The Finite Element Method with High-Order Enrichment Functions for Elastodynamic Analysis

Xunbai Du, Sina Dang, Yuzheng Yang and Yingbin Chai ()
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Xunbai Du: School of Ship and Ocean Engineering, Jiangsu Maritime Institute, Nanjing 211170, China
Sina Dang: Air and Missile Defense School, Air Force Engineering University, Xi’an 710051, China
Yuzheng Yang: School of Naval Architecture and Ocean Engineering, Huazhong University of Science and Technology, Wuhan 430074, China
Yingbin Chai: School of Naval Architecture, Ocean and Energy Power Engineering, Wuhan University of Technology, Wuhan 430063, China

Mathematics, 2022, vol. 10, issue 23, 1-27

Abstract: Elastodynamic problems are investigated in this work by employing the enriched finite element method (EFEM) with various enrichment functions. By performing the dispersion analysis, it is confirmed that for elastodynamic analysis, the amount of numerical dispersion, which is closely related to the numerical error from the space domain discretization, can be suppressed to a very low level when quadric polynomial bases are employed to construct the local enrichment functions, while the amount of numerical dispersion from the EFEM with other types of enrichment functions (linear polynomial bases or first order of trigonometric functions) is relatively large. Consequently, the present EFEM with a quadric polynomial enrichment function shows more powerful capacities in elastodynamic analysis than the other considered numerical techniques. More importantly, the attractive monotonic convergence property can be broadly realized by the present approach with the typical two-step Bathe temporal discretization technique. Three representative numerical experiments are conducted in this work to verify the abilities of the present approach in elastodynamic analysis.

Keywords: high-order enrichment functions; numerical methods; numerical dispersion; transient analysis; wave propagation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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