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  • 1
    Electronic Resource
    Electronic Resource
    On artificial strain of thin curved elements (1987)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 24 (1987), S. 2167-2181 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper presents an attempt to clarify further the nature of the overstiffness of thin curved structural elements. It follows the approach presented by Ashwell and co-workers1,2 who based their study on shape functions of arch elements. Such elements display the same stiff behaviour as complex shell elements but are simpler to study and understand. An examination of several discretizations for a two-dimensional curved beam-column element for linear elastic analysis of arches is performed. This examination and the numerical results obtained from these approximations provide a new interpretation of the artificial strains based on the mapping variables of shape functions. Two new methods to reduce the artificial stiffness of the element are proposed.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620241110
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  • 2
    Electronic Resource
    Electronic Resource
    Equilibrium considerations of the updated Lagrangian formulation of beam-columns with natural concepts (1987)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 24 (1987), S. 2119-2141 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Bathe and co-workers'1,2 updated Lagrangian formulation is reviewed for a two-dimensional beam-column element. From this review a physical interpretation and properties are derived for the matrices of the method. A variant of Argyris and co-workers'4,5 natural concept is introduced in the updated Lagrangian formulation, and a new method to derive element matrices arises. A detailed derivation of the matrices of the twodimensional beam-column element is presented to clarify further the UL formulations. Explicit expressions for these matrices, computed with the use of symbolic manipulation,17 are also presented to illustrate the concepts discussed. Finally, numerical results are shown to compare and evaluate different methods and matrices.
    Additional Material: 12 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620241108
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  • 3
    Electronic Resource
    Electronic Resource
    Convected systems for curved structural elements (1987)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 24 (1987), S. 2143-2166 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper presents a new approach to the use of the updated Lagrangian formulation with convected systems. The development of this new method is similar to the updated Lagrangian formulation presented by Bathe et al.4 The main difference is that here the tensors are written in their components in the curvilinear convected system, while Bathe, Ramm, and Wilson employ Cartesian components. A special form of the natural approach5 is also introduced in this formulation to simplify the element computations. The matrices of a two-dimensional curved beam-column element are derived as an example of this new formulation. Finally, a numerical evaluation is performed to evaluate critically the new curved element and the method proposed here.
    Additional Material: 12 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620241109
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  • 4
    Electronic Resource
    Electronic Resource
    Node and element resequencing using the Laplacian of a finite element graph: Part II - Implementation and numerical results (1994)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 37 (1994), S. 1531-1555 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In Part I of this work, Paulino et al.1 have presented an algorithm for profile and wavefront reduction of large sparse matrices of symmetric configuration. This algorithm is based on spectral properties of a Finite Element Graph (FEG), An FEG has been defined as a nodal graph G, a dual graph G* or a communication graph G· associated with a generic finite element mesh. The novel algorithm has been called Spectral FEG Resequencing (SFR). This algorithm has specific features that distinguish it from previous algorithms. These features include (1) use of global information in the graph, (2) no need of a pseudoperipheral vertex or the endpoints of a pseudodiameter, and (3) no need of any type of level structure of the FEG. To validate this algorithm in a numerical sense, extensive computational testing on a variety of problems is presented here. This includes algorithmic performance evaluation using a library of benchmark test problems which contains both connected and non-connected graphs, study of the algebraic connectivity (λ2) of an FEG, eigensolver convergence verification, running time performance evaluation and assessment of the algorithm on a set of practical finite element examples. It is shown that the SFR algorithm is effective in reordering nodes and/or elements of generic finite element meshes. Moreover, it computes orderings which compare favourably with the ones obtained by some previous algorithms that have been published in the technical literature.
    Additional Material: 13 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620370908
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  • 5
    Electronic Resource
    Electronic Resource
    A new algorithm for finding a pseudoperipheral vertex or the endpoints of a pseudodiameter in a graph (1994)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 10 (1994), S. 913-926 
    Details
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Based on the concept of the Laplacian matrix of a graph, this paper presents the SGPD (spectral graph pseudoperipheral and pseudodiameter) algorithm for finding a pseudoperipheral vertex or the end-points of a pseudodiameter in a graph. This algorithm is compared with the ones by Grimes et al. (1990), George and Liu (1979), and Gibbs et al. (1976). Numerical results from a collection of benchmark test problems show the effectiveness of the proposed algorithm. Moreover, it is shown that this algorithm can be efficiently used in conjunction with heuristic algorithms for ordering sparse matrix equations. Such heuristic algorithms, of course, must be the ones which use the pseudoperipheral vertex or pseudodiameter concepts.
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640101107
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  • 6
    Electronic Resource
    Electronic Resource
    Natural approach for thin-walled beam-columns with elastic-plasticity (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 1653-1679 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In a realistic analysis of thin-walled steel frames the warping of beam-columns of open cross-section must be considered. To model the behaviour of these structures up to collapse load, the plasticity of the material also has to be included in the analysis. This work presents the derivation of a new finite element for three-dimensional non-linear analysis of steel frames with bi-symmetrical cross-sections that models warping and elastic-plasticity. The displacement field is described by the Principle of Sectorial Areas and is modelled with Hermitian functions. For the material non-linearity the Incremental Plasticity Theory in a concentrated plasticity model has been used. The yield surfaces based on the natural stress resultants which include torsion and bimoment are used in the formulation of the element. The matrices of the proposed element are derived explicitly and implemented in a computer program which uses the Natural Approach. The implemented stress recovery process is insensitive to rigid-body motions. The accuracy of the finite element and the efficiency of the implementation are illustrated through examples.
    Additional Material: 13 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620290804
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  • 7
    Electronic Resource
    Electronic Resource
    Natural approach for geometric non-linear analysis of thin-walled frames (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 30 (1990), S. 207-231 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new stiffness matrix for geometrically non-linear analysis of three-dimensional beam-columns with bisymmetrical, thin-walled, I-type cross-sections is presented. The displacement field is described in terms of natural and rigid-body displacements and both Cartesian and natural matrices are derived. A novelty of the resulting method is the use of this dual description in all aspects of the analysis including the computer implementation. A companion paper1 that introduces the plastic behaviour of the material also justifies the need for this dual approach as a means to separate nodal forces from stress resultants in the cross-section of the 3D beam-column element. The current development uses the updated Lagrangian formulation and corrections in the element matrix are made to properly consider the behaviour under finite rotation. It is shown that accuracy and convergence of the solution process can be improved if the natural matrices derived here are used in a new force recovery process that is insensitive to rigid-body displacements.
    Additional Material: 10 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620300202
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  • 8
    Electronic Resource
    Electronic Resource
    Authors' reply (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 32 (1991), S. 213-213 
    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.1620320114
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  • 9
    Electronic Resource
    Electronic Resource
    Node and element resequencing using the Laplacian of a finite element graph: Part I - General concepts and algorithm (1994)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 37 (1994), S. 1511-1530 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A Finite Element Graph (FEG) is defined here as a nodal graph (G), a dual graph (G*), or a communication graph (G·) associated with a generic finite element mesh. The Laplacian matrix (L(G),L(G*) or L(G·)), used for the study of spectral properties of an FEG, is constructed from usual vertex and edge connectivities of a graph. An automatic algorithm, based on spectral properties of an FEG (G, G* or G·), is proposed to reorder the nodes and/or elements of the associated finite element mesh. The new algorithm is called Spectral PEG Resequencing (SFR). This algorithm uses global information in the graph, it does not depend on a pseudoperipheral vertex in the resequencing process, and it does not use any kind of level structure of the graph. Moreover, the SFR algorithm is of special advantage in computing environments with vector and parallel processing capabilities.Nodes or elements in the mesh can be reordered depending on the use of an adequate graph representation associated with the mesh. If G is used, then the nodes in the mesh are properly reordered for achieving profile and wavefront reduction of the finite element stiffness matrix. If either G* or G· is used, then the elements in the mesh are suitably reordered for a finite element frontai solver, A unified approach involving FEGs and finite element concepts is presented. Conclusions are inferred and possible extensions of this research are pointed out.In Part II of this work,1 the computational implementation of the SFR algorithm is described and several numerical examples are presented. The examples emphasize important theoretical, numerical and practical aspects of the new resequencing method.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620370907
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  • 10
    Electronic Resource
    Electronic Resource
    Geometrical properties in the B-spline representation of arbitrary domains (1987)
    New York, NY [u.a.] : Wiley-Blackwell
    Communications in Applied Numerical Methods 3 (1987), S. 345-349 
    Details
    ISSN: 0748-8025
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper presents a new method to compute areas and moments of arbitrary domains bounded by periodic cubic B-splines. The proposed method gives exact answers, it is very efficient and relies only on the control points co-ordinates of the B-spline. One example is presented and compared with analytical results and with previous numerical work.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1630030417
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