Consistent generalized finite element method: An accurate and robust mesh-based method even in distorted meshes

A consistent generalized finite element method (C-GFEM) is proposed, showing excellent accuracy and convergence in distorted quadrilateral and hexahedral meshes. Both displacement approximation and domain integration are taken into consideration regarding the declining performance of the finite element method (FEM) in distorted meshes. In the displacement approximation, extra-degrees of freedom-free and linearly independent enrichments developed in GFEM are employed, which restores the reproducibility of the approximation in distorted meshes. In the domain integration, the idea of correcting nodal derivatives in the framework of the Hu-Washizu three-field variational principle is introduced into GFEM, based on which consistent integration schemes using quadrilateral and hexahedral elements are developed in this work. Furthermore, to consistently enforce the essential boundary condition, additional terms of boundary integral are introduced into the weak form. As a result, the proposed C-GFEM can pass patch tests and keep high accuracy even though the computational mesh is distorted. Its perfect performance in distorted meshes is sufficiently demonstrated by the numerical investigation of several benchmark examples.