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    Formulation methods of geometric and material nonlinearity problems

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    Date
    1984-05
    Type
    Article
    Author
    Dokainish, M. A.
    Gadala, Mohamed S.
    Oravas, G. Ae
    Metadata
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    Abstract
    A concise survey of formulation methods of geometric and material nonlinearity problems is given. Differences between existing formulations in the literature are discussed. A consistent Lagrangian and updated Lagrangian formulations are derived from the energy balance equation transformed to the proper reference configuration. Differences between the existing formulations and similar ones in the literature are found to be in specific geometric nonlinear terms in the final incremental equation as well as in the definition of the load increment vector. Specific forms of constitutive equations for elastic and elastoplastic materials are presented. Some of the forms used by other authors in application to elastoplastic materials are shown to be inconsistent. Sample numerical examples intended for checking some particular points in the formulation are presented.
    URI
    https://dspace.adu.ac.ae/handle/1/1991
    DOI
    https://doi.org/10.1002/nme.1620200508
    Citation
    Gadala, M. S., Dokainish, M. A., & Oravas, G. A. (1984). Formulation methods of geometric and material nonlinearity problems. International journal for numerical methods in engineering, 20(5), 887-914.
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