series expansion. This regularization procedure introduces the stress intensity factors as additional unknowns in the problem; hence extra conditions are required to obtain a solution. Extra conditions are defined such that the local solution in the neighbourhood of the notch tip is identical to the Williams solution; the procedure can take into account any number of terms of the series expansion. The standard boundary element method is modified to handle additional unknowns and extra boundary conditions. Analysis of plates with symmetry boundary conditions is shown to be straightforward, with the modified boundary element method. In the case of non‐symmetrical plates, the singular tip‐tractions are not primary boundary element unknowns. The boundary element method must be further modified to introduce the boundary integral stress equations of an internal point, approaching the notch‐tip, as primary unknowns in the formulation. The accuracy and efficiency of the method is demonstrated with some benchmark tests of mixed‐mode problems. New results are presented for the mixed‐mode analysis of a non‐symmetrical configuration of a single edg

ISSN:0029-5981    

DOI:10.1002/nme.1620320302

出版商:John Wiley&Sons, Ltd    

年代:1991

数据来源: WILEY

摘要:

AbstractEfficiency in solving differential equations is improved by increasing the order of a Taylor series approximation. Computing time can be reduced up to a factor of 40 and an amount of memory storage can be saved, up to a factor of 70.The truncation error can be estimated not only by order but also by magnitude.

ISSN:0029-5981    

DOI:10.1002/nme.1620320303

出版商:John Wiley&Sons, Ltd    

年代:1991

数据来源: WILEY

摘要:

AbstractA point‐based two‐stage hierarchical method for automatic finite element mesh generation from a solid model is presented.Given the solid model of a component and the required nodal density distribution, nodes are generated according to the hierarchy—vertex, edge, face and solid. At the vertices, nodes are established naturally. Nodes on the edges, faces and inside the solid model are generated by recursive subdivision. The nodes are then connected to form a valid and well‐conditioned finite element mesh of tetrahedron elements using modified Delaunay Triangulation. Checks are conducted to ensure the compatibility of geometry and topology between the solid model and t

ISSN:0029-5981    

DOI:10.1002/nme.1620320304

出版商:John Wiley&Sons, Ltd    

年代:1991

数据来源: WILEY

摘要:

AbstractThe behaviour is compared of two solvers for the discrete equations arising from the discretization using Chebyshev collocation of a second‐order linear partial differential equation on a square. The alternative solvers considered are a direct solver and an iterative solver based on preconditioning with the matrix arising from finite‐difference discretization of the governing equation. The total error of the collocation derivatives and the separate contributions from round‐off and discretization error are examined. The efficiency of the two solvers is compared. The iterative solver is more efficient than the direct solver on fine grids for equations similar to the Poisson equation, provided that there are Dirichlet boundary conditions on at least three of the sides of the s

ISSN:0029-5981    

DOI:10.1002/nme.1620320305

出版商:John Wiley&Sons, Ltd    

年代:1991

数据来源: WILEY

摘要:

AbstractA new formulation was proposed recently for the removal of the shear and membrane locking mechanisms from theC0structural elements. The performance of the new formulation was shown to be excellent in many cases of beam, plate and shell element applications, completely eliminating all locking problems. However, this formulation has its own problems. The potential introduction of softening effects (yielding softer models) and a rotational zero energy mode describe the problematic behaviour of the new formulation in cases ofC0plate and shell element applications. Analysis of this behaviour reveals some interesting aspects of the classical finite element formulation and allows for a better insight into the overall behaviour of theC0structural elements. As a result of the present analysis, a modification of new formulation, remedying its problematic behaviour, will appear soon.

ISSN:0029-5981    

DOI:10.1002/nme.1620320306

出版商:John Wiley&Sons, Ltd    

年代:1991

数据来源: WILEY

摘要:

AbstractAn essentially physical approach is utilized to derive a finite element formulation of conduction‐type problems. The same systems of algebraic equations, which are usually yielded by Galerkin or variational methods, are obtained here on the basis of energy balances which lead to conservative numerical models, both at element and at node levels. As a result, it is shown that, in conventional implementations of the finite element method for conduction‐type problems, there is no artificial creation or destruction of a conserved variable. Therefore, for such formulations, inaccuracies that arise with finite sizes of elements do not depend on non‐conservation but are due solely to approximation erros. In the paper, a clear physical interpretation is also given for all the matrices and vectors which are commonly defined in most finite element formulations of conduction‐type p

ISSN:0029-5981    

DOI:10.1002/nme.1620320307

出版商:John Wiley&Sons, Ltd    

年代:1991

数据来源: WILEY

摘要:

AbstractA general computational technique is developed for the accurate analysis of forced non‐synchronous harmonic vibration of linear structures rotating with constant speed about a fixed axis in the inertial space. The structures studied are built up from piecewise uniform straight Rayleigh‐Timoshenko beam members having coinciding cross‐sectional centres of geometry, shear and mass, and vibrating in coupled tension, torsion, bending and shearing. Hysteretic and viscous dampings in the beam material and in a Winkler‐type ambient medium are considered. Rigid bodies and modal bodies and also discrete masses, springs and dampers can be included in the structure. The six coupled scalar partial linear differential equations governing the motion of a loaded beam are established in a corotating local co‐ordinate system. A transcendentally frequency‐dependent non‐symmetric complex‐valued 12 × 12 stiffness matrix is derived, over a state‐space analogy and an associated eigenproblem, for a harmonically vibrating beam member non‐synchronously excited at its ends. This matrix is exact in the sense that no assumed shape functions and no lumped masses are used. The general computational technique is here applied to a simple beam rotating about (1) its longitudinal axis and (2) about a transverse axis. The study clarifies the influence of gyroscopic effects and of material and support dampings on the dynamical behaviour of the beam at different rotational speeds and forcing frequencies. Resonance frequencies are found. Frequency response functions and freque

ISSN:0029-5981    

DOI:10.1002/nme.1620320308

出版商:John Wiley&Sons, Ltd    

年代:1991

数据来源: WILEY

摘要:

AbstractThe paper deals with the development of a numerical method for determining Weight Functions in two‐dimensional problems. After a short review of some recent numerical techniques an original approach is presented. The method is based on Finite Element calculations with coarse meshes and on the knowledge of some values of the Stress Intensity Factor for one reference loading condition. The validity of the method is demonstrated for a theoretical case and its accuracy and suitability are discussed with reference to practical application

ISSN:0029-5981    

DOI:10.1002/nme.1620320309

出版商:John Wiley&Sons, Ltd    

年代:1991

数据来源: WILEY

摘要:

AbstractA direct boundary element formulation which produces equilibrium satisfaction in the numerical solutions is presented. It consistently originates from the standard boundary integral equation with a simple modification in the fundamental solution and can be applied to general potential and elasticity problems. Since boundary equilibrium is guaranteed for any problem discretization, the procedure is also found useful to generate improved stiffness matrices, which permits combination with finite elements.Some elastostatic examples are included to demonstrate the applicability of the formulation.

ISSN:0029-5981    

DOI:10.1002/nme.1620320310

出版商:John Wiley&Sons, Ltd    

年代:1991

数据来源: WILEY

摘要:

AbstractA new finite element model for the contact/impact problem is presented, and both its static and dynamic implementations are described. In this geometrical non‐linear formulation, contact (from node to surface) is simulated through fictitious equivalent pressure along the boundary. Contrary to most existing models, this formulation entails relatively few matrix decompositions and thus is computationally inexpensive. The model is first assessed through some classical contact problems, and is subsequently applied to the fracture mechanics based analysis of a cracked dam under seismic excitatio

ISSN:0029-5981    

DOI:10.1002/nme.1620320311

出版商:John Wiley&Sons, Ltd    

年代:1991

数据来源: WILEY