epSFEM: A Julia-Based Software Package of Parallel Incremental Smoothed Finite Element Method (S-FEM) for Elastic-Plastic Problems

Meijun Zhou, Jiayu Qin, Zenan Huo, Fabio Giampaolo and Gang Mei
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Meijun Zhou: School of Engineering and Technology, China University of Geosciences (Beijing), Beijing 100083, China
Jiayu Qin: School of Engineering and Technology, China University of Geosciences (Beijing), Beijing 100083, China
Zenan Huo: School of Engineering and Technology, China University of Geosciences (Beijing), Beijing 100083, China
Fabio Giampaolo: Consorzio Interuniversitario Nazionale per l’Informatica (CINI), 80100 Naples, Italy
Gang Mei: School of Engineering and Technology, China University of Geosciences (Beijing), Beijing 100083, China

Mathematics, 2022, vol. 10, issue 12, 1-25

Abstract: In this paper, a parallel Smoothed Finite Element Method (S-FEM) package epSFEM using incremental theory to solve elastoplastic problems is developed by employing the Julia language on a multicore CPU. The S-FEM, a new numerical method combining the Finite Element Method (FEM) and strain smoothing technique, was proposed by Liu G.R. in recent years. The S-FEM model is softer than the FEM model for identical grid structures, has lower sensitivity to mesh distortion, and usually produces more accurate solutions and a higher convergence speed. Julia, as an efficient, user-friendly and open-source programming language, balances computational performance, programming difficulty and code readability. We validate the performance of the epSFEM with two sets of benchmark tests. The benchmark results indicate that (1) the calculation accuracy of epSFEM is higher than that of the FEM when employing the same mesh model; (2) the commercial FEM software requires 10,619 s to calculate an elastoplastic model consisting of approximately 2.45 million triangular elements, while in comparison, epSFEM requires only 5876.3 s for the same computational model; and (3) epSFEM executed in parallel on a 24-core CPU is approximately 10.6 times faster than the corresponding serial version.

Keywords: elastic-plastic problems; incremental theory; Smoothed Finite Element Method (S-FEM); Julia language; parallel programming (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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