A three-dimensional finite element for gradient elasticity based on a mixed-type formulation

This paper presents a novel three-dimensional finite element for gradient elasticity. The new finite element BR153L9 is a straightforward extension of the two-dimensional element QU34L4 developed by Shu et al. (1999) [1], which is based on a mixed-type formulation. Within this paper the derivation of the mixed-type finite element scheme is reviewed and details of the implementation are given. Finally, numerical results of an extended patch test and a benchmark test with the three-dimensional finite element are presented in order to validate the formulation and prove the convergence.

New finite element for gradient elasticity based on a mixed-type formulation. Finite element scheme and the implementation of the finite element are presented. Patch test is used to validate the finite element formulation. Numerical results of a benchmark test show the convergence of the element.