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  • 1
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 1677-1696 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The paper presents a classification of mathematical commonly encountered in connection with solution of non-linear finite element problems. The principal methods for numerical solution of the non-linear equations are surveyed and discussed. Special emphasis is placed upon the description of an automatic load incrementation procedure with equilibrium iterations. It is shown how this algorithm can be adapted for solving problems involving instabilities, snap-through and snap-back. A simple scalar quantity denoted the current stiffness parameter is suggested; this parameter is used to characterize the overall behaviour of non-linear problems. It can also be used as a steering parameter in the solution process. The use of the present technique is illustrated by several examples.
    Additional Material: 15 Ill.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 15 (1980), S. 1541-1555 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: It is shown how the convergence requirements for a finite element may be written as a set of linear constraints on the stiffness matrix. It is then attempted to construct a best possible stiffness matrix. The constraint equations restrict the way in which these stiffness terms may be chosen; however, there is normally still room for improving or optimizing an element. It is demonstrated how an element stiffness matrix may be found using rigid body, constant strain and higher order deformation modes. Further, it is shown how the constraint equations may be exploited in deriving an ‘energy orthogonality theorem’. This theorem opens the door to a whole new class of simple finite elements which automatically satisfy the convergence requirements. Examples of deriving plane stress and plate bending elements are given.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 34 (1992), S. 61-71 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Additional Material: 10 Ill.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 5 (1973), S. 543-556 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The finite element method is applied to stability and large deflection analysis of plates and shallow shells. Based on the von Karman strain expressions for plates and the Marguerre shallow shell theory, equilibrium and incremental equations for a non-linear analysis by finite elements is developed. Great emphasis is placed on the specific matrix formulation, thereby obtaining a highly efficient method that is well suited to modern electronic computer analysis. A doubly curved, non-linear quadrilateral element is developed. The versatility and efficiency of the present method is illustrated by several examples including large deflection and post shear-buckling behaviour of plates and snap-through of shallow shells.
    Additional Material: 10 Ill.
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 15 (1980), S. 790-790 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
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  • 6
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 20 (1984), S. 643-663 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Starting with a mathematical statement of the convergence requirements for an element stiffness matrix, the paper discusses displacement shape functions that may be used in connection with the potential energy principle. In short, these functions must be force orthogonal and energy orthogonal, but they need not be conforming (satisfy interelement compatibility). It is shown that the requirements to the displacement functions may be greatly relaxed through slight modifications of the coupling stiffness between fundamental and higher order displacement modes. Several alternative formulations are examined. In particular, a new ‘free formulation’ is suggested. Using this form, which is very simple, the only requirement to the displacement patterns used is that they should contain the fundamental deformation modes and be linearly independent. Applications of the theory to triangular and rectangular plate bending elements are shown; the simple stiffness matrix for the latter is given explicitly. The numerical results compare favourably with other types of finite elements.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
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  • 7
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 22 (1986), S. 575-595 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A method for the computation of hydrostatic forces on cable, truss, beam, plate and shell type structures is presented. A general large displacement formulation is assumed which allows for displacements and rotations of unlimited size. Equilibrating forces for nodal points as well as incremental force-displacement relationships are given. Various ways of making the geometric load matrix symmetric for incremental analysis is discussed. Alternative strategies for the incremental-iterative solution is also treated. A method for the determination of the hydrostatic stability of floating structures is suggested. Metacentres and centres of buoyancy for rotations about principal axes in the water plane are automatically computed. The paper presents three examples of applications: a pipe which is partially submerged, a full overturning of a floating space frame and, finally, a hydrostatic stability analysis of a ship.
    Additional Material: 12 Ill.
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  • 8
    Publication Date: 2022-05-26
    Description: © The Author(s), 2017. This article is distributed under the terms of the Creative Commons Attribution License. The definitive version was published in Earth-Science Reviews 169 (2017): 132–145, doi:10.1016/j.earscirev.2017.04.005.
    Description: The impact of anthropogenic ocean acidification (OA) on marine ecosystems is a vital concern facing marine scientists and managers of ocean resources. Euthecosomatous pteropods (holoplanktonic gastropods) represent an excellent sentinel for indicating exposure to anthropogenic OA because of the sensitivity of their aragonite shells to the OA conditions less favorable for calcification. However, an integration of observations, experiments and modelling efforts is needed to make accurate predictions of how these organisms will respond to future changes to their environment. Our understanding of the underlying organismal biology and life history is far from complete and must be improved if we are to comprehend fully the responses of these organisms to the multitude of stressors in their environment beyond OA. This review considers the present state of research and understanding of euthecosomatous pteropod biology and ecology of these organisms and considers promising new laboratory methods, advances in instrumentation (such as molecular, trace elements, stable isotopes, palaeobiology alongside autonomous sampling platforms, CT scanning and high-quality video recording) and novel field-based approaches (i.e. studies of upwelling and CO2 vent regions) that may allow us to improve our predictive capacity of their vulnerability and/or resilience. In addition to playing a critical ecological and biogeochemical role, pteropods can offer a significant value as an early-indicator of anthropogenic OA. This role as a sentinel species should be developed further to consolidate their potential use within marine environmental management policy making.
    Description: M.I. Berning is financed by the German Research Foundation Priority Programme 1158 Antarctic Research with Comparable Investigations in Arctic Sea Ice Areas (Project DFG-1158 SCHR 667/15-1).
    Keywords: Euthecosomatous pteropods ; Ocean acidification ; Calcifying organisms ; Marine ecosystem ; Carbonate chemistry
    Repository Name: Woods Hole Open Access Server
    Type: Article
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