Comparison of different numerical methods for calculating stress intensity factors in analysis of fractured structures

Document Type : Research

Authors

1 Graduate Student, Civil Engineering Faculty, Sirjan University of Technologhy, Sirjan, Iran.

2 Assistant Professor, Civil Engineering Faculty, Sirjan University of Technologhy, Sirjan, Iran,

3 Professor, Civil Engineering Department, K.N.Toosi University of Technology, Tehran, Iran.

Abstract

In this research, an efficient Galerkin Finite Volume Method (GFVM) along with the h–refinement adaptive process and post–processing error estimation analysis is presented for fracture analysis. The adaptive strategy is used to produce more accurate solution with the least computational cost. To investigate the accuracy and efficiency of the developed model, the GFVM is compared with two versions of the Finite Element Method known in solid mechanics, the adaptive Galerkin Finite Element Method (GFEM) and Extended Finite Element Method (XFEM), for the two dimensional fracture analysis of structures. After the discretization of the governing equations, the above three methods are implemented in FORTRAN. In the adaptive GFVM and GFEM methods, the discrete crack concept is used to model the crack surface, but in the XFEM, the crack surface is modeled through the enrichment of the displacement approximation around the crack. Several test cases are used to validate the developed dimensional numerical models for the analysis of cracked structures. After verification, the fracture analysis of a plate under pure mode I and mixed mode I/II is performed using the above-mentioned numerical methods. The numerical results show that three methods accurately calculate the stress intensity factors. The average percent error of the XFEM, adaptive GFEM and adaptive GFVM is ,  and , respectively. The results show that the CPU time of the adaptive GFVM is 5.5 and 3 times less than the XFEM and adaptive GFEM, respectively.

Keywords

References

1. Amiri, T., "2D adaptive finite volume method development for mass concrete structures analysis considering thermal cracking and nonlinear changes of material properties", PhD Dissertation, K.N.Toosi University of Technology, 2015.
2. Bailey, C., Cross, M., "A finite volume procedure to solve elastic solid mechanics problems in three dimensions on an unstructured mesh", Int. J. Numer. Methods. Eng., vol. 38(10), 1995, p. 1757-1776. [DOI:10.1002/nme.1620381010]
3. Demirdzic, I., Muzaferija, S., "Finite volume method for stress analysis in complex domains", Int. J. Numer. Methods. Eng., vol. 37(21), 1994, p. 3751-3766. [DOI:10.1002/nme.1620372110]
4. Dhatt, G., Touzot, G., Lefrançois, E., "finite element method", ISTE Ltd and John Wiley & Sons, Inc. London, 2012. [DOI:10.1002/9781118569764]
5. Ebrahimnejad, M., Fallah, N., Khoei, A.R., "Adaptive refinement in the meshless finite volume method for elasticity problems", Comput. Math. Appl., vol. 69(12), 2015, p. 1420-1443. [DOI:10.1016/j.camwa.2015.03.023]
6. Hay, A., Visonneau, M., "Adaptive finite-volume solution of complex turbulent flows", Comput. Fluids., vol. 36(8), 2007, p. 1347-1363. [DOI:10.1016/j.compfluid.2006.12.008]
7. Jasak, H., Weller, H.G., "Application of the finite volume method and unstructured meshes to linear elasticity", Int. J. Numer. Meth. Eng., vol. 48, 2000, p. 267-287. https://doi.org/10.1002/(SICI)1097-0207(20000520)48:2<267::AID-NME884>3.0.CO;2-Q [DOI:10.1002/(SICI)1097-0207(20000520)48:23.0.CO;2-Q]
8. Jiang, Y., Xuedong, C., Fan, Z., "Combined extended finite element method and cohesive element for fracture analysis", Proceedings of the ASME, Pressure Vessels and Piping Conference, 2016, p. 1-6. [DOI:10.1115/PVP2016-63750]
9. Khoei, A.R., Azadi, H., Moslemi, H., "Modeling of crack propagation via an automatic adaptive mesh refinement based on modified superconvergent patch recovery Technique", Eng. Fract. Mech., vol. 75, 2008, p. 2921-2945. [DOI:10.1016/j.engfracmech.2008.01.006]
10. Khoei, A. R., "Extended finite element method: theory and applications", John Wiley & Sons, Pondicherry, 2015. [DOI:10.1002/9781118869673]
11. Kim, J.W., "A contour integral computation of stress intensity factors in the cracked orthotropic elastic plates", Eng. Fract. Mech., vol. 21(2), 1985, p. 353-364. [DOI:10.1016/0013-7944(85)90023-2]
12. Limtrakarn, W., Yodsangkham, A., Namlaow, A., Dechaumphai, P., "Determination of KI, KII and trajectory of initial crack by adaptive finite element method and photoelastic technique", Exp. Tech., vol. 34(4), 2010, p. 27-35. [DOI:10.1111/j.1747-1567.2009.00527.x]
13. Logan, D.R., "A first course in the finite element method", Cengage Learning, United States of America, 2012.
14. McNeice, G.M., Marcal, P.V., "Optimization of finite element grids based on minimum potential energy", J. Eng. Ind., vol. 95(1), 1973, p. 186-190. [DOI:10.1115/1.3438097]
15. Meng, Q., Wang, Z., "Extended finite element method for power-law creep crack growth", Eng. Fract. Mech., Vol. 127, 2014, p. 148-160. [DOI:10.1016/j.engfracmech.2014.06.005]
16. Mohammadi, S., "Extended finite element method for fracture analysis of structures", Wiley-Blackwell, Hoboken, New Jersey, 2008.
17. Murotani, K., Yagawa, G., Choi, J.B., "Adaptive finite elements using hierarchical mesh and its application to crack propagation analysis", Comput. Methods. Appl. Mech. Eng., vol. 253, 2013, p. 1-14. [DOI:10.1016/j.cma.2012.07.024]
18. Oliveira, S.L.G. de., Oliveira Chagas, G., "Adaptive mesh refinement for finite-volume discretization with scalene triangles", Procedia. Comput. Sci., vol. 51, 2015, p. 239-245. [DOI:10.1016/j.procs.2015.05.233]
19. Sabbagh-Yazdi, S.R., Amiri-SaadatAbadi, T., Wegian, F.M., "2D linear Galerkin finite volume analysis of thermal stresses during sequential layer settings of mass concrete considering contact interface and variations of material properties, Part 2: Stress Analysis", J. S. Afr. Inst. Civ. Eng., vol. 55(1), 2013, p. 104-113.
20. Song, S.H., Paulino, G.H., "Dynamic stress intensity factors for homogeneous and smoothly heterogeneous materials using the interaction integral method", Int. J. Solids. Struct., vol. 43, 2006, p. 4830-4866. [DOI:10.1016/j.ijsolstr.2005.06.102]
21. Vasiliauskiene, L., Valentinavicius S, Sapalas A., "Adaptive finite element analysis for solution of complex engineering problems". International Conference on Applied and Theoretical Mechanics, 2006, p. 378-383.
22. Waisman, H., "An analytical stiffness derivative extended finite element technique for extraction of crack tip Strain Energy Release Rates", Eng. Fract. Mech., vol. 77, 2016, p. 3204-3215. [DOI:10.1016/j.engfracmech.2010.08.015]
23. Yip, S., "Handbook of materials modeling, volume I: methods and models", Springer, 2005. [DOI:10.1007/978-1-4020-3286-8]
24. Zienkiewicz, O.C., Boroomand, B., Zhu, J.Z., "Recovery procedures in error estimation and adaptivity, part I: adaptivity in linear problems", Comput. Methods. Appl. Mech. Eng., vol. 176(1-4), 1999, p. 111-125. [DOI:10.1016/S0045-7825(98)00332-6]
25. Zienkiewicz, O.C., Zhu, J.Z., "A simple error estimator and adaptive procedure for practical engineering analysis", Int. J. Numer. Meth. Eng., vol. 24(2), 1987, p. 333-357. [DOI:10.1002/nme.1620240206]
Numerical Methods in Civil Engineering
Volume 3, Issue 1
September 2018
Pages 1-12

Files

History

  • Receive Date: 15 December 2017
  • Revise Date: 04 June 2018
  • Accept Date: 15 September 2018

Share

How to cite

Statistics