Reference
- G.P. Dube, S. Kapuria, and P.C. Dumir, Exact piezothermoelastic solution of simply-supported orthotropic circular cylindrical panel in cylindrical bending, Arch. Appl. Mech., vol. 66, no. 8, pp. 537–554, 1996. DOI: https://doi.org/10.1007/BF00808143.
- P.C. Dumir, G.P. Dube, and S. Kapuria, Exact piezoelastic solution of simply-supported orthotropic circular cylindrical panel in cylindrical bending, Int. J. Solids Struct., vol. 34, no. 6, pp. 685–702, 1997. DOI: https://doi.org/10.1016/S0020-7683(96)00047-9.
- S. Kapuria, P.C. Dumir, and S. Sengupta, An exact axisymmetric solution for a simply supported piezoelectric cylindrical shell, Arch. Appl. Mech., vol. 67, no. 4, pp. 260–273, 1997. DOI: https://doi.org/10.1007/s004190050116.
- S. Kapuria, S. Sengupta, and P.C. Dumir, Three-dimensional solution for simply-supported piezoelectric cylindrical shell for axisymmetric load, Comput. Methods Appl. Mech. Eng., vol. 140, no. 1–2, pp. 139–155, 1997. DOI: https://doi.org/10.1016/S0045-7825(96)01075-4.
- C. Chen, Y. Shen, and X. Liang, Three dimensional analysis of piezoelectric circular cylindrical shell of finite length, Acta Mech., vol. 134, no. 3–4, pp. 235–249, 1999. DOI: https://doi.org/10.1007/BF01312657.
- C.P. Wu, and Y.S. Syu, Exact solutions of functionally graded piezoelectric shells under cylindrical bending, Int. J. Solids Struct., vol. 44, no. 20, pp. 6450–6472, 2007. DOI: https://doi.org/10.1016/j.ijsolstr.2007.02.037.
- C.P. Wu, and Y.H. Tsai, Cylindrical bending vibration of functionally graded piezoelectric shells using the method of perturbation, J. Eng. Math., vol. 63, no. 1, pp. 95–119, 2009. DOI: https://doi.org/10.1007/s10665-008-9234-2.
- M. Arefi, and E.M.R. Bidgoli, Electro-elastic displacement and stress analysis of the piezoelectric doubly curved shells resting on Winkler’s foundation subjected to applied voltage, Mech. Adv. Mater. Struct., vol. 26, no. 23, pp. 1981–1994, 2018. DOI: https://doi.org/10.1080/15376494.2018.1455937.
- M. Arefi, Analysis of a doubly curved piezoelectric nano shell: nonlocal electro-elastic bending solution, Eur. J. Mech. A Solid., vol. 70, pp. 226–237, 2018. DOI: https://doi.org/10.1016/j.euromechsol.2018.02.012.
- M. Arefi, and T. Rabczuk, A nonlocal higher order shear deformation theory for electro-elastic analysis of a piezoelectric doubly curved nano shell, Compos. Part B Eng.., vol. 168, pp. 496–510, 2019. DOI: https://doi.org/10.1016/j.compositesb.2019.03.065.
- P. Heyliger, K.C. Pei, and D. Saravanos, Layerwise mechanics and finite element model for laminated piezoelectric shells, AIAA J., vol. 34, no. 11, pp. 2353–2360, 1996. DOI: https://doi.org/10.2514/3.13401.
- H. Santos, C.M.M. Soares, C.A.M. Soares, and J.N. Reddy, A finite element model for the analysis of 3D axisymmetric laminated shells with piezoelectric sensors and actuators, Compos. Struct., vol. 75, no. 1–4, pp. 170–178, 2006. DOI: https://doi.org/10.1016/j.compstruct.2006.04.008.
- C.M.M. Soares, H. Santos, C.A.M. Soares, and J.N. Reddy, A semi-analytical finite element model for the analysis of piezolaminated cylindrical shells. In: Smart Structures and Materials 2006: Modeling, Signal Processing, and Control, International Society for Optics and Photonics, Bellingham, vol. 6166, pp. 61661Q, 2006. DOI: https://doi.org/10.1117/12.655605.
- H. Santos, C.M.M. Soares, C.A.M. Soares, and J.N. Reddy, A finite element model for the analysis of 3D axisymmetric laminated shells with piezoelectric sensors and actuators: bending and free vibrations, Comput. Struct., vol. 86, no. 9, pp. 940–947, 2008. DOI: https://doi.org/10.1016/j.compstruc.2007.04.013.
- S. Klinkel, and W. Wagner, A piezoelectric solid shell element based on a mixed variational formulation for geometrically linear and nonlinear applications, Comput. Struct., vol. 86, no. 1–2, pp. 38–46, 2008. DOI: https://doi.org/10.1016/j.compstruc.2007.05.032.
- W. Zouari, T. Ben Zineb, and A. Benjeddou, A FSDT-MITC piezoelectric shell finite element with ferroelectric non-linearity, J. Intell. Mater. Syst. Struct., vol. 20, no. 17, pp. 2055–2075, 2009. DOI: https://doi.org/10.1177/1045389X09345560.
- Z. Ying, and X. Zhu, Response analysis of piezoelectric shells in plane strain under random excitations, Acta Mech. Solida Sin., vol. 22, no. 2, pp. 152–160, 2009. DOI: https://doi.org/10.1016/S0894-9166(09)60100-2.
- P. Vidal, M. D’Ottavio, M. Ben Thaïer, and O. Polit, An efficient finite shell element for the static response of piezoelectric laminates, J. Intell. Mater. Syst. Struct., vol. 22, no. 7, pp. 671–690, 2011. DOI: https://doi.org/10.1177/1045389X11402863.
- Y. Lu, L.K. Wang, L. Qin, et al., The finite analysis of the piezoelectric shell stack transducer, AMR., vol. 430–432, pp. 1890–1893, 2012. DOI: https://doi.org/10.4028/www.scientific.net/AMR.430-432.1890.
- M. Cinefra, E. Carrera, and S. Valvano, Variable kinematic shell elements for the analysis of electro-mechanical problems, Mech. Adv. Mater. Struct., vol. 22, no. 1–2, pp. 77–106, 2015. DOI: https://doi.org/10.1080/15376494.2014.908042.
- G.M. Kulikov, and S.V. Plotnikova, The use of 9-parameter shell theory for development of exact geometry 12-node quadrilateral piezoelectric laminated solid-shell elements, Mech. Adv. Mater. Struct., vol. 22, no. 6, pp. 490–502, 2015. DOI: https://doi.org/10.1080/15376494.2013.813096.
- X. Liang, et al., Three-dimensional dynamics of functionally graded piezoelectric cylindrical panels by a semi-analytical approach, Compos. Struct., vol. 226, pp. 111176, 2019. DOI: https://doi.org/10.1016/j.compstruct.2019.111176.
- J.C.T. Siao, S.B. Dong, and J. Song, Frequency spectra of laminated piezoelectric cylinders, J. Vibr. Acoust., vol. 116, no. 3, pp. 364–370, 1994. DOI: https://doi.org/10.1115/1.2930437.
- P. Heyliger, and S. Brooks, Free vibration of piezoelectric laminates in cylindrical bending, Int. J. Solids Struct., vol. 32, no. 20, pp. 2945–2960, 1995. DOI: https://doi.org/10.1016/0020-7683(94)00270-7.
- M. Hussein, and P.R. Heyliger, Discrete layer analysis of axisymmetric vibrations of laminated piezoelectric cylinders, J. Sound Vib., vol. 192, no. 5, pp. 995–1013, 1996. DOI: https://doi.org/10.1006/jsvi.1996.0230.
- M. Hussein, and P. Heyliger, Three-dimensional vibrations of layered piezoelectric cylinders, J. Eng. Mech., vol. 124, no. 11, pp. 1294–1298, 1998. DOI: https://doi.org/10.1061/(ASCE)0733-9399(1998)124:11(1294).
- C.Q. Chen, and Y.P. Shen, Three-dimensional analysis for the free vibration of finite-length orthotropic piezoelectric circular cylindrical shells, J. Vibr. Acoust., vol. 120, no. 1, pp. 194–198, 1998. DOI: https://doi.org/10.1115/1.2893804.
- M. D’ottavio, D. Ballhause, B. Kröplin, and E. Carrera, Closed-form solutions for the free-vibration problem of multilayered piezoelectric shells, Comput. Struct., vol. 84, no. 22–23, pp. 1506–1518, 2006. DOI: https://doi.org/10.1016/j.compstruc.2006.01.030.
- P. Kumari, J.K. Nath, P.C. Dumir, and S. Kapuria, 2D exact solutions for flat hybrid piezoelectric and magnetoelastic angle-ply panels under harmonic load, Smart Mater. Struct., vol. 16, no. 5, pp. 1651–1661, 2007. DOI: https://doi.org/10.1088/0964-1726/16/5/018.
- S. Kapuria, P. Kumari, and J.K. Nath, Analytical piezoelasticity solution for vibration of piezoelectric laminated angle-ply circular cylindrical panels, J. Sound Vib., vol. 324, no. 3–5, pp. 832–849, 2009. DOI: https://doi.org/10.1016/j.jsv.2009.02.035.
- S. Kapuria, and P. Kumari, Three-dimensional piezoelasticity solution for dynamics of cross-ply cylindrical shells integrated with piezoelectric fiber reinforced composite actuators and sensors, Compos. Struct., vol. 92, no. 10, pp. 2431–2444, 2010. DOI: https://doi.org/10.1016/j.compstruct.2010.02.016.
- J.K. Nath, and S. Kapuria, Coupled efficient layerwise and smeared third order theories for vibration of smart piezolaminated cylindrical shells, Compos. Struct., vol. 94, no. 5, pp. 1886–1899, 2012. DOI: https://doi.org/10.1016/j.compstruct.2011.12.015.
- F. Gao, H. Hu, Y. Hu, and C. Xiong, An analysis of a cylindrical thin shell as a piezoelectric transformer, Acta Mech. Solida Sin., vol. 20, no. 2, pp. 163–170, 2007. DOI: https://doi.org/10.1007/s10338-007-0719-8.
- A. Alibeigloo, and A.M. Kani, 3D free vibration analysis of laminated cylindrical shell integrated piezoelectric layers using the differential quadrature method, Appl. Math. Modell., vol. 34, no. 12, pp. 4123–4137, 2010. DOI: https://doi.org/10.1016/j.apm.2010.04.010.
- A. Alibeigloo, A.M. Kani, and M.H. Pashaei, Elasticity solution for the free vibration analysis of functionally graded cylindrical shell bonded to thin piezoelectric layers, Int. J. Press. Vessels Pip., vol. 89, pp. 98–111, 2012. DOI: https://doi.org/10.1016/j.ijpvp.2011.10.020.
- M.K. Kwak, D.H. Yang, and J.H. Lee, Active vibration control of a submerged cylindrical shell by piezoelectric sensors and actuators. In: Active and Passive Smart Structures and Integrated Systems 2012, International Society for Optics and Photonics, Bellingham, vol. 8341, pp. 83412F–834121-13, 2012.
- J.H. Yang, D.L. Chen, and C. Jiang, Free vibration of piezoelectric laminated cylindrical shell with delamination, AMR., vol. 538–541, pp. 2576–2581, 2012. DOI: https://doi.org/10.4028/www.scientific.net/AMR.538-541.2576.
- K.C. Le, An asymptotically exact theory of functionally graded piezoelectric shells, Int. J. Eng. Sci., vol. 112, pp. 42–62, 2017. DOI: https://doi.org/10.1016/j.ijengsci.2016.12.001.
- H. SafarPour, B. Ghanbari, and M. Ghadiri, Buckling and free vibration analysis of high speed rotating carbon nanotube reinforced cylindrical piezoelectric shell, Appl. Math. Modell., vol. 65, pp. 428–442, 2019. DOI: https://doi.org/10.1016/j.apm.2018.08.028.
- C. Song, and J.P. Wolf, The scaled boundary finite element method-alias consistent infinitesimal finite element cell method for elastodynamics, Comput. Methods Appl. Mech. Eng., vol. 147, no. 3–4, pp. 329–355, 1997. DOI: https://doi.org/10.1016/S0045-7825(97)00021-2.
- J.P. Wolf, and C. Song, The scaled boundary finite-element method-aprimer: derivations, Comput. Struct., vol. 78, no. 1–3, pp. 191–210, 2000. DOI: https://doi.org/10.1016/S0045-7949(00)00099-7.
- C. Song, and J.P. Wolf, The scaled boundary finite-element method-aprimer: solution procedures, Comput. Struct., vol. 78, no. 1–3, pp. 211–225, 2000. DOI: https://doi.org/10.1016/S0045-7949(00)00100-0.
- J.L. Wegner, and Xiong Zhang, Free-vibration analysis of a three-dimensional soil-structure system, Earthquake Engng. Struct. Dyn., vol. 30, no. 1, pp. 43–57, 2001. DOI: https://doi.org/10.1002/1096-9845(200101)30:1<43::AID-EQE994>3.0.CO;2-L.
- M.C. Genes, and S. Kocak, Dynamic soil-structure interaction analysis of layered unbounded media via a coupled finite element boundary element scaled boundary finite element model, Int. J. Numer. Meth. Engng., vol. 62, no. 6, pp. 798–823, 2005. DOI: https://doi.org/10.1002/nme.1212.
- K. Chen, D. Zou, X. Kong, and Y. Zhou, Global concurrent cross-scale nonlinear analysis approach of complex CFRD systems considering dynamic impervious panel-rockfill material-foundation interactions, Soil Dyn. Earthquake Eng., vol. 114, pp. 51–68, 2018. DOI: https://doi.org/10.1016/j.soildyn.2018.06.027.
- Z. Yang, Application of scaled boundary finite element method in static and dynamic fracture problems, Acta Mech. Mech. Sinica., vol. 22, no. 3, pp. 243–256, 2006. DOI: https://doi.org/10.1007/s10409-006-0110-x.
- Z. Yang, Fully automatic modelling of mixed-mode crack propagation using scaled boundary finite element method, Eng. Fract. Mech., vol. 73, no. 12, pp. 1711–1731, 2006. DOI: https://doi.org/10.1016/j.engfracmech.2006.02.004.
- C. Song, Evaluation of power-logarithmic singularities, T-stresses and higher order terms of in-plane singular stress fields at cracks and multi-material corners, Eng. Fract. Mech., vol. 72, no. 10, pp. 1498–1530, 2005. DOI: https://doi.org/10.1016/j.engfracmech.2004.11.002.
- Z. Sun, E.T. Ooi, and C. Song, Finite fracture mechanics analysis using the scaled boundary finite element method, Eng. Fract. Mech., vol. 134, pp. 330–353, 2015. DOI: https://doi.org/10.1016/j.engfracmech.2014.12.002.
- C. Song, E.T. Ooi, and S. Natarajan, A review of the scaled boundary finite element method for two-dimensional linear elastic fracture mechanics, Eng. Fract. Mech., vol. 187, pp. 45–73, 2018. DOI: https://doi.org/10.1016/j.engfracmech.2017.10.016.
- Z. Zhang, D.D. Dissanayake, A. Saputra, D. Wu, and C. Song, Three-dimensional damage analysis by the scaled boundary finite element method, Comput. Struct., vol. 206, pp. 1–17, 2018. DOI: https://doi.org/10.1016/j.compstruc.2018.06.008.
- Z. Zhang, Y. Liu, D.D. Dissanayake, A.A. Saputra, and C. Song, Nonlocal damage modelling by the scaled boundary finite element method, Eng. Anal. Bound. Elem., vol. 99, pp. 29–45, 2019. DOI: https://doi.org/10.1016/j.enganabound.2018.10.006.
- W. Wang, Z. Guo, Y. Peng, and Q. Zhang, A numerical study of the effects of the T-shaped baffles on liquid sloshing in horizontal elliptical tanks, Ocean Eng., vol. 111, pp. 543–568, 2016. DOI: https://doi.org/10.1016/j.oceaneng.2015.11.020.
- W. Wang, Y. Peng, Y. Zhou, and Q. Zhang, Liquid sloshing in partly-filled laterally-excited cylindrical tanks equipped with multi baffles, Appl. Ocean Res., vol. 59, pp. 543–563, 2016. DOI: https://doi.org/10.1016/j.apor.2016.07.009.
- W. Wang, G. Tang, X. Song, and Y. Zhou, Transient sloshing in partially filled laterally excited horizontal elliptical vessels with T-shaped baffles, J. Pressure Vessel Technol., vol. 139, no. 2, pp. 021302, 2017. DOI: https://doi.org/10.1115/1.4034148.
- W. Wang, Y. Peng, Q. Zhang, L. Ren, and Y. Jiang, Sloshing of liquid in partially liquid filled toroidal tank with various baffles under lateral excitation, Ocean Eng., vol. 146, pp. 434–456, 2017. DOI: https://doi.org/10.1016/j.oceaneng.2017.09.032.
- W. Wang, Q. Zhang, Q. Ma, and L. Ren, Sloshing effects under longitudinal excitation in horizontal elliptical cylindrical containers with complex baffles, J. Waterway Port Coastal Ocean Eng., vol. 144, no. 2, pp. 04017044, 2018. DOI: https://doi.org/10.1061/(ASCE)WW.1943-5460.0000433.
- X.Y. Long, C. Jiang, X. Han, W. Gao, and R.G. Bi, Sensitivity analysis of the scaled boundary finite element method for elastostatics, Comput. Methods Appl. Mech. Eng., vol. 276, pp. 212–232, 2014. DOI: https://doi.org/10.1016/j.cma.2014.03.005.
- F. Bause, H. Gravenkamp, J. Rautenberg, and B. Henning, Model based sensitivity analysis in the determination of viscoelastic material properties using transmission measurements through circular wave guides, Phys. Proc., vol. 70, pp. 204–207, 2015. DOI: https://doi.org/10.1016/j.phpro.2015.08.127.
- N.M. Syed, and B.K. Maheshwari, Improvement in the computational efficiency of the coupled FEM-SBFEM approach for 3D seismic SSI analysis in the time domain, Comput. Geotech., vol. 67, pp. 204–212, 2015. DOI: https://doi.org/10.1016/j.compgeo.2015.03.010.
- D. Zou, X. Teng, K. Chen, and X. Yu, An extended polygon scaled boundary finite element method for the nonlinear dynamic analysis of saturated soil, Eng. Anal. Bound. Elem., vol. 91, pp. 150–161, 2018. DOI: https://doi.org/10.1016/j.enganabound.2018.03.019.
- D. Zou, X. Teng, K. Chen, and J. Liu, A polyhedral scaled boundary finite element method for three-dimensional dynamic analysis of saturated porous media, Eng. Anal. Bound. Elem., vol. 101, pp. 343–359, 2019. DOI: https://doi.org/10.1016/j.enganabound.2019.01.012.
- H. Man, C. Song, W. Gao, and F. Tin-Loi, A unified 3D‐based technique for plate bending analysis using scaled boundary finite element method, Int. J. Numer. Meth. Engng., vol. 91, no. 5, pp. 491–515, 2012. DOI: https://doi.org/10.1002/nme.4280.
- H. Man, C. Song, T. Xiang, W. Gao, and F. Tin-Loi, High-order plate bending analysis based on the scaled boundary finite element method, Int. J. Numer. Meth. Engng., vol. 95, no. 4, pp. 331–360, 2013. DOI: https://doi.org/10.1002/nme.4519.
- H. Man, C. Song, W. Gao, and F. Tin-Loi, Semi-analytical analysis for piezoelectric plate using the scaled boundary finite-element method, Comput. Struct., vol. 137, pp. 47–62, 2014. DOI: https://doi.org/10.1016/j.compstruc.2013.10.005.
- J. Li, Z. Shi, and S. Ning, A two-dimensional consistent approach for static and dynamic analyses of uniform beams, Eng. Anal. Boundary Elem., vol. 82, pp. 1–16, 2017. DOI: https://doi.org/10.1016/j.enganabound.2017.05.009.
- J. Li, Z. Shi, and L. Liu, A scaled boundary finite element method for static and dynamic analyses of cylindrical shells, Eng. Anal. Boundary Elem., vol. 98, pp. 217–231, 2019. DOI: https://doi.org/10.1016/j.enganabound.2018.10.024.
- J.N. Reddy, Mechanics of Laminated Composite Plates and Shells Theory and Analysis, 2nd ed., CRC Press, Boca Raton, 2003.