Abstract
In finite element analyses, mesh refinement is frequently performed to obtain accurate stress or strain values or to accurately define the geometry. After mesh refinement, equivalent nodal forces should be calculated at the nodes in the refined mesh. If field variables and material properties are available at the integration points in each element, then the accurate equivalent nodal forces can be calculated using an adequate numerical integration. However, in certain circumstances, equivalent nodal forces cannot be calculated because field variable data are not available. In this study, a very simple nodal force distribution method was proposed. Nodal forces of the original finite element mesh are distributed to the nodes of refined meshes to satisfy the equilibrium conditions. The effect of element size should also be considered in determining the magnitude of the distributing nodal forces. A program was developed based on the proposed method, and several example problems were solved to verify the accuracy and effectiveness of the proposed method. From the results, accurate stress field can be recognized to be obtained from refined meshes using the proposed nodal force distribution method. In example problems, the difference between the obtained maximum stress and target stress value was less than 6 % in models with 8-node hexahedral elements and less than 1 % in models with 20-node hexahedral elements or 10-node tetrahedral elements.
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A. Trädegård, F. Nilsson and S. Östlund, FEM-remeshing technique applied to crack growth problems, Computer Methods in Applied Mechanics and Engineering, 160 (1–2) (1998) 115–131.
D. Peric, C. Hochard, M. Dutko and D. R. J. Owen, Transfer operators for evolving meshes in small strain elastoplasticity, Computer Methods in Applied Mechanics and Engineering, 137 (3–4) (1996) 331–344.
M. Nazem, D. Sheng and J. P. Carter, Stress integration and mesh refinement for large deformation in geomechanics, Int. J. Numer. Meth. Engng, 65 (2006) 1002–1027.
J. Mediavilla, R. H. J. Peerlings and M. G. D. Geers, A robust and consistent remeshing-transfer operator for ductile fracture simulations, Computers & Structures, 84 (8–9) (2006) 604–623.
A. R. Khoei, H. Azadi and H. Moslemi, Modeling of crack propagation via an automatic adaptive mesh refinement based on modified superconvergent patch recovery technique, Eng. Fract. Mech., 75 (2008) 2921–2945.
A. R. Raffray and M. Merola, Overview of the design and R&D of the ITER blanket system, Fusion Eng. Des., 87 (2012) 769–776.
S. Pak et al., Electromagnetic load calculation of the ITER machine using a single finite element model including narrow slits of the in-vessel components, Fusion Eng. Des., 88 (2013) 3224–3237.
D. W. Lee et al., Structural analysis by electro-magnetic loads for conceptual design of HCCR TBM-set, Fusion Eng. and Des., 109–111 (2016) 554–560.
O. C. Zienkiewicz and R. L. Taylor, The Finite Element Method, 4th Ed., McGraw-Hill, London, 1(1989).
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Recommended by Associate Editor Yang Zheng
Jai Hak Park received his M.S. and Ph.D. degrees in Mechanical Engineering from KAIST, Korea in 1981 and 1987, respectively. Dr. Park is currently a Professor at the Department of Safety Engineering, Chungbuk National University, Cheongju, Korea. His research interests include numerical fracture mechanics, safety of mechanical equipment, and applied mechanics.
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Park, J.H., Shin, K.I., Lee, D.W. et al. A simple nodal force distribution method in refined finite element meshes. J Mech Sci Technol 31, 2221–2228 (2017). https://doi.org/10.1007/s12206-017-0418-4
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DOI: https://doi.org/10.1007/s12206-017-0418-4