참고문헌
- Afsar, A. and Go, J. (2010), "Finite element analysis of thermoelastic field in a rotating FGM circular disk", Appl. Math Modelling, 34(11), 3309-3320. https://doi.org/10.1016/j.apm.2010.02.022
- Arefi, M. and Rahimi, G. H. (2013), "Thermo elastic analysis of a functionally graded cylinder under internal pressure using first order shear deformation theory", Sci. Res. Essays., 5(12), 1442-1454.
- Arefi, M. and Rahimi, G. (2011), "Nonlinear analysis of a functionally graded square plate with two smart layers as sensor and actuator under normal pressure", Smart. Struct. Syst., 8(5), 433-447. http://dx.doi.org/10.12989/sss.2011.8.5.433.
- Arefi, M. and Rahimi, G. (2012), "Studying the nonlinear behavior of the functionally graded annular plates with piezoelectric layers as a sensor and actuator under normal pressure", Smart. Struct. Syst., 9(2), 127-143. http://doi.org/10.12989/sss.2012.9.2.127.
- Arefi, M., Rahimi, G.H. and Khoshgoftar, M.J. (2012), "Exact solution of a thick walled functionally graded piezoelectric cylinder under mechanical, thermal and electrical loads in the magnetic field", Smart. Struct. Syst., 9(5), 427-439. http://doi.org/10.12989/sss.2012.9.5.427.
- Arefi, M. and Rahimi, G. (2012), "Three-dimensional multi-field equations of a functionally graded piezoelectric thick shell with variable thickness, curvature and arbitrary nonhomogeneity", Acta. Mech., 223(1), 63-79. https://doi.org/10.1007/s00707-011-0536-5.
- Arefi, M. and Rahimi, G.H. (2014), "Comprehensive piezothermo-elastic analysis of a thick hollow spherical shell", Smart. Struct. Syst., 14(2), 225-246. http://doi.org/10.12989/sss.2014.14.2.225.
- Arefi, M. and Allam, M.N.M., (2015), "Nonlinear Responses of an Arbitrary FGP Circular Plate Resting on Foundation", Smart. Struct. Syst., 16(1), 81-100. http://dx.doi.org/10.12989/sss.2015.16.1.081.
- Arefi, M., Rahimi, G.H. and Khoshgoftar, M.J. (2011), "Optimized design of a cylinder under mechanical, magnetic and thermal loads as a sensor or actuator using a functionally graded piezomagnetic material", Int. J. Phys. Sci., 6(27), 6315-6322.
- Arefi, M. (2015), "Nonlinear electromechanical analysis of a functionally graded square plate integrated with smart layers resting on Winkler-Pasternak foundation", Smart. Struct. Syst., 16(1), 195-211. https://doi.org/10.12989/sss.2015.16.1.195.
- Arefi, M. and Zenkour, A.M. (2017a), "Effect of thermo-magnetoelectro-mechanical fields on the bending behaviors of a threelayered nanoplate based on sinusoidal shear-deformation plate theory", J. Sandw. Struct. Mater. https://doi.org/10.1177/1099636217697497.
- Arefi, M. and Zenkour, A.M. (2017b), "Employing the coupled stress components and surface elasticity for nonlocal solution of wave propagation of a functionally graded piezoelectric Love nanorod model", J. Intel. Mater. Syst. Struct., 28(17), 2403-2413. https://doi.org/10.1177/1045389X17689930.
- Bayat, M., Sahari, B., Saleem, M., Aidy, A. and Wong, S. (2009), "Bending analysis of a functionally graded rotating disk based on the first shear deformation theory", Appl. Math. Modeling., 33(11), 4215-4230. https://doi.org/10.1016/j.apm.2009.03.001.
- Bayat, M., Sahari, B., Saleem, M., Hambouda, A. and Mahdi, E. (2007), "Thermoelastic analysis of a functionally graded rotating disk with small and large deflections", Thin. Wall. Struct., 45(7), 677-691. https://doi.org/10.1016/j.tws.2007.05.005.
- Chen, J., Ding, H. and Chen, W. (2007), "Three-dimensional analytical solution for a rotating disc of functionally graded materials with transverse isotropy", Arch. Appl. Mech., 77(4), 241-251. https://doi.org/10.1007/s00419-006-0098-5.
- Dai, H. and Dai, H. (2017), "Analysis of a rotating FGMME circular disk with variable thickness under thermal environment", Appl. Math. Modelling., 45, 900-924. https://doi.org/10.1016/j.apm.2017.01.007.
- Durodola, J. and Attia, O. (2000), "Deformations and stresses in functionally graded graded rotating disks", Compos. Sci. Tech., 60(7), 897-995. https://doi.org/10.1016/S0266-3538(99)00197-9.
- Durodola, J. and Attia, O. (2000), "Property gradation for modification response of rotating MMC discs", Mater. Sci. Tech., 16(7-8), 919-924. https://doi.org/10.1179/026708300101508694.
- Ghasemi, H., Park, H.S. and Rabczuk, T. (2018), "A multi-material level set based topology optimization of flexoelectric composites", Comput. Meth. Appl. Mech. Eng., 332, 47-62. https://doi.org/10.1016/j.cma.2017.12.005.
- Ghasemi, H., Park, H. and Rabczuk, T. (2017), "A leve-set based IGA formulation for topology optimization of flexoelectric materials", Comput. Meth. Appl. Mech. Eng., 313, 239-258. https://doi.org/10.1016/j.cma.2016.09.029.
- Hamdia, K.M., Silani, M., Zhuang, X., He, P. and Rabczuk, T. (2017), "Stochastic analysis of the fracture toughness of polymeric nanoparticle composite using polynomial chaos expansion", Int. J. Frac., 206(2), 215-227. https://doi.org/10.1007/s10704-017-0210-6.
- Holt, J., Koizumi, M., Hirai, T. and Munir, Z. (1993), "Ceramic transactions: Functionally Gradient Materials", American Ceramic Soc., 34.
- Jahed, H. and Sherkatti, S. (2000), "Thermoplastic analysis of inhomogeneous rotating disk with variable thickness", EMHS Conference of Fatigue, Cambridge, Untied Kingdom, April.
- Kheirkhah, S. and Loghman, A. (2015), "Electric potential redistribution due to time dependent creep in thick walled FGPM cylinder based on Mendelson method of successive approximation", Struct. Eng. Mech., 53(6), 1167-1182. https://doi.org/10.12989/sem.2015.53.6.1167.
- Li, X., Ding, H. and Chen, W. (2006), "Pure bending of a simply supported circular plate of transversely isotropic functionally graded material", J. Zhej. Uni. Sci., A7(8), 1324-1328. https://doi.org/10.1631/jzus.2006.A1324.
- Li, X., Ding, H. and Chen, W. (2008), "Elasticity solutions for a transversely isotropic functionally graded circular plate subject to an axisymmetric transverse load qr K", Int. J. Solids. Struct., 45(1), 191-210. https://doi.org/10.1016/j.apm.2010.02.022.
- Loghman, A., Abdollahian, M., Jazi, A. and Arani, A. (2013), "Semi-analytical solution for electromagne to thermoelastic creep response of a functionally graded piezo-electric rotating disk", Int. J. Therm. Sci., 65, 254-266. https://doi.org/10.1016/j.ijthermalsci.2012.10.011.
- Nanthakumar, S., Lahmer, T., Zhuang, X., Zi, G. and Rabczuk, T. (2016), "Detection of material interfaces using a regularized level set method in piezoelectric structures", Inv. Prob. Sci. Eng., 24(1), 153-176. https://doi.org/10.1080/17415977.2015.1017485.
- Nguyen, B., Nanthakumar, S., Zhuang, X., Wriggers, P., Jiang, X. and Rabczuk, T. (2018), "Dynamic flexoelectric effect on piezoelectric nanostructures", Euro. J. Mech.- A/Solids, 71, 404-409. https://doi.org/10.1016/j.euromechsol.2018.06.002.
- Nguyen, B., Zhuang, X. and Rabczuk, T. (2018), "Numerical model for the characterization of Maxwell-Wagner relaxation in piezoelectric and flexoelectric composite material", Comput. Struct., 208, 75-91. https://doi.org/10.1016/j.compstruc.2018.05.006.
- Deneva, P., Gross, D., Muller, R. and Rangelov, T. (2014), Dynamic Fracture of Piezoelectric Materials, Springer, Germany.
- Parveen, G. and Reddy, J. (1998), "Nonlinear transient thermoelastic analysis of functionally graded ceramic-metal plates", Int. J. Solids. Struct., 35(33), 4457-4476. https://doi.org/10.1016/S0020-7683(97)00253-9.
- Reddy, J. (2000), "Analysis of functionally graded plates", Int. J. Numer. Meth. Eng., 47(1-3), 663-684. https://doi.org/10.1002/(SICI)1097-0207(20000110/30)47:1/3<663::AID-NME787>3.0.CO;2-8
- Reddy, J., Wang, C. and Kitipornchai, S. (1999), "Axisymmetric bending of a functionally graded circular and annular plare", J. Mech.-A/solids, 18(2), 185-199. https://doi.org/10.1016/S0997-7538(99)80011-4.
- Suresh, S. and Mortensen, A. (1998), Fundamentals of Functionally Graded Materials, The Institute of Materials, United Kingdom.
- Thai, T., Rabczuk, T. and Zhuang, X. (2018), "A large deformation isogeometric approach for flexoelectric and soft materials", Comput. Meth. Appl. Eng., 341, 7 18-739. https://doi.org/10.1016/j.cma.2018.05.019
- Vu Bac, N., Lahmer, T., Zhuang, X., Nguyen-Thoi, T. and Rabczuk, T. (2016), "A software framework for probabilistic sensitivity analysis for computational expensive models", Adv. Eng. Soft., 100, 19-31. https://doi.org/10.1016/j.advengsoft.2016.06.005
- Zenkour, A. and Mashat, D. (2011), "Stress function of a variable-thickness annular disk using exact and numerical methods", Engineering., 3(04), 422. https://:10.4236/eng.2011.34048.