Discretisation of gradient elasticity problems using C1 finite elements

Fischer, Paul, Mergheim, Julia and Steinmann, Paul (2010) Discretisation of gradient elasticity problems using C1 finite elements. In, Mechanics of Generalized Continua. (Advances in Mechanics and Mathematics, 21) EUROMECH 510, G. Maugin (ed), Springer (24/03/10) United States, US. Springer, pp. 279-286. (doi:10.1007/978-1-4419-5695-8_29).

Abstract

For the numerical solution of gradient elasticity, the appearance of strain gradients in the weak form of the equilibrium equation leads to the need for C 1-continuous discretization methods. In the present work, the performances of a variety of C 1-continuous elements as well as the C 1 Natural Element Method are investigated for the application to nonlinear gradient elasticity. In terms of subparametric triangular elements the Argyris, Hsieh–Clough–Tocher and Powell–Sabin split elements are utilized. As an isoparametric quadrilateral element, the Bogner–Fox–Schmidt element is used. All these methods are applied to two different numerical examples and the convergence behavior with respect to the L 2, H 1 and H 2 error norms is examined.

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