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  • 1
    Electronic Resource
    Electronic Resource
    Numerical analysis on singular solutions of the Poisson equation in two-dimensions (1997)
    Springer
    Computational mechanics 20 (1997), S. 320-330 
    Details
    ISSN: 1432-0924
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract  A numerical method for extracting the coefficients of the asymptotic series solution of the Poisson equation in two dimensions in the vicinity of singular points is presented. This method is an extension of that presented in (Szabó and Yosibash 1996) to non-homogeneous boundary value problems, and is general in the sense that it is applicable to almost any type of point singularity. Numerical experiments for crack-tip singularities, re-entrant corner singularities, abrupt change in boundary conditions, and singularities associated with a multi-material inclusion are presented to substantiate the proposed techniques. Constant as well as varying non-homogeneous “right-hand-side” functions are studied.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s004660050254
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    A superelement for two-dimensional singular boundary value problems in linear elasticity (1993)
    Springer
    International journal of fracture 62 (1993), S. 325-340 
    Details
    ISSN: 1573-2673
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract The finite element method for elliptic boundary value problems has been modified to deal with boundary singularities. We introduce a singular-super-element (SSE) which incorporates the known expansion for the singular solution explicitly over the internal region surrounding the singular point, whilst using blended trial functions over the intermediate region, which joins the internal and external regions smoothly. The SSE conforms with the mesh used in the external region, and may be easily incorporated into standard finite element programs. The calculations yield the expansion coefficients directly, as well as an accurate representation of the displacements in the vicinity of the singular point, for a crack or V-notch of any angle subject to any mode of loading. The SSE has been applied to determine stress intensity factors for two-dimensional crack and V-notch problems, including mixed mode. The computations converge rapidly, yielding results of high accuracy.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00017239
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    Paper (German National Licenses)
    Fulltext
  • 3
    Electronic Resource
    Electronic Resource
    NUMERICAL ANALYSIS OF SINGULARITIES IN TWO DIMENSIONS. PART 2: COMPUTATION OF GENERALIZED FLUX/STRESS INTENSITY FACTORS (1996)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 39 (1996), S. 409-434 
    Details
    ISSN: 0029-5981
    Keywords: finite element methods ; p-version ; singular points ; stress intensity factors ; flux intensity factors ; complementary energy ; fracture mechanics ; bi-material interfaces ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A numerical method for the computation of the generalized flux/stress intensity factors (GFIFs/GSIFs) for the asymptotic solution of linear second-order elliptic partial differential equations in two dimensions in the vicinity of singular points is described. Special attention is given to heat transfer and elasticity problems. The singularities may be caused by re-entrant corners and abrupt changes in material properties.Such singularities are of great interest from the point of view of failure initiation: The eigenpairs, computed in a companion paper, characterize the straining modes and their amplitudes (the GFIFs/GSIFs) quantify the amount of energy residing in particular straining modes. For this reason, failure theories directly or indirectly involve the GFIFs/GSIFs.This paper addresses a general method based on the complementary weak formulation for determining the GFIFs/GSIFs numerically as a post-solution operation on the finite element solution vector. Importantly, the method is applicable to anisotropic materials, multi-material interfaces, and cases where the singularities are characterized by complex eigenpairs. An error analysis is sketched and numerical examples are presented to illustrate the effectiveness of the technique.
    Additional Material: 13 Ill.
    Type of Medium: Electronic Resource
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    Paper (German National Licenses)
  • 4
    Electronic Resource
    Electronic Resource
    THE p-VERSION OF THE FINITE ELEMENT METHOD IN INCREMENTAL ELASTO-PLASTIC ANALYSIS (1996)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 39 (1996), S. 1859-1878 
    Details
    ISSN: 0029-5981
    Keywords: p-version ; finite element method ; elasto-plasticity ; cold-working ; non-linear problems ; continuum mechanics ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Whereas the higher-order versions of the finite element method (p- and hp-versions) are fairly well established as highly efficient methods for monitoring and controlling the discretization error in linear problems, little has been done to exploit their benefits in elasto-plastic structural analysis. In this paper, we discuss which aspects of incremental elasto-plastic finite element analysis are particularly amenable to improvements by the p-version. These theoretical considerations are supported by several numerical experiments. First, we study an example for which an analytical solution is available. It is demonstrated that the p-version performs very well even in cycles of elasto-plastic loading and unloading, not only as compared with the traditional h-version but also with respect to the exact solution. Finally, an example of considerable practical importance - the analysis of a cold-working lug - is presented which demonstrates how the modelling tools offered by higher-order finite element techniques can contribute to an improved approximation of practical problems.
    Additional Material: 13 Ill.
    Type of Medium: Electronic Resource
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    Paper (German National Licenses)
  • 5
    Electronic Resource
    Electronic Resource
    Computing flux intensity factors by a boundary method for elliptic equations with singularities (1998)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 14 (1998), S. 657-670 
    Details
    ISSN: 1069-8299
    Keywords: flux intensity factors ; singularities ; multiple singular points ; eliptic PDEs ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A simple method for computing the flux intensity factors associated with the asymptotic solution of elliptic equations having a large convergence radius in the vicinity of singular points is presented. The Poisson and Laplace equations over domains containing boundary singularities due to abrupt change of the boundary geometry or boundary conditions are considered. The method is based on approximating the solution by the leading terms of the local symptotic expansion, weakly enforcing boundary conditions by minimization of a norm on the domain boundary in a least-squares sense. The method is applied to the Motz problem, resulting in extremely accurate estimates for the flux intensity factors. It is shown that the method converges exponentially with the number of singular functions and requires a low computational cost. Numerical results to a number of problems concerned with the Poisson equation over an L-shaped domain, and over domains containing multiple singular points, demonstrate accurate estimates for the flux intensity factors. © 1998 John Wiley & Sons, Ltd.
    Additional Material: 10 Ill.
    Type of Medium: Electronic Resource
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    Paper (German National Licenses)
  • 6
    Electronic Resource
    Electronic Resource
    An accurate semi-analytic finite difference scheme for two-dimensional elliptic problems with singularities (1998)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 14 (1998), S. 281-296 
    Details
    ISSN: 0749-159X
    Keywords: singularities ; elliptic PDE ; Laplace equation ; high-order Finite Difference Schemes ; Mathematics and Statistics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A high-order semi-analytic finite difference scheme is presented to overcome degradation of numerical performance when applied to two-dimensional elliptic problems containing singular points. The scheme, called Least-Square Singular Finite Difference Scheme (L-S SFDS), applies an explicit functional representation of the exact solution in the vicinity of the singularities, and a conventional finite difference scheme on the remaining domain. It is shown that the L-S SFDS is “pollution” free, i.e., no degradation in the convergence rate occurs because of the singularities, and the coefficients of the asymptotic solution in the vicinity of the singularities are computed as a by-product with a very high accuracy. Numerical examples for the Laplace and Poisson equations over domains containing re-entrant corners or abrupt changes in the boundary conditions are presented. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14: 281-296, 1998
    Additional Material: 9 Ill.
    Type of Medium: Electronic Resource
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    Paper (German National Licenses)
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