Mixed finite element formulations for strain-gradient elasticity problems using the FEniCS environment

作者：Phunpeng V^*; Baiz P M

来源：Finite Elements in Analysis and Design, 2015, 96: 23-40.

DOI：10.1016/j.finel.2014.11.002

• Mixed finite element formulation
• Strain gradient elasticity
• FEniCS

This paper presents finite element implementations for the solution of gradient elasticity problems using the FEniCS project. The FEniCS Project provides a novel tool for the automated solution of partial differential equations by the finite element method. In particular, it offers a significant flexibility with regards to modelling and numerical discretization choices. The weak form of the gradient elasticity problem is derived from the Principal of Virtual Work. An equivalent mixed type finite element formulation for the strain gradient elasticity problem is implemented in order to avoid the use of C-1 continuous elements. The complete methodology and source codes (python scripts) are provided. Numerical results are presented and compared with well-known benchmark examples, demonstrating the applicability of FEniCS for such applications.

• 出版日期2015-4