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  • 1
    Electronic Resource
    Electronic Resource
    Boundary element calculation of shallow water waves (1990)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 10 (1990), S. 811-825 
    Details
    ISSN: 0271-2091
    Keywords: Boundary element method ; Shallow water equation ; Wave reflection ; Wave diffraction ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A boundary element method is proposed for studying periodic shallow water problems. The numerical model is based on the shallow water equation. The key feature of this method is that the boundary integral equations are derived using the weighted residual method and the fundamental solutions for shallow water wave problems are obtained by solving the simultaneous singular equations. The accuracy of this method is studied for the wave reflection problem in a rectangular tank. As a result of this test, it has been shown that the number of element divisions and the distribution of nodes are significant to the accuracy. For numerical examples of external problems, the wave diffraction problems due to single cylindrical, double cylindrical and plate obstructions are analysed and compared with the exact and other numerical solutions. Relatively accurate solutions are obtained.
    Additional Material: 13 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650100707
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  • 2
    Electronic Resource
    Electronic Resource
    A mathematical programming method for the inelastic analysis of reinforced concrete frames (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 1137-1154 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A mathematical programming method is presented for solving problems of (i) determining the moments and rotations and (ii) determining the safety factor of reinforced concrete frames. The proposed method is essentially a reformulation of those developed by De Donato and Maier. However, the reformulation results in a new mathematical programming model for which an efficient algorithm is developed. The advantage of the proposed method is mainly computational; in fact it requires roughly one half computer time and storage space as compared with those De Donato and Maier employ to solve the same problem.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620110709
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  • 3
    Electronic Resource
    Electronic Resource
    Piecewise linear elastic-plastic analysis (1979)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 14 (1979), S. 757-767 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The purpose of this paper is to show that a mathematical programming method, due to Maier and his co-workers, of nonlinear structural analysis can be rerformulated so that greater computational efficiences are achived. The methods are designed for a class of elastic-plastic structures under ‘piecewise linear’ assumptions and solve among others the problem of determining the stresses and strains in the structure. The reformulation gives rise to a class of mathematical programming problems calles a ‘n by dn linear complementarity problem’, for which the author has developed an efficient algorithm. It will be explained why and by how much the proposed method (the reformulation and its solution by the author's algorithm) solves the structural problems more efficiently than the existing one. Results of a systematic computer experiment supporting the efficiency of the proposed method are also presented.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620140509
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  • 4
    Electronic Resource
    Electronic Resource
    A decomposition procedure for large-scale optimum plastic design problemsSponsored by the United States Army under Contract Nos. DAAG29-75-C-0024 and DAAG29-80-C-0041. (1983)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 19 (1983), S. 873-889 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A decomposition procedure is proposed in this paper for solving a class of large-scale optimum design problems for perfectly-plastic structures under several alternative loading conditions. The conventional finite element method is used to cast the problem into a finite dimensional constrained nonlinear programming problem. Structures of practically meaningful size and complexity tend to give rise to a large number of variables and constraints in the corresponding mathematical model. The difficulty is that the state-of-the-art mathematical programming theory does not provide reliable and efficient ways of solving large-scale constrained nonlinear programming problems. The natural idea to deal with the large-scale structural problem is somehow to decompose the problem into a collection of small-size problems each of which represents an analysis of the behaviour of each finite element under a single loading condition. This paper proposes one such way of decomposition based on duality theory and a recently developed iterative algorithm called the proximal point algorithm.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620190609
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  • 5
    Electronic Resource
    Electronic Resource
    Minimum norm solutions to linear elastic analysis problems (1984)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 20 (1984), S. 983-998 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A basic problem in the linear elastic analysis is that of finding the vectors of stresses and strains, given a finite element model of a structure and a set of external loads. One purpose of this paper is to show that the problem is a special case of the minimum norm problem for underdetermined systems of linear equations. In this regard, the three conventional structural analysis approaches, i.e. the displacement method, the natural factor formulation and the force method, are unified and interpreted in the framework of the minimum norm problem, which is divided into two approaches - the primal formulation and the dual formulation. Numerical comparisons of several computational procedures capable of solving the minimum norm problem are given from computational efficiency and accuracy points of view. Included in the comparisons are the three conventional structural analysis approaches mentioned above, and several alternative approaches.
    Additional Material: 1 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620200602
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  • 6
    Electronic Resource
    Electronic Resource
    On computational procedures for the force method (1982)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 18 (1982), S. 1469-1495 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: It is known that the matrix force method has certain advantages over the displacement method for a class of structural problems. It is also known that the force method, when carried out by the conventional Gauss-Jordan procedure, tends to fill in the problem data, making the method unattractive for large size, sparse problems. This poor fill-in property, however, is not necessarily inherent to the method, and the sparsity may be maintained if one uses what we call the Turn-Back LU Procedure. The purpose of this paper is two-fold. First, it is shown that there exist some close relationships between the force method and the least squares problem, and that many existing algebraic procedures to perform the force method can be regarded as applications/extensions of certain well-known matrix factorization schemes for the least squares problem. Secondly, it is demonstrated that these algebraic procedures for the force method can be unified form the matrix factorization viewpoint. Included in this unification is the Turn-Back LU Procedure, which was originally proposed by Topçu in his thesis.8 It is explained why this procedure tends to produce sparse and banded ‘self-stress’ and flexibility matrices with small band width. Some computational results are presented to demonstrate the superiority of the Turn-Back LU Procedure over the other schemes considered in this paper.
    Additional Material: 11 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620181004
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