An improved meshless Shepard and least squares method possessing the delta property and requiring no singular weight function

By Xiaoying Zhuang, Hehua Zhu, Charles E. Augarde. 2014

109 citations recorded by the source corpus.

The meshless Shepard and least squares (MSLS) method and the meshless Shepard method are partition of unity based meshless interpolations which eliminate the problems by other meshless methods such as the difficulty in direct imposition of the essential boundary conditions. However, singular weight functions have to be used in both methods to enforce the approximation interpolatory, which leads to the loss of smoothness in approximation and locally oscillatory results. In this paper, an improved MSLS interpolation is developed by using dually defined nodal supports such that no singular weight function is required. The proposed interpolation satisfies the delta property at boundary nodes and the compatibility condition throughout the domain, and is capable of exactly reproducing the basis function. The computational cost of the present interpolation is much lower than the moving least-squares approximation which is probably the most widely used meshless interpolation at present.

Subfields: Civil and Structural Engineering, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/c67601b64c5aa5909d28ae27ccb7ae5b4e98ced2

Citations in the corpus

• Phase-field modeling of fracture in linear thin shells (2014, unknown): “1 Single edge notch tensile To get a better understanding of the proposed methodology, we consider a well studied benchmark example of 2D solid under plane stress state [51, 52].”
• Meshfree Methods: Progress Made after 20 Years (2017, unknown): “This approximation, as well as the RK and MLS approximations, were recently generalized under a unified framework (Wu et al. 2011), and have been employed for convex approximations and the weak Kronecker-delta property in the meshfree method (Wang and Chen 2014; Wu et al. 2015; Zhuang et al. 2014).”