Smoothed finite element method (SFEM) was introduced by application of the stabilized conforming nodal integration in the conventional finite element method. In this method, integration is performed on “smoothing domains” rather than elements. Smoothing domains are created based on cells, nodes or edges for two dimensional problems. Based on the smoothing domain creation method, different types of SFEM are developed that have different properties. It has been shown that these methods are insensitive to mesh distortion and are generally more computationally efficient than mesh-free and finite element methods for the same accuracy level. Because of their interesting features, they have been used to solve different problems. This paper investigates the performance of these methods in coupled hydro-mechanical (consolidation) analysis, by solution of some problems using a developed SFEM/FEM code. Biot’s consolidation theory is reviewed, and after introduction of the idea and formulation of SFEMs, discretized form of equations is given. Requirements for creation of stable coupled hydro-mechanical models are discussed and based on them, two methods for creation of stable SFEM models are introduced. To investigate the effectiveness of the methods, a number of examples are solved and results are compared with the finite element and analytical ones.
Oliaei, M.N. and Pak, A. Element free Galerkin meshless method for fully coupled analysis of consolidation process", Scientia Iranica, Transaction A, 16(1), pp. 65-77 (2009(. 2. Oliaei, M.N., Soga, K., and Pak, A. Some numerical issues using element-free Galerkin mesh-less method for coupled hydro-mechanical problems", International Journal for Numerical and Analytical Methods in Geomechanics, 33(7), pp. 915-938 (2009). 3. Oliaei, M.N., Pak, A., and Soga, K. A coupled hydromechanical analysis for prediction of hydraulic fracture propagation in saturated porous media using EFG mesh-less method", Computers and Geotechnics, 55, pp. 254-266 (2014). 4. Khoshghalb, A. and Khalili, N. A stable meshfree method for fully coupled ow-deformation analysis of saturated porous media", Computers and Geotechnics, 37(6), pp. 789-795 (2010). 5. Beissel, S. and Belytschko, T. Nodal integration of the element-free Galerkin method", Computer Methods in Applied Mechanics and Engineering, 139(1), pp. 49-74 (1996). 6. Chen, J.S., Wu, C.T., Yoon, S., and You, Y. A stabilized conforming nodal integration for Galerkin meshfree methods", International Journal for Numerical Methods in Engineering, 50(2), pp. 435-466 (2001). 7. Liu, G.R., Li, Y., Dai, K.Y., Luan, M.T., and Xue, W. A linearly conforming radial point interpolation method for solid mechanics problems", International Journal of Computational Methods, 3(04), pp. 401-428 (2006). 8. Liu, G. and Nguyen, T., Smoothed Finite Element Methods, 1st Edn., CRC Press, Boca Raton, USA (2010). 9. Liu, G.R., Dai, K.Y., and Nguyen, T.T. A smoothed _nite element method for mechanics problems", Computational Mechanics, 39(6), pp. 859-877 (2007). 10. Liu, G.R., Nguyen-Thoi, T., Nguyen-Xuan, H., and Lam, K.Y. A node-based smoothed _nite element method (NS-FEM) for upper bound solutions to solid mechanics problems", Computers & Structures, 87(1), pp. 14-26 (2009). 11. Liu, G.R., Nguyen-Thoi, T., and Lam, K.Y. An edgebased smoothed _nite element method (ES-FEM) for static, free and forced vibration analyses of solids", Journal of Sound and Vibration, 320(4), pp. 1100-1130 (2009). 244 E. Karimian and M. Oliaei/Scientia Iranica, Transactions A: Civil Engineering 26 (2019) 234{245 12. Nguyen-Thoi, T., Phung-van, P., Rabczuk, T., Nguyen-Xuan, H., and Le-Van, C. Free and forced vibration analysis using the n-sided polygonal cell-based smoothed _nite element method (nCS-FEM)", International Journal of Computational Methods, 10(01), p. 1340008 (2013). 13. Cui, X.Y., Hu, X.B., Li, G.Y., and Liu, G.R. A modi- _ed smoothed _nite element method for static and free vibration analysis of solid mechanics", International Journal of Computational Methods, 13(06), p. 1650043 (2016). 14. Cui, X.Y., Liu, G.R., Li, G.Y., Zhang, G.Y., and Sun, G.Y. Analysis of elastic-plastic problems using edgebased smoothed _nite element method", International Journal of Pressure Vessels and Piping, 86(10), pp. 711-718 (2009). 15. Lee, K., Son, Y., and Im, S. Three-dimensional variable-node elements based upon CS-FEM for elastic-plastic analysis", Computers & Structures, 158, pp. 308-332 (2015). 16. Liu, G.R., Chen, L., Nguyen-Thoi, T., Zeng, K.Y., and Zhang, G.Y. A novel singular node-based smoothed _nite element method (NS-FEM) for upper bound solutions of fracture problems", International Journal for Numerical Methods in Engineering, 83(11), pp. 1466-1497 (2010). 17. Zeng, W., Liu, G.R., Kitamura, Y., and Nguyen- Xuan, H. A three-dimensional ES-FEM for fracture mechanics problems in elastic solids", Engineering Fracture Mechanics, 114, pp. 127-150 (2013). 18. Liu, G.R., Chen, L., and Li, M. S-FEM for fracture problems, theory, formulation and application", International Journal of Computational Methods, 11(03), p. 1343003 (2014). 19. Li, E., Zhang, Z., He, Z.C., Xu, X., Liu, G.R., and Li, Q. Smoothed _nite element method with exact solutions in heat transfer problems", International Journal of Heat and Mass Transfer, 78, pp. 1219-1231 (2014). 20. Cui, X.Y., Li, Z.C., Feng, H., and Feng, S.Z. Steady and transient heat transfer analysis using a stable node-based smoothed _nite element method", International Journal of Thermal Sciences, 110, pp. 12-25 (2016). 21. He, Z.C., Li, G.Y., Liu, G.R., Cheng, A.G., and Li, E. Numerical investigation of ES-FEM with various mass re-distribution for acoustic problems", Applied Acoustics, 89, pp.222-233 (2015). 22. Wang, G., Cui, X.Y., Feng, H., and Li, G.Y. A stable node-based smoothed _nite element method for acoustic problems", Computer Methods in Applied Mechanics and Engineering, 297, pp. 348-370 (2015). 23. Chai, Y.B., Li, W., Gong, Z.X., and Li, T.Y. Hybrid smoothed _nite element method for two dimensional acoustic radiation problems", Applied Acoustics, 103, pp. 90-101 (2016). 24. Li, Y., Zhang, G.Y., Liu, G.R., Huang, Y.N., and Zong, Z. A contact analysis approach based on linear complementarity formulation using smoothed _nite element methods", Engineering Analysis with Boundary Elements, 37(10), pp. 1244-1258 (2013). 25. Nguyen-Xuan, H., Liu, G.R., Bordas, S., Natarajan, S., and Rabczuk, T. An adaptive singular ES-FEM for mechanics problems with singular _eld of arbitrary order", Computer Methods in Applied Mechanics and Engineering, 253, pp. 252-273 (2013). 26. Nguyen-Xuan, H., Wu, C.T., and Liu, G.R. An adaptive selective ES-FEM for plastic collapse analysis", European Journal of Mechanics-A/Solids, 58, pp. 278- 290 (2016). 27. Kumar, V. and Metha, R. Impact simulations using smoothed _nite element method", International Journal of Computational Methods, 10(04), p. 1350012 (2013). 28. Biot, M.A. General theory of three-dimensional consolidation", Journal of Applied Physics, 12(2), pp. 155- 164 (1941). 29. Babu_ska, I. The _nite element method with Lagrange multipliers", Numerische Mathematik, 20(3), pp. 179- 192 (1973). 30. Brezzi, F. On the existence, uniqueness and approximation of saddle-point problems arising from Lagrangian multipliers", Revue Fran_caise D_automatique, Informatique, Recherche Op_e Rationnelle. Analyse Num_erique, 8(2), pp. 129-151 (1974). 31. Zhu, J.Z., Taylor, Z.R.L., and Zienkiewicz, O.C., The Finite Element Method: Its Basis and Fundamentals, 7th Edn., Elsevier, USA (2013). 32. Bordas, S., Natarajan, S., Kerfriden, P., Augarde, C.E., Mahapatra, D.R., Rabczuk, T., and Pont, S.D. On the performance of strain smoothing for quadratic and enriched _nite element approximations (XFEM/GFEM/PUFEM)", International Journal for Numerical Methods in Engineering, 86(4-5), pp. 637- 666 (2011). 33. Terzaghi, K., Peck, R.B., and Mesri, G., Soil Mechanics in Engineering Practice, 3rd Edn., John Wiley & Sons, USA (1996).
Karimian, E., Oliaei, M. (2019). Application of smoothed finite element method in coupled hydro-mechanical analyses. Scientia Iranica, 26(1), 234-245. doi: 10.24200/sci.2017.4235
MLA
E. Karimian; M. Oliaei. "Application of smoothed finite element method in coupled hydro-mechanical analyses". Scientia Iranica, 26, 1, 2019, 234-245. doi: 10.24200/sci.2017.4235
HARVARD
Karimian, E., Oliaei, M. (2019). 'Application of smoothed finite element method in coupled hydro-mechanical analyses', Scientia Iranica, 26(1), pp. 234-245. doi: 10.24200/sci.2017.4235
VANCOUVER
Karimian, E., Oliaei, M. Application of smoothed finite element method in coupled hydro-mechanical analyses. Scientia Iranica, 2019; 26(1): 234-245. doi: 10.24200/sci.2017.4235
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