Browse > Article
http://dx.doi.org/10.12989/sem.2022.83.3.353

An efficient adaptive finite element method based on EBE-PCG iterative solver for LEFM analysis  

Hearunyakij, Manat (Department of Mechanical Engineering Technology, College of Industrial Technology, King Mongkut's University of Technology North Bangkok)
Phongthanapanich, Sutthisak (Department of Mechanical Engineering Technology, College of Industrial Technology, King Mongkut's University of Technology North Bangkok)
Publication Information
Structural Engineering and Mechanics / v.83, no.3, 2022 , pp. 353-361 More about this Journal
Abstract
Linear Elastic Fracture Mechanics (LEFM) has been developed by applying stress analysis to determine the stress intensity factor (SIF, K). The finite element method (FEM) is widely used as a standard tool for evaluating the SIF for various crack configurations. The prediction accuracy can be achieved by applying an adaptive Delaunay triangulation combined with a FEM. The solution can be solved using either direct or iterative solvers. This work adopts the element-by-element preconditioned conjugate gradient (EBE-PCG) iterative solver into an adaptive FEM to solve the solution to heal problem size constraints that exist when direct solution techniques are applied. It can avoid the formation of a global stiffness matrix of a finite element model. Several numerical experiments reveal that the present method is simple, fast, and efficient compared to conventional sparse direct solvers. The optimum convergence criterion for two-dimensional LEFM analysis is studied. In this paper, four sample problems of a two-edge cracked plate, a center cracked plate, a single-edge cracked plate, and a compact tension specimen is used to evaluate the accuracy of the prediction of the SIF values. Finally, the efficiency of the present iterative solver is summarized by comparing the computational time for all cases.
Keywords
finite element method; iterative solver; LEFM; stress intensity factor;
Citations & Related Records
Times Cited By KSCI : 1  (Citation Analysis)
연도 인용수 순위
1 Martinez-Frutos, M. and Herrero-Perez, D.H. (2015), "Efficient matrix-free GPU implementation of fixed grid finite element analysis", Finite Elem. Anal. Des., 104(13-14), 61-71. https://doi.org/10.1016/j.finel.2015.06.005.   DOI
2 Martinez-Frutos, J., Martinez-Castejon, P.J. and Herrero-Perez, D. (2015), "Fine-grained GPU implementation of assembly-free iterative solver for finite element problems", Comput. Struct., 15, 9-18. https://doi.org/10.1016/j.compstruc.2015.05.010.   DOI
3 Nakajima, K. and Okuda, H. (2004), "Parallel iterative solvers with selective blocking preconditioning for simulations of fault-zone contact", Numer. Linear. Algebr., 11(8-9), 831-852. https://doi.org/10.1002/nla.349.   DOI
4 Phongthanapanich, S. and Dechaumphai, P. (2006), "Easy FEM-An object-oriented graphics interface finite element/finite volume software", Adv. Eng. Softw., 37(2), 797-804. https://doi.org/10.1016/j.advengsoft.2006.05.006.   DOI
5 Ruppert, J. (1995), "A Delaunay refinement algorithm for quality 2-dimensional mesh generation", J. Algorithm, 18(3), 548-585. https://doi.org/10.1006/jagm.1995.1021.   DOI
6 Koric, S., Lu, Q. and Guleryuz, E. (2014), "Evaluation of massively parallel linear sparse solvers on unstructured finite element meshes", Comput. Struct., 141, 19-25. https://doi.org/10.1016/j.compstruc.2014.05.009.   DOI
7 Murakami, Y. (1987), Stress Intensity Factors Handbook, Pergamon Press, Oxford, NY, USA.
8 Phongthanapanich, S. and Dechaumphai, P. (2009), "Combined finite volume element method for singularly perturbed reaction-diffusion problems", Appl. Math. Comput., 209(2), 177-185. https://doi.org/10.1016/j.amc.2008.10.047.   DOI
9 Smith, I.M., Griffiths, D.V. and Margetts, L. (2014), Programming the Finite Element Method, 5th Edition, Wiley, Chennai, India.
10 Shewchuck, J.R. (1994), "An introduction to the conjugate gradient method without the agonizing pain", Carnegie Mellon University, Pittsburgh, PA.
11 Hales, J.D., Novascone, S.R., Williamson, R.L., Gaston, D.R. and Tonks, M.R. (2012), "Solving nonlinear solid mechanics problems with the Jacobian-free Newton Krylov method", CMES-Comput. Model Eng., 84(2), 123-152. https://doi:10.3970/cmes.2012.084.123.   DOI
12 Dechaumphai, P. and Phongthanapanich, S. (2004), "Adaptive Delaunay triangulation with object-oriented programming for crack propagation analysis", Finite Elem. Anal. Des., 40(13-14), 1753-1771. https://doi.org/10.1016/j.finel.2004.01.002.   DOI
13 Anderson, T.L. (2005), Fracture Mechanics: Fundamentals and Applications, 7th Edition, CRC Press, Boca Raton, FL, USA.
14 Augarde, C.E., Ramage, A. and Staudacher, J. (2006), "An element-based displacement preconditioner for linear elasticity problems", Comput. Struct., 84(31-32), 2306-2315. https://doi.org/10.1016/j.compstruc.2006.08.057.   DOI
15 Barsoum, R.S. (1977), "Triangular quarter-point elements as elastic and perfectly-plastic crack tip elements", Int. J. Numer. Meth. Eng., 11(1), 85-98. https://doi.org/10.1002/nme.1620110109.   DOI
16 Dechaumphai, P., Phongthanapanich, S. and Srichareonchai, T. (2003b), "Combined Delaunay triangulation and adaptive finite element method for crack growth analysis", Acta Mechanica Sinica, 19, 161-171. https://doi.org/10.1007/BF02487678.   DOI
17 Dechaumphai, P., Phongthanapanich, S. and Bhandhubanyong, P. (2003a), "Adaptive finite elements by Delaunay triangulation for fracture analysis of cracks", Struct. Eng. Mech., 15(5), 563-578. https://doi.org/10.12989/sem.2003.15.5.563.   DOI
18 Koric, S. and Gupta, A. (2016), "Sparse matrix factorization in the implicit finite element method on petascale architecture", Comput. Meth. Appl. Mech. Eng., 302, 281-292. https://doi.org/10.1016/j.cma.2016.01.011.   DOI
19 ASTM E647-00 (2000), Standard Test Method for Measurement of Fatigue Crack Growth Rates, ASTM International, West Conshohocken, PA, USA.
20 Cecka, C., Lew, A.J. and Darve, E. (2011), "Assembly of finite element methods on graphics processors", Int. J. Numer. Meth. Eng., 85(5), 640-669. https://doi.org/10.1002/nme.2989.   DOI
21 Hughes, T.J.R., Levit, I. and Winget, J. (1983), "An element-by-element solution algorithm for problems of structural and solid mechanics", Comput. Meth. Appl. Mech. Eng., 36(2), 241-254. https://doi.org/10.1016/0045-7825(83)90115-9.   DOI
22 Goddeke, D., Strzodka, R., Mohd-Yusof, J., McCormick, P., Wobker, H., Becker, C. and Turek, S. (2008), "Using GPUs to improve multigrid solver performance on a cluster", Int. J. Comput. Eng. Sci., 4(1), 36-55. https://doi.org/10.1504/IJCSE.2008.021111.   DOI
23 Guinea, G.V., Planas, J. and Elices, M. (2000), "KI evaluation by the displacement extrapolation technique", Eng. Fract. Mech., 66(3), 243-255. https://doi.org/10.1016/S0013-7944(00)00016-3.   DOI