\شماره٪٪۱
Gdoutos, E.E. ``Fracture mechanics: an introduction'', {\it Springer
Science} \& {\it Business Media,. 2nd Edn. , Waterloo, Ontario, Canada},
pp. 1-15, (2006).
\شماره٪٪۲
Lin, M., et al. ``Application of the extendedfFiniteeElement
method (XFEM) to simulate crack propagation in pressurized steel
pipes''. {\it In ASME 2017 Pressure Vessels and Piping Conference}.
pp. 16-20, Waikoloa, Hawaii, USA, (2017).
\شماره٪٪۳
Khademalrasoul, A. and R. Maghsoudi, ``Estimation of facture
path in the Structures and the influences of non-singular term
on crack propagation'', {\it Journal of Hydraulic Structures}, {\bf 1},
pp. 1-21, (in Persian)(2017).
\شماره٪٪۴
Mo\"{e}s, N., Dolbow, J. and Belytschko, T.``A finite element
method for crack growth without remeshing'', {\it International journal
for numerical methods in engineering}, {\bf 46}, pp. 131-150 (1999).
\شماره٪٪۵
Arnesson, S. ``XFEM-analysis and implementation,'' {\it Division
of Solid Mechanics, M.Sc. dissertation, Lund University, Sweden},
(2014).
\شماره٪٪۶
Tan, P., Nguyen-Thanh, N. and Zhou, K. ``Extended
isogeometric analysis based on B'ezier extraction for an FGM
plate by using the two-variable refined plate theory'', {\it Theoretical
and Applied Fracture Mechanics}, {\bf 89}, pp. 127-138, (2017).
\شماره٪٪۷
Nguyen - Thanh, N. and Zhou, K. `` Extended isogeometric analysis based on PHT
- splines for crack propagation near inclusions'',
{\it International Journal for Numerical Methods in Engineering}, {\bf
112}, pp.
1777-1800, (2017).
\شماره٪٪۸
Karatarakis, A., Karakitsios, P. and Papadrakakis, M.. ``Computation
of the isogeometric analysis stiffness matrix on GPU'', {\it In Proc.
of the 3rd South-East European Conference on Computational Mechanics
(SEECCM). elsevier. Athens , Greece} (2013).
\شماره٪٪۹
Naderi, R. and Khademalrasoul, A. ``Comparison between isogeometric
analysis and extended Finite element methods in discontinuities
modeling and stress intensity factor calculation '', {\it Journal
of Computational Methods in Engineering (Esteghlal) }, {\bf 5}, pp. 83-109,
(in Persian) (Summer 2016).
\شماره٪٪۱۰
1.logan, d., {\it A First Course in the Finite Element Method}.
Thomson Canada., Fourth Edition, University of Wisconsin-Platteville:
pp. 1-343 (2007).
\شماره٪٪۱۱
Barsoum, R., ``An assessment of the quarter-point elements
in pressure vessel fracture analysis'', {\it In Structural mechanics
in Reactor Technology, 6th International Conference on Structural
Mechanics in Reactor Technology; Paris, France} (1981).
\شماره٪٪۱۲
Henshell, R. and Shaw, K.``Crack tip finite elements are
unnecessary'', {\it International journal for numerical methods in
engineering}, {\bf 9}, pp. 495-507 (1975).
\شماره٪٪۱۳
Banks-Sills, L. and Sherman, ``Comparison of methods
for calculating stress intensity factors with quarter-point elements'',
{\it International Journal of Fracture}, {\bf 32}, pp. 127-140 (1986).
\شماره٪٪۱۴
Mirzaei, M. ``Fracture mechanics; theory and applications
'', Department of Mechanical Engineering,TMU, (2016).
\شماره٪٪۱۵
Sukumar, N., Mo\"{e}s, N., Belytschko, T. and et al. ``Extended finite
element method for three-dimensional crack modelling '',
{\it International Journal for Numerical Methods in Engineering},
{\bf 48}11, pp. 1549-1570 (2000).
\شماره٪٪۱۶
Melenk, J.M. and Babu\v{s}ka, I. ``The partition of unity
finite element method: basic theory and applications'', {\it Computer
methods in applied mechanics and engineering}, {\bf 139}, 289-314 (1996).
\شماره٪٪۱۷
Mohammadi, S. ``Extended finite element method: for fracture
analysis of structures'', {\it Blackwell Publishing}, Oxford, UK, pp. 1-115
(2008).
\شماره٪٪۱۸
Lan, M., Waisman, H. and Harari, I.``A direct analytical
mode components of strain energy release-method to extract mixed
rates from Irwin's integral using extended finite element method''.
{\it International Journal for Numerical Methods in Engineering}, {\bf
95}, pp.
1033-1052
(2013).
\شماره٪٪۱۹
Naderi, R. and Khademalrasoul, A.``Fully automatic crack
propagation modeling in the interaction with void and inclusion
without remeshing'', {\it Modares Mechanical Engineering}, {\bf
15}, pp. 261-273
(in Persian)(2015).
\شماره٪٪۲۰
Naderi, R. and Khademalrasoul, A. ``Automatic mixed-mode
crack propagation and fatigue growth without domain remeshing''.
{\it Journal of Solid and Fluid Mechanics}, Summer 2011,
pp. 27-38 (in
Persian).(2011)
\شماره٪٪۲۱
Cottrell, J.A., Hughes, T.J. and Bazilevs, Y. ``Isogeometric
analysis: toward integration of CAD and FEA'', {\it John Wiley} \& {\it Sons,
UK} (2009).
\شماره٪٪۲۲
Hughes, T.J., Cottrell, J.A. and Bazilevs, Y. ``Isogeometric
analysis: CAD, finite elements, NURBS, exact geometry and mesh
refinement'', {\it Computer methods in applied mechanics and engineering},
{\bf 194}, 4135-4195 (2005).
\شماره٪٪۲۳
De Luycker, E., et al. ``X -FEM in isogeometric analysis for linear fracture
mechanics'',
{\it International Journal for Numerical
Methods in Engineering}, {\bf 87}, pp. 541-565 (2011).
\شماره٪٪۲۴
Khademalrasoul, A. and Naderi, R.``Local and global approaches
to fracture mechanics using isogeometric analysis method'', {\it Journal
of Applied and Computational Mechanics}, {\bf 1}, pp. 168-180 (2015).
\شماره٪٪۲۵
Khademalrasoul, A.``NURBS-based isogeometric analysis method
application to mixed-mode computational fracture mechanics''.
{\it Journal of Applied and Computational Mechanics},
{\bf 5}, pp. 217-230 (2019).
\شماره٪٪۲۶
Nguyen, V.P., et al., ``Isogeometric analysis: an overview
and computer implementation aspects'', {\it Mathematics and Computers
in Simulation}, {\bf 117}, pp. 89-116 (2015).
\شماره٪٪۲۷
Khademalrasoul, Abdolghafoor, and Reza Naderi. ``Local and
global approaches to fracture mechanics using isogeometric analysis
method", {\it Journal of Applied and Computational Mechanics}, pp. 168-180
(in Persian)(2015).
\شماره٪٪۲۸
Kosti\'{c}, A., {\it Eigenvalue Problems}, in Applied Linear Algebra
in Action, IntechOpen, Bosnia and Herzegovina (2016).
\شماره٪٪۲۹
Tani, M. ``A preconditioning strategy for linear systems
arising from nonsymmetric sch