Meshless Generalized Finite Difference Method Based on Nonlocal Differential Operators for Numerical Simulation of Elastostatics

Yeying Zhou, Chunguang Li (), Xinshan Zhuang and Zhifen Wang
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Yeying Zhou: School of Civil Engineering Architecture and the Environment, Hubei University of Technology, Wuhan 430068, China
Chunguang Li: State Key Laboratory of Geomechanics and Geotechnical Engineering, Institute of Rock and Soil Mechanics, Chinese Academy of Sciences, Wuhan 430071, China
Xinshan Zhuang: School of Civil Engineering Architecture and the Environment, Hubei University of Technology, Wuhan 430068, China
Zhifen Wang: Beijing Municipal Construction Group Co., Ltd., Beijing 100048, China

Mathematics, 2024, vol. 12, issue 9, 1-20

Abstract: This study proposes an innovative meshless approach that merges the peridynamic differential operator (PDDO) with the generalized finite difference method (GFDM). Based on the PDDO theory, this method introduces a new nonlocal differential operator that aims to reduce the pre-assumption required for the PDDO method and simplify the calculation process. By discretizing through the particle approximation method, this technique proficiently preserves the PDDO’s nonlocal features, enhancing the numerical simulation’s flexibility and usability. Through the numerical simulation of classical elastic static problems, this article focuses on the evaluation of the calculation accuracy, calculation efficiency, robustness, and convergence of the method. This method is significantly stronger than the finite element method in many performance indicators. In fact, this study demonstrates the practicability and superiority of the proposed method in the field of elastic statics and provides a new approach to more complex problems.

Keywords: nonlocal differential operator; generalized finite difference method; elastostatics; numerical simulation; computational efficiency; robustness (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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