[1] Oh Y, Yoo HH (2016) Vibration analysis of rotating pretwisted tapered blades made of functionally graded materials. Int J Mech Sci 119: 68-79.

[2] Kapania RK, Raciti S (1989) Recent advances in analysis of laminated beams and plates. Part I - Sheareffects and buckling. AIAA J 27(7): 923-935.

[3] Shi G, Lam KY, Tay TE (1998) On efficient finite element modeling of composite beams and plates using higher-order theories and an accurate composite beam element. Compos Struct 41(2): 159-165.

[4] Sankar BV (2001) An elasticity solution for functionally graded beams. Compos Sci Tech 61(5): 689-696.

[5] Sankar BV, Tzeng JT (2002) Thermal Stresses in Functionally Graded Beams. AIAA J 40(6): 1228-1232.

[6] Chakraborty A, Gopalakrishnan S, Reddy J N (2003) A new beam finite element for the analysis of functionally graded materials. Int J Mech Sci 45(3): 519-539.

[7] Kadoli R, Akhtar K, Ganesan N (2008) Static analysis of functionally graded beams using higher order shear deformation theory. Appl Math Modelling 32(12): 2509-2525.

[8] Li XFA (2008) Unified approach for analyzing static and dynamic behaviors of functionally graded Timoshenko and Euler–Bernoulli beams. J Sound Vib 318(4): 1210-1229.

[9] Kiani Y, Eslami MR (2010) Thermal buckling analysis of functionally graded material beams. Int J Mech Materi Design 6(3): 229-238.

[10] Xu Y, Zhou D (2012) Two-dimensional thermoelastic analysis of beams with variable thickness subjected to thermo-mechanical loads. Appl Math Modelling 36(12): 5818-5829.

[11] Nguyen TK, Vo TP, Thai HT (2013) Static and free vibration of axially loaded functionally graded beams based on the first-order shear deformation theory. Compos B: Eng 55 147-157.

[12] Niknam H, Fallah A, Aghdam MM (2014) Nonlinear bending of functionally graded tapered beams subjected to thermal and mechanical loading. Int J Nonlinear Mech 65: 141-147.

[13] Arefi M, Faegh RK, Loghman A (2016) The effect of axially variable thermal and mechanical loads on the 2D thermoelastic response of FG cylindrical shell. J Therm Stresses 39(12): 1539-1559.

[14] Heshmati M, Daneshmand F (2018) Vibration analysis of non-uniform porous beams with functionally graded porosity distribution. Proc Inst Mech Eng, Part L: J Mater: Design Appl  1464420718780902.

[15] Zappino E, Viglietti A, Carrera E (2018) Analysis of tapered composite structures using a refined beam theory. Compos Struct 183 42-52.

[16] Poursaeidi E, Bakhtiari H (2014) Fatigue crack growth simulation in a first stage of compressor blade. Eng Fail Anal 45(Supplement C): 314-325.

[17] Zenkour AM (2009) The effect of transverse shear and normal deformations on the thermomechanical bending of functionally graded sandwich plates. International J Appl Mech 1(04): 667-707.

[18] Arefi M, Zenkour AM (2017) Size-dependent electro-elastic analysis of a sandwich microbeam based on higher-order sinusoidal shear deformation theory and strain gradient theory. J Intel Mater Syst Struct 0(0): 1045389X17733333.

[19] Kordkheili SAH, Naghdabadi R (2007) Thermoelastic analysis of a functionally graded rotating disk. Compos Struct 79(4): 508-516.

[20] Loghman A, Ghorbanpour Arani A, Shajari A R, Amir S (2011) Time-dependent thermoelastic creep analysis of rotating disk made of Al–SiC composite. Arch Appl Mech 81(12): 1853-1864.

[21] Loghman A, Hammami M, Loghman E (2017) Effect of the silicon-carbide micro- and nanoparticle size on the thermo-elastic and time-dependent creep response of a rotating Al–SiC composite cylinder. J Appl Mech Tech Phys 58(3): 443-453.

[22] لقمان ع، اعظمی م، تورنگ ح (2016) تحلیل الکترومگنتوترمومکانیک دیسک دوار پلیمری هوشمند تقویت شده با نانولوله‌های کربنی چندجداره با رفتار غیرخطی. مجله مکانیک سازه­ها و شاره­ها 108-97 :(2)6.

[23] محمدی هویه هـ، صفری م، لقمان ع (2018) تحلیل خزش وابسته به زمان و پیش بینی عمر خزشی استوانه های چرخان توخالی ساخته شده از فولاد آلیاژی به کمک معادله ساختاری گستره تتا و پارامترشکست لارسن میلر. مجلهمهندسی مکانیک امیرکبیر 684-673 :(4)49.  

[24] Poursaeidi E, Aieneravaie M, Mohammadi MR (2008) Failure analysis of a second stage blade in a gas turbine engine. Eng Fail Anal 15(8): 1111-1129.

[25] ABAQUS Documentation User‘s Manual.