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  • 1
    Electronic Resource
    Electronic Resource
    A hybrid-element approach to crack problems in plane elasticityPortions of this work were accomplished when the first author served as a visiting professor at the Istituto di Elaborazione dell'Informazione, Consiglio Nazionale delle Ricerche, Pisa, Italy, during the summer of 1972. The completion of this work was supported by the AFOSR under Contract No. F44620-72-C-18. (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 7 (1973), S. 297-308 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The hybrid-element concept and the complex variable technique have been adopted for constructing a special super-element to be used jointly with conventional finite elements for the analysis of elastic stress intensity factors for plane cracks. The use of the complex variable technique permits the proper consideration of the stress intensity at the crack tip, and it also leads to very efficient programming. The use of such a super-element in the finite element solution has been shown to be highly accurate when only a very coarse element mesh is used near the crack.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620070307
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  • 2
    Electronic Resource
    Electronic Resource
    A hybrid crack element for rectilinear anisotropic material (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 377-382 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620110211
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  • 3
    Electronic Resource
    Electronic Resource
    A family of hybrid plate elements (1982)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 18 (1982), S. 1455-1468 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Hybrid stress elements are known to provide accurate results for analyses of plate bending; in particular, for the prediction of moment distribution. The construction of hybrid stiffness matrix requires numerical inversion of a moment matrix, evaluation of some relatively complicated boundary integrals and several matrix transformations. Each of these operations can be time-consuming, and the matrix inversion can result in a loss of numerical accuracy.This paper devises methods to explicitly invert the moment matrices. We find that for triangular elements the inverse is independent of the element shape and is only inversely proportional to its size. We also use a novel set of displacement variables, which greatly simplifies the boundary integration. The displacement variables are chosen in a hierarchical form so that lower order elements can be determined by straightforward reduction of excess terms in a higher order element. Except for the nodal displacements at the vertices, the present approach involves only variables at the midpoints of the sides of an element.
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620181003
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  • 4
    Electronic Resource
    Electronic Resource
    Relations between incompatible displacement model and hybrid stress model (1986)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 22 (1986), S. 173-181 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An examination of the variational formulations confirms the similarity between the incompatible displacement model and the assumed stress hybrid model that was pointed out by Irons in 1972. But the basic differences between the two are also identified. For 8-node solid elements the assumed stress terms obtained through a rational procedure also agree with those deduced by Irons purely from his physical insight.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620220112
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  • 5
    Electronic Resource
    Electronic Resource
    Basis of finite element methods for solid continua (1969)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 1 (1969), S. 3-28 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Finite element methods can be formulated from the variational principles in solid mechanics by relaxing the continuity requirements along the interelement boundaries. The combination of different variational principles and different boundary continuity conditions yields numerous types of approximate methods. This paper reviews and reinterprets the existing finite element methods and indicates other alternative schemes. Plate bending problems are used to compare the relative merits of the various methods.
    Additional Material: 10 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620010103
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  • 6
    Electronic Resource
    Electronic Resource
    New displacement hybrid finite element models for solid continuaThis work was supported by the Office of Scientific Research of the United States Air Force under Contract No. F44620-67-C-0019.The author wishes to express his appreciation to Professor T. H. H. Pian for his useful comments and suggestions. (1970)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 2 (1970), S. 73-83 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The proposed finite element model is based on separate assumptions of interior and interelement displacements and on the assumed boundary tractions of each individual element. The associated variational functional for this model is presented. This method has the same merits of the assumed stress method (References 3 and 4) in that a compatible displacement function at the interelement boundary can be easily constructed, while it can easily be used for shells with distributed loads.
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620020108
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  • 7
    Electronic Resource
    Electronic Resource
    Letters to the editor (1979)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 14 (1979), S. 1872-1874 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620141209
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  • 8
    Electronic Resource
    Electronic Resource
    Simplex elements of C0 continuity with varying polynomial degrees (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 27-38 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A hierarchical approach is used to construct the simplex elements which permits easy merging of elements of different orders. The explicit interpolation functions and the algorithm of using such elements are presented.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620110105
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  • 9
    Electronic Resource
    Electronic Resource
    Singular finite elements for the fracture analysis of V-notched plate (1980)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 15 (1980), S. 1343-1354 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Special accurate and efficient hybrid elements were developed to account for notch-tip singularities of type rγ, where γ can be complex. Proper normalization of the notch-tip element size was used to minimize the oscillation of the assumed function around the boundaries of the element and to improve the accuracy of the solution. Examples of various notch angles and sizes are presented.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620150907
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  • 10
    Electronic Resource
    Electronic Resource
    Unified Relaxation Spectrum for Polymers of Multiple Scales Based upon a Fuzzy Constraint Method and Non-Equilibrium Statistical Thermodynamics (1999)
    Springer
    Mechanics of time-dependent materials 3 (1999), S. 263-278 
    Details
    ISSN: 1573-2738
    Keywords: fuzzy constraint method ; multiple scales ; non-equilibrium statistical thermodynamics ; polymers ; unified relaxation spectrum
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract The molecular relaxation mechanisms of polymers withmulti-scale units of motion in glassy, rubbery and melt states areproposed based upon a fuzzy constraint method and non-equilibriumstatistical thermodynamics. The entanglement effects due to cohesiveforce and steric hindrance are expressed quantitatively in terms of amembership function. The micro-Brownian motion of a polymer chain isgoverned by the Langevin equation, which accounts for viscous force,nonuniform tension, entanglement constraint force and random force.Perturbation solutions have been established for different time and sizescales. The solutions account for the effects of both intramolecular andintermolecular interactions in the relaxation process. The unifiedrelaxation spectrum over many orders of time scale is a naturalconsequence of macromolecular structure, which satisfies thetime-temperature equivalence in the form of the Arrhenius equation atlow and high temperatures and in the form of the WLF equation near theglass transition temperature. The barrier model, the normal mode theory,the retraction and reptation theories can be taken as special casescorresponding to different scales.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1009895812870
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