Available online at www.sciencedirect.com ScienceDirect Comput. Methods Appl. Mech. Engrg. 373 (2021) 113481 www.elsevier.com/locate/cma The strain-smoothed 4-node quadrilateral finite element Chaemin Lee a , San Kim a,b , Phill-Seung Lee a ,∗ a Department of Mechanical Engineering, Korea Advanced Institute of Science and Technology, 291 Daehak-ro, Yuseong-gu, Daejeon 34141, Republic of Korea b Department of Mechanical Convergence Engineering, Gyeongsang National University, 54, Charyong-ro 48beon-gil, Uichang-gu, Changwon-si, Gyeongsangnam-do 51391, Republic of Korea Received 20 January 2020; received in revised form 3 September 2020; accepted 2 October 2020 Available online xxxx Abstract Recently, the strain-smoothed element (SSE) method has been developed for 3-node triangular and 4-node tetrahedral solid elements. The method was also applied for enhancing the membrane performance of a 3-node triangular shell element (MITC3+ element). Using the SSE method, convergence behaviors of the finite elements were significantly improved without additional degrees of freedom. However, the application of the SSE method is limited to constant strain finite elements such as 3-node triangular and 4-node tetrahedral elements. In this paper, the SSE method is applied to a 4-node quadrilateral finite element. Doing so, the piecewise linear shape functions are employed instead of standard bilinear shape functions. The proposed strain- smoothed 4-node quadrilateral element passes all the basic tests, and shows a significantly improved accuracy in various numerical examples. c ⃝ 2020 Elsevier B.V. All rights reserved. Keywords: Finite element analysis; Strain-smoothed element method; Solid elements; 4-node quadrilateral elements 1. Introduction In the last decades, with the efforts of numerous researchers, the finite element method (FEM) has evolved significantly and has become the most useful tool for the analysis of solids and structures. It has also been commercially successful. While FEM is still developing, the pace of development has not been as fast as in the past. Obviously, the focus on improving FEM is to obtain more accurate and reliable solutions with less degrees of freedom (DOFs) or less computational cost [1–3]. Various attempts have been made to effectively improve the finite element method. The enriched FEM, XFEM (eXtended FEM) and GFEM (Generalized FEM) are good examples [4–14]. These methods introduce special enrichment functions such as analyzing discontinuities and singularities in solid mechanics problems and wave propagation problems [6–9], or improving the solution accuracy in the general analysis of solids and shells [10–14]. For these methods, the use of additional DOFs is inevitable compared with the standard FEM. Unlike these methods, strain smoothing methods are noteworthy in that solution accuracy can be improved without increasing the degrees of freedom [15–39]. In the well-known edge, node and cell-based smoothed finite element methods (S-FEM), new strain fields are constructed by referring strains from neighboring finite elements ∗ Corresponding author. E-mail address: [email protected] (P.S. Lee). https://doi.org/10.1016/j.cma.2020.113481 0045-7825/ c ⃝ 2020 Elsevier B.V. All rights reserved.
The strain-smoothed 4-node quadrilateral finite element
Jun 30, 2023
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