Abstract
Starting with a recently developed three-dimensional eight node brick Cosserat element for nonlinear elastic materials, a simplified Cosserat element is developed for torsionless axisymmetric motions. The equations are developed within the context of the theory of a Cosserat point and the resulting theory is hyperelastic and is valid for dynamics of nonlinear elastic materials. The axisymmetric Cosserat element has four nodes with a total of eight degrees of freedom. As in the more general element, the constitutive equations are algebraic expressions determined by derivatives of a strain energy function and no integration is needed throughout the element region. Examples of large deformations of a nearly incompressible circular cylindrical tube and large deflections of a compressible clamped circular plate are considered to test the accuracy of the element.
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Rubin, M.B. Numerical solution of axisymmetric nonlinear elastic problems including shells using the theory of a Cosserat point. Comput Mech 36, 266–288 (2005). https://doi.org/10.1007/s00466-005-0665-6
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DOI: https://doi.org/10.1007/s00466-005-0665-6