A two-level nesting smoothed meshfree method for structural dynamic analysis.

• A novel two-level nesting smoothed meshfree method (NSMM) is proposed. • The NSMM is applied for structural dynamic analysis. • The NSMM is directly extended to solving dynamic fracture problems. • The NSMM is efficient, accurate and stable. This paper presents a novel two-level nesting smoothed meshfree method (NSMM), which significantly improves the computational efficiency of the meshfree Galerkin methods without losing their accuracy, thus facilitates the employment of meshfree methods in applications where background integration cells would be prohibitively expensive. In the NSMM, the system stiffness matrix is calculated using the general smoothing strain technique over the two-level nesting smoothing sub-domains where fewer integration points are used and the costly derivative computation of meshfree shape functions is avoided. The accuracy, efficiency and stability of the present method are assessed by virtue of several numerical examples for problems involving free and forced vibration analysis of the linear elastic continua and dynamic crack response of elastic solid. The results reveal that the NSMM stands out and achieves better performance compared to other existing approaches in the literature. [ABSTRACT FROM AUTHOR]