C1 Discretizations for the Application to Gradient Elasticity
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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- 2.Argyris, J.H., Fried, I., Scharpf, D.W.: The TUBA family of elements for the matrix displacement method. Aeronaut. J. 72, 701–709 (1968) Google Scholar
- 5.Bogner, F.K., Fox, R.L.: The generation of inter-element-compatible stiffness and mass matrices by the use of interpolation formulas. In: Proceedings of the Conference held at Wright-Patterson Air Force Base, pp. 397–443. Wright-Patterson Air Force Base, Ohio (1965) Google Scholar
- 6.Clough, R.W., Tocher, J.L.: Finite element stiffness matrices for analysis of plate bending. In: Proceedings of the Conference held at Wright-Patterson Air Force Base, pp. 515–545. Wright-Patterson Air Force Base, Ohio (1965) Google Scholar
- 14.Rajagopal, A., Scherer, M., Steinmann, P., Sukumar, N.: Smooth conformal α-nem for gradient elasticity. Int. J. Struct. Changes Solids 1, 83–109 (2009) Google Scholar