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Implementing the Node Based Smoothed Finite Element Method as User Element in Abaqus for Linear and Nonlinear Elasticity

S. Kshrisagar1, A. Francis1, J. J. Yee2, S. Natarajan1, C. K. Lee3,*

Integrated Modelling and Simulation Lab, Department of Mechanical Engineering, Indian Institute of Technology Madras, Chennai, 600036, India.
The Department of Architectural Engineering, Dong-A University, S04-0302, Engineering 2, 37, Nakdong-daero 550beon-gil, Saha-gu, Busan, 49315, Korea.
National Research Center for Disaster-free & Safe Ocean City, Dong-A University, S04-0311-3, Engineering 2, 37, Nakdong-daero 550beon-gil, Saha-gu, Busan, 49315, Korea.

*Corresponding Author: C. K. Lee. Email: email.

Computers, Materials & Continua 2019, 61(2), 481-502.


In this paper, the node based smoothed-strain Abaqus user element (UEL) in the framework of finite element method is introduced. The basic idea behind of the node based smoothed finite element (NSFEM) is that finite element cells are divided into subcells and subcells construct the smoothing domain associated with each node of a finite element cell [Liu, Dai and Nguyen-Thoi (2007)]. Therefore, the numerical integration is globally performed over smoothing domains. It is demonstrated that the proposed UEL retains all the advantages of the NSFEM, i.e., upper bound solution, overly soft stiffness and free from locking in compressible and nearly-incompressible media. In this work, the constant strain triangular (CST) elements are used to construct node based smoothing domains, since any complex two dimensional domains can be discretized using CST elements. This additional challenge is successfully addressed in this paper. The efficacy and robustness of the proposed work is obtained by several benchmark problems in both linear and nonlinear elasticity. The developed UEL and the associated files can be downloaded from


Cite This Article

S. Kshrisagar, A. Francis, J. J. Yee, S. Natarajan and C. K. Lee, "Implementing the node based smoothed finite element method as user element in abaqus for linear and nonlinear elasticity," Computers, Materials & Continua, vol. 61, no.2, pp. 481–502, 2019.


cc This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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