Abstract: Combined finite element formulation is built according to modified H -R variation principle and minimum potential principle. Firstly, the Euler equation expressing the relationship between out -plane stress and displacement is derived from discretized H-R variation principle. Secondly, the Euler equation expressing the relationship between displacement and out-load is deduced from potential principle, the displacement solution can be independently obtained from Euler equation. Substituting the displacement solution into the first Euler equation, the out-plane stress solution can be obtained. Considering the different materials consisting of the structure, the in-plane stress solution can be obtained by a set of linear equations, avoiding the direct stress solution method basing on constitutive relationship at element level. Example shows that the numerical result of linear eight-noded NCCFE is stably convergent, balanced and reliable with fast convergence speed and high accuracy.

Key words: H-R variational principle, potential principle, constitutive relation, combined finite element method