Abstract
In this paper, a novel enriched three-node triangular element with the augmented interpolation cover functions is proposed based on the original linear triangular element for two-dimensional solids. In this enriched triangular element, the augmented interpolation cover functions are employed to enrich the original standard linear shape functions over element patches. As a result, the original linear approximation space can be effectively enriched without adding extra nodes. To eliminate the linear dependence issue of the present method, an effective scheme is used to make the system matrices of the numerical model completely positive-definite. Through several typical numerical examples, the abilities of the present enriched three node triangular element in forced and free vibration analysis of two-dimensional solids are studied. The results show that, compared with the original linear triangular element, the present element can not only provide more accurate numerical results, but also have higher computational efficiency and convergence rate.
Highlights
Finite element method (FEM) [1,2,3] is a mature and powerful numerical method, which has become one of the most widely used numerical approaches in practical engineering applications because of its effectiveness and stability
From the results shown in the table, we can again find that more accurate natural frequency results can be predicted by the present enriched finite element method (EFEM)-N3 than the other mentioned elements
A novel linear triangular element enriched by interpolation cover functions (EFEM-N3) is used in tackling the two-dimensional dynamic problems
Summary
Finite element method (FEM) [1,2,3] is a mature and powerful numerical method, which has become one of the most widely used numerical approaches in practical engineering applications because of its effectiveness and stability. The strong form based meshfree techniques have been developed, such as the generalized finite difference method (GFDM) [32,33,34], the finite point method (FPM) [35,36] and various collocation techniques [37,38,39,40]. All of these different meshless techniques have their own associated merits, demerits and conditions of applicability. It should be pointed out that the meshless methods still can not match the classical FEM in terms versatility and flexibility in engineering applications and many challenging problems still remain unsolved so far
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