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  • 1
    Electronic Resource
    Electronic Resource
    Computing edge singularities in elastic anisotropic three-dimensional domains (1997)
    Springer
    International journal of fracture 86 (1997), S. 221-245 
    Details
    ISSN: 1573-2673
    Keywords: Singularities ; Finite Element Methods ; Steklov method ; multi-material interfaces ; p-version ; delamination ; three-dimensional elasticity ; fracture-mechanics.
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract Computation of eigen-pairs characterizing the linear elastostatic solution in three-dimensional anisotropic domains in the vicinity of edge singularities is addressed. The singularities may be caused by re-entrant corners, abrupt changes in boundary conditions or material properties. Edge singularities in three-dimensional domains are of great interest from the point of view of failure initiation: The eigen-pairs characterize the straining modes and their amplitudes quantify the amount of energy residing in particular straining modes. For this reason, failure theories directly or indirectly involve the eigen-pairs and their amplitudes. Herein we address the problem of determining the edge eigen-pairs numerically on the basis of the modified Steklov formulation in conjunction with the p-version of the finite element method. The method is very accurate, efficient and robust, and provides complex eigen-pairs if they exist. Several practical problems are studied, and examples are presented for cases including multi-material inclusion problems, cracks in dissimilar materials, and multi-material interfaces at free and clamped edges.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1007480830248
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  • 2
    Electronic Resource
    Electronic Resource
    Generalized stress intensity factors in linear elastostatics (1995)
    Springer
    International journal of fracture 72 (1995), S. 223-240 
    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 solution of two-dimensional linear elastostatic problems in the neighborhood of singular points is discussed. A reliable and efficient method for computing the eigenpairs that characterize the exact solution and their coefficients, called the generalized stress intensity factors, by the finite element method is demonstrated. Examples, representing three very different kinds of singular points demonstrate that the method works well and produces results of high accuracy. Importantly, the method is applicable to anisotropic materials, multi-material interfaces, and cases where the singularities are characterized by complex eigenpairs.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00037312
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  • 3
    Electronic Resource
    Electronic Resource
    Numerical thermo-elastic analysis of singularities in two-dimensions (1995)
    Springer
    International journal of fracture 74 (1995), S. 341-361 
    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 Linear elastic two-dimensional problems with singular points subjected to steady-state temperature distribution are considered. The stress tensor in the vicinity of the singular points exhibits singular behavior characterized by the strength of the singularity and the associated thermal stress intensity factors (TSIFs). It is shown that the TSIFs and the strength of the stress singularity can be obtained using the principle of complementary energy together with the modified Steklov method and the p-version of the finite element method. Importantly, the proposed method is applicable not only to singularities associated with crack tips, but also to multi-material interfaces and non-homogeneous materials. Numerical results of crack-tip singularities in a rectangular plate and singular points associated with a two-material inclusion are presented.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00035847
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  • 4
    Electronic Resource
    Electronic Resource
    Accurate stress extraction for nearly incompressible materials by the displacement formulation of the p-version FEM (1996)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 12 (1996), S. 807-826 
    Details
    ISSN: 1069-8299
    Keywords: incompressible materials ; finite element method ; p-version ; elasticity ; stress extraction ; complementary energy ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Direct methods for computing the pointwise stresses for nearly incompressible elastic materials fail to provide meaningful results when applied to the displacement formulation of the finite element method (FEM). A new extraction method for accurate computation of pointwise stresses for nearly incompressible elastic materials is presented. It is based on the complementary energy principle applied over a local domain in the postprocessing phase in conjunction with the p-version finite element solution. It is shown that accurate pointwise stresses are obtained, that the relative error in the pointwise stresses converges at a rate which is as fast as the relative error measured in the energy norm or faster, and importantly, the extracted stresses are virtually independent of Poisson's ratio. Numerical results for two problems, one having a smooth solution and the other containing a singular point, are provided.
    Additional Material: 11 Ill.
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    Convergence of stress maxima in finite element computations (1994)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 10 (1994), S. 683-697 
    Details
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The convergence of stress maxima, computed directly from finite element solutions, is investigated with respect to a family of exact solutions characterized by varying degrees of smoothness. The performances of h- and p-extensions and the product and trunk spaces are evaluated and documented with respect to a family of benchmark problems. In uniform p-extensions a characteristic pattern in the convergence of stress maxima was observed. There does not appear to be a clear-cut advantage of the product space over the trunk space in this respect. The much faster convergence of stress maxima in the case of p-extensions, as compared with h-extensions, is evident from the results.
    Additional Material: 10 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640100903
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  • 6
    Electronic Resource
    Electronic Resource
    Numerical analysis of singularities in two-dimensions part 1: Computation of eigenpairs (1995)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 38 (1995), S. 2055-2082 
    Details
    ISSN: 0029-5981
    Keywords: finite element method ; Steklov method ; singular points ; failure/fracture analysis ; eigenpairs ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A numerical method is described for the computation of eigenpairs which characterize the exact solution of linear second-order elliptic partial differential equations in two dimensions in the vicinity of singular points. The singularities may be caused by re-entrant corners and abrupt changes in boundary conditions or material properties.Such singularities are of great interest from the point of view of failure initiation: The eigenpairs characterize the straining modes and their amplitudes quantify the amount of energy residing in particular straining modes. For this reason, failure theories directly or indirectly involve the eigenpairs and their amplitudes.This paper addresses the problem of determining the eigenpairs numerically on the basis of the Steklov formulation. Numerical results are presented for several cases. Importantly, the method is applicable to three-dimensional cases.
    Additional Material: 14 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620381207
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  • 7
    Electronic Resource
    Electronic Resource
    FINITE ELEMENT STRESS EXTRACTION BY THE COMPLEMENTARY ENERGY PRINCIPLE (1997)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 40 (1997), S. 1335-1354 
    Details
    ISSN: 0029-5981
    Keywords: finite element methods ; complementary energy ; p-version ; stress extraction ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper presents a new method for accurate pointwise stress extraction from finite element solutions, applied to two-dimensional linear elastostatic problem shaving bounded value stresses. The method, denoted by SEC(Stress Extraction by Complementary principle), is based on the complementary energy principle applied overalocal domain in thepost-processing phase. Detailed formulation of the SEC method is provided, and numerical experiments with the h- and p-versions of the finite element method are presented for a family of exact solutions characterized by varying degree of smoothness. It is shown that on the boundaries of the domain, as well as in the interior, accurate pointwise stresses are obtained, and the relative error in the pointwise stresses converges with a rate which is as fast as the relative error measured in energy norm or faster. Importantly, the SEC method in conjunction with the p-version of the finite element method is virtually independent of the Poisson's ratio, and is equally applicable to nearly in compressible materials. © 1997 by John Wiley & Sons, Ltd.
    Additional Material: 11 Ill.
    Type of Medium: Electronic Resource
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  • 8
    Electronic Resource
    Electronic Resource
    Numerical analysis of edge singularities in three-dimensional elasticity (1997)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 40 (1997), S. 4611-4632 
    Details
    ISSN: 0029-5981
    Keywords: three-dimensional elasticity ; singularities ; finite element methods ; p-version ; Steklov method ; failure/fracture analysis ; multi-material interfaces ; delamination ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A numerical method is described for the computation of eigenpairs which characterize the exact solution of linear elastostatic problems in three-dimensions in the vicinity of edge singularities. These may be caused by re-entrant corners, abrupt changes in boundary conditions or material properties.Such singularities are of great interest from the point of view of failure initiation: The eigenpairs characterize the straining modes and their amplitudes quantify the amount of energy residing in particular straining modes. For this reason, failure theories directly or indirectly involve the eigenpairs and their amplitudes.This paper addresses the problem of determining the edge eigenpairs numerically on the basis of the modified Steklov formulation (presented in Reference 1 in a 2-D framework) in conjunction with the p-version of the finite element method. Numerical results are presented for several cases including isotropic as well as anisotropic multi-material interfaces. © 1997 John Wiley & Sons, Ltd.
    Additional Material: 13 Ill.
    Type of Medium: Electronic Resource
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  • 9
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    Numerical methods for extracting edge stress intensity functions in anisotropic three-dimensional domains (2007)
    Elsevier
    Details
    Publication Date: 2007-08-01
    Print ISSN: 0045-7825
    Electronic ISSN: 1879-2138
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Technology
    Published by Elsevier
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  • 10
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    Numerical thermo-elastic analysis of singularities in two-dimensions (1995)
    Springer
    Details
    Publication Date: 1995-12-01
    Print ISSN: 0376-9429
    Electronic ISSN: 1573-2673
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Published by Springer
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