Effect of flexoelectricity on the nonlinear static and dynamic response of functionally graded porous graphene platelets-reinforced composite plates integrated with piezoelectric layers
Bibliographic record
Abstract
No abstract is available for this record. The assistant can identify its topic from the title, but cannot infer the study’s results.
Source: Not provided · Quality: missing
Research context
OpenAlex topics: Composite Structure Analysis and Optimization · Nonlocal and gradient elasticity in micro/nano structures · Aeroelasticity and Vibration Control
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
References (87)
Show source-provided references
1. Abbaspour, F., Arvin, H.: Thermo-electro-mechanical buckling analysis of sandwich nanocomposite microplates reinforced with graphene platelets integrated with piezoelectric facesheets resting on elastic foundation. Comput. Math. Appl. 101, 38–50 (2021)10.1016/j.camwa.2021.09.009 ↗
2. Al-Shewailiah, D.M.R., Al-Shujairi, M.A.: Static bending of functionally graded single-walled carbon nanotube conjunction with modified couple stress theory. Mater. Today: Proc. 61, 1023–1037 (2022)
3. Alshenawy, R., Safaei, B., Sahmani, S., Elmoghazy, Y., Al-Alwan, A., Nuwairan, M.A.: Buckling mode transition in nonlinear strain gradient-based stability behavior of axial-thermal-electrical loaded FG piezoelectric cylindrical panels at microscale. Eng. Anal. Bound. Elem. 141, 36–64 (2022)10.1016/j.enganabound.2022.04.010 ↗
4. Anamagh, M.R., Bediz, B.: Free vibration and buckling behavior of functionally graded porous plates reinforced by graphene platelets using spectral Chebyshev approach. Compos. Struct. 253, 112765 (2020)10.1016/j.compstruct.2020.112765 ↗
5. Arshid, E., Amir, S., Loghman, A.: Static and dynamic analyses of FG-GNPs reinforced porous nanocomposite annular micro-plates based on MSGT. Int. J. Mech. Sci. 180, 105656 (2020)10.1016/j.ijmecsci.2020.105656 ↗
6. Atif Shahzad, M., Sahmani, S., Safaei, B.: Nonlocal couple stress-based meshless collocation model for nonlinear dynamic performance of microbeam-type piezoelectric energy harvesters. Eur. J. Mech. A/Solids 101, 105059 (2023)10.1016/j.euromechsol.2023.105059 ↗
7. Balamurugan, V., Ganapathi, M., Varadan, T.K.: Nonlinear dynamic instability of laminated composite plates using finite element method. Comput. Struct. 60, 125–130 (1996)10.1016/0045-7949(95)00368-1 ↗
8. Chen, Q., Zheng, S., Li, Z., Zeng, C.: Size-dependent free vibration analysis of functionally graded porous piezoelectric sandwich nanobeam reinforced with graphene platelets with consideration of flexoelectric effect. Smart Mater. Struct. 30, 035008 (2021)10.1088/1361-665X/abd963 ↗
9. Fakhari, V., Ohadi, A., Yousefian, P.: Nonlinear free and forced vibration behavior of functionally graded plate with piezoelectric layers in thermal environment. Compos. Struct. 93, 2310–2321 (2011)10.1016/j.compstruct.2011.03.019 ↗
10. Ganapathi, M., Varadan, T.K., Sarma, B.S.: Nonlinear flexural vibrations of laminated orthotropic plates. Comput. Struct. 39, 685–688 (1991)10.1016/0045-7949(91)90211-4 ↗
11. Gao, H., Wang, B.: A first-principles study on structural stability and magnetoelectric coupling of two-dimensional BaTiO3 ultrathin film with Cr and Cu substituting Ti site. APL Mater. 12, 091117 (2024)10.1063/5.0223008 ↗
12. Gao, W., Qin, Z., Chu, F.: Wave propagation in functionally graded porous plates reinforced with graphene platelets. Aerosp. Sci. Technol. 102, 105860 (2020)10.1016/j.ast.2020.105860 ↗
13. Ghasemi, H., Kerfriden, P., Bordas, S.P.A., Muthu, J., Zi, G., Rabczuk, T.: Interfacial shear stress optimization in sandwich beams with polymeric core using non-uniform distribution of reinforcing ingredients. Compos. Struct. 120, 221–230 (2015)10.1016/j.compstruct.2014.10.005 ↗
14. Ghasemi, H., Park, H.S., Rabczuk, T.: A level-set based IGA formulation for topology optimization of flexoelectric materials. Comput. Methods Appl. Mech. Eng. 313, 239–258 (2017)10.1016/j.cma.2016.09.029 ↗
15. Ghasemi, H., Park, H.S., Rabczuk, T.: A multi-material level set-based topology optimization of flexoelectric composites. Comput. Methods Appl. Mech. Eng. 332, 47–62 (2018)10.1016/j.cma.2017.12.005 ↗
16. Ghasemi, H., Park, H.S., Zhuang, X., Rabczuk, T.: Three-dimensional isogeometric analysis of flexoelectricity with MATLAB implementation. Comput. Mater. Contin. 65, 1157–1179 (2020)
17. Hu, B., Liu, J., Zhang, B., Shen, H.: Wave propagation in graphene platelet-reinforced piezoelectric sandwich composite nanoplates with nonlocal strain gradient effects. Acta Mech. Solida Sin. 34, 494–505 (2021)10.1007/s10338-021-00230-2 ↗
18. Hwang, W.-S., Park, H.C.: Finite element modeling of piezoelectric sensors and actuators. AIAA J. 31, 930–937 (1993)10.2514/3.11707 ↗
19. Lei, Z.X., Zhang, L.W., Liew, K.M.: Free vibration analysis of laminated FG-CNT reinforced composite rectangular plates using the kp-Ritz method. Compos. Struct. 127, 245–259 (2015)10.1016/j.compstruct.2015.03.019 ↗
20. Lei, Z., Su, Q., Zeng, H., Zhang, Y., Yu, C.: Parametric studies on buckling behavior of functionally graded graphene-reinforced composites laminated plates in thermal environment. Compos. Struct. 202, 695–709 (2018)10.1016/j.compstruct.2018.03.079 ↗
21. Li, K., Wu, D., Chen, X., Cheng, J., Liu, Z., Gao, W., Liu, M.: Isogeometric analysis of functionally graded porous plates reinforced by graphene platelets. Compos. Struct. 204, 114–130 (2018)10.1016/j.compstruct.2018.07.059 ↗
22. Liu, Y., Zhou, S., Wu, K., Qi, L.: Size-dependent electromechanical responses of a bilayer piezoelectric microbeam. Int. J. Mech. Mater. des. 16, 443–460 (2019)10.1007/s10999-019-09478-6 ↗
23. Liu, H., Sahmani, S., Safaei, B.: Nonlinear buckling mode transition analysis in nonlocal couple stress-based stability of FG piezoelectric nanoshells under thermo-electromechanical load. Mech. Adv. Mater. Struct. 30, 3385–3405 (2022)10.1080/15376494.2022.2073620 ↗
24. Liu, T., Liu, Q.-Y., Zhao, Y.-F., Wang, M., Zhang, S.-Q.: Bi-nonlinear isogeometric analysis of graphene platelets reinforced functionally graded porous plates bonded with piezoelectrics. Compos. Struct. 306, 116569 (2023)10.1016/j.compstruct.2022.116569 ↗
25. Lv, S., Liu, H., Wang, F., Liu, X., Peng, M., Wei, Y., Li, C.: Effect of axial misalignment on the microstructure, mechanical, and corrosion properties of magnetically impelled arc butt welding joint. Mater. Today Commun. 40, 109866 (2024)10.1016/j.mtcomm.2024.109866 ↗
26. Majidi-Mozafari, K., Bahaadini, R., Saidi, A.R., Khodabakhsh, R.: An analytical solution for vibration analysis of sandwich plates reinforced with graphene nanoplatelets. Eng. Comput. 38, 2107–2123 (2020)10.1007/s00366-020-01183-9 ↗
27. Mirzaei, M., Kiani, Y.: Isogeometric thermal buckling analysis of temperature dependent FG graphene reinforced laminated plates using NURBS formulation. Compos. Struct. 180, 606–616 (2017)10.1016/j.compstruct.2017.08.057 ↗
28. Moghaddasi, M., Kiani, Y.: Free and forced vibrations of graphene platelets reinforced composite laminated arches subjected to moving load. Meccanica 57, 1105–1124 (2022)10.1007/s11012-022-01476-x ↗
29. Nguyen, N.V., Phan, D.-H.: A refined quasi-3D isogeometric model for dynamic instability of graphene nanoplatelets-reinforced porous sandwich plates. Aerosp. Sci. Technol. 142, 108595 (2023)10.1016/j.ast.2023.108595 ↗
30. Nguyen, L.B., Nguyen, N.V., Thai, C.H., Ferreira, A.M.J., Nguyen-Xuan, H.: An isogeometric Bézier finite element analysis for piezoelectric FG porous plates reinforced by graphene platelets. Compos. Struct. 214, 227–245 (2019a)10.1016/j.compstruct.2019.01.077 ↗
31. Nguyen, N.V., Lee, J., Nguyen-Xuan, H.: Active vibration control of GPLs-reinforced FG metal foam plates with piezoelectric sensor and actuator layers. Compos. B Eng. 172, 769–784 (2019b)10.1016/j.compositesb.2019.05.060 ↗
32. Nguyen, N.V., Nguyen-Xuan, H., Lee, D., Lee, J.: A novel computational approach to functionally graded porous plates with graphene platelets reinforcement. Thin-Walled Struct. 150, 106684 (2020a)10.1016/j.tws.2020.106684 ↗
33. Nguyen, Q.H., Nguyen, L.B., Nguyen, H.B., Nguyen-Xuan, H.: A three-variable high order shear deformation theory for isogeometric free vibration, buckling and instability analysis of FG porous plates reinforced by graphene platelets. Compos. Struct. 245, 112321 (2020b)10.1016/j.compstruct.2020.112321 ↗
34. Nguyen, V.-L., Limkatanyu, S., Bui, T.Q., Rungamornrat, J.: Free vibration analysis of rotating stiffened functionally graded graphene-platelet-reinforced composite toroidal shell segments with novel four-unknown refined theories. Int. J. Mech. Mater. des. 19, 319–350 (2022)10.1007/s10999-022-09626-5 ↗
35. Nguyen, L.B., Nguyen-Xuan, H., Thai, C.H., Phung-Van, P.: A size-dependent effect of smart functionally graded piezoelectric porous nanoscale plates. Int. J. Mech. Mater. des. 19, 817–830 (2023)10.1007/s10999-023-09660-x ↗
36. Nguyen-Quang, K., Dang-Trung, H., Ho-Huu, V., Luong-Van, H., Nguyen-Thoi, T.: Analysis and control of FGM plates integrated with piezoelectric sensors and actuators using cell-based smoothed discrete shear gap method (CS-DSG3). Compos. Struct. 165, 115–129 (2017)10.1016/j.compstruct.2017.01.006 ↗
37. Nguyen Van Do, V., Lee, C.-H.: Isogeometric analysis for buckling and postbuckling of graphene platelet reinforced composite plates in thermal environments. Eng. Struct. 244, 112746 (2021)10.1016/j.engstruct.2021.112746 ↗
38. Niu, Y., Yao, M.: Linear and nonlinear vibrations of graphene platelet reinforced composite tapered plates and cylindrical panels. Aerosp. Sci. Technol. 115, 106798 (2021)10.1016/j.ast.2021.106798 ↗
39. Pham, Q.-H., Nguyen, P.-C., Tran, V.K., Nguyen-Thoi, T.: Isogeometric analysis for free vibration of bidirectional functionally graded plates in the fluid medium. Def. Technol. 18, 1311–1329 (2022)10.1016/j.dt.2021.09.006 ↗
40. Phan, D.-H.: Isogeometric analysis of functionally-graded graphene platelets reinforced porous nanocomposite plates using a refined plate theory. Int. J. Struct. Stab. Dyn. 20, 2050076 (2020)10.1142/S0219455420500765 ↗
41. Phung-Van, P., Thai, C.H., Nguyen-Xuan, H., Abdel Wahab, M.: Porosity-dependent nonlinear transient responses of functionally graded nanoplates using isogeometric analysis. Compos. B Eng. 164, 215–225 (2019)10.1016/j.compositesb.2018.11.036 ↗
42. Phung-Van, P., Lieu, Q.X., Ferreira, A.J.M., Thai, C.H.: A refined nonlocal isogeometric model for multilayer functionally graded graphene platelet-reinforced composite nanoplates. Thin-Walled Struct. 164, 107862 (2021)10.1016/j.tws.2021.107862 ↗
43. Phung-Van, P., Nguyen, L.B., Hung, P.T., Nguyen-Xuan, H., Thai, C.H.: Nonlocal nonlinear analysis of functionally graded piezoelectric porous nanoplates. Int. J. Mech. Mater. des. 20, 743–753 (2024)10.1007/s10999-023-09701-5 ↗
44. Rafiee, M.A., Rafiee, J., Wang, Z., Song, H., Yu, Z.Z., Koratkar, N.: Enhanced mechanical properties of nanocomposites at low graphene content. ACS Nano 3, 3884–3890 (2009)10.1021/nn9010472 ↗
45. Rajasekaran, S., Murray, D.W.: Incremental finite element matrices. J. Struct. Div. 99, 2423–2438 (1973)10.1061/JSDEAG.0003667 ↗
46. Roberts, A.P., Garboczi, E.J.: Elastic moduli of model random three-dimensional closed-cell cellular solids. Acta Mater. 49, 189–197 (2001)10.1016/S1359-6454(00)00314-1 ↗
47. Roberts, A.P., Garboczi, E.J.: Computation of the linear elastic properties of random porous materials with a wide variety of microstructure. Proc. r. Soc. Lond. Ser. a: Math. Phys. Eng. Sci. 458, 1033–1054 (2002)10.1098/rspa.2001.0900 ↗
48. Sahmani, S., Aghdam, M.M., Rabczuk, T.: A unified nonlocal strain gradient plate model for nonlinear axial instability of functionally graded porous micro/nano-plates reinforced with graphene platelets. Mater. Res. Express 5, 045048 (2018)10.1088/2053-1591/aabdbb ↗
49. Sahmani, S., Safaei, B., Rabczuk, T.: Nonlinear in-plane buckling of small-curved and large-curved FG porous microbeams via strain gradient-based isogeometric collocation formulations. Compos. Struct. 334, 117969 (2024a)10.1016/j.compstruct.2024.117969 ↗
50. Sahmani, S., Safaei, B., Rabczuk, T.: On the role of surface elasticity in nonlinear planar stability of FG porous reinforced nanosize curved beams having different degrees of curvature. Eur. J. Mech. A/Solids 107, 105384 (2024b)10.1016/j.euromechsol.2024.105384 ↗
51. Shan, Z., Yang, Y., Shi, H., Zhu, J., Tan, X., Luan, Y., Jiang, Z., Wang, P., Qin, J.: Hollow dodecahedra graphene oxide-cuprous oxide nanocomposites with effective photocatalytic and bactericidal activity. Front. Chem. 9, 755836 (2021)10.3389/fchem.2021.755836 ↗
52. Sharma, S., Kumar, A., Kumar, R., Talha, M., Vaish, R.: Geometry independent direct and converse flexoelectric effects in functionally graded dielectrics: an isogeometric analysis. Mech. Mater. 148, 103456 (2020)10.1016/j.mechmat.2020.103456 ↗
53. Sivakumar, K., Iyengar, N.G.R., Deb, K.: Free vibration of laminated composite plates with cutout. J. Sound Vib. 221, 443–470 (1999)10.1006/jsvi.1998.2034 ↗
54. Song, M., Yang, J., Kitipornchai, S., Zhu, W.: Buckling and postbuckling of biaxially compressed functionally graded multilayer graphene nanoplatelet-reinforced polymer composite plates. Int. J. Mech. Sci. 131–132, 345–355 (2017)10.1016/j.ijmecsci.2017.07.017 ↗
55. Sundararajan, N., Prakash, T., Ganapathi, M.: Nonlinear free flexural vibrations of functionally graded rectangular and skew plates under thermal environments. Finite Elem. Anal. des. 42, 152–168 (2005)10.1016/j.finel.2005.06.001 ↗
56. Tabak, A., Safaei, B., Memarzadeh, A., Arman, S., Kizilors, C.: An extensive review of piezoelectric energy-harvesting structures utilizing auxetic materials. J. Vib. Eng. Technol. 12, 3155–3192 (2023)10.1007/s42417-023-01038-9 ↗
57. Tao, C., Dai, T.: Modified couple stress-based nonlinear static bending and transient responses of size-dependent sandwich microplates with graphene nanocomposite and porous layers. Thin-Walled Struct. 171, 108704 (2022)10.1016/j.tws.2021.108704 ↗
58. Thai, C.H., Ferreira, A.J.M., Tran, T.D., Phung-Van, P.: Free vibration, buckling and bending analyses of multilayer functionally graded graphene nanoplatelets reinforced composite plates using the NURBS formulation. Compos. Struct. 220, 749–759 (2019)10.1016/j.compstruct.2019.03.100 ↗
59. Thai, L.M., Luat, D.T., Phung, V.B., Minh, P.V., Thom, D.V.: Finite element modeling of mechanical behaviors of piezoelectric nanoplates with flexoelectric effects. Arch. Appl. Mech. 92, 163–182 (2021)10.1007/s00419-021-02048-3 ↗
60. Thai, S., Do, D.T.T., Tan, T.N.: Nonlinear bending analysis of variable thickness multi-directional functionally graded plates based on isogeometric analysis. Mech. Adv. Mater. Struct. 30, 4091–4109 (2022)10.1080/15376494.2022.2088909 ↗
61. Thi, T.-H.N., Tran, V.K., Pham, Q.H.: Flexoelectric and size-dependent effects on hygro-thermal vibration of variable thickness fluid-infiltrated porous metal foam nanoplates. Heliyon 10, e26150 (2024)10.1016/j.heliyon.2024.e26150 ↗
62. Tjong, S.C.: Recent progress in the development and properties of novel metal matrix nanocomposites reinforced with carbon nanotubes and graphene nanosheets. Mater. Sci. Eng. r. Rep. 74, 281–350 (2013)10.1016/j.mser.2013.08.001 ↗
63. Ton-That, H.L., Nguyen-Van, H., Chau-Dinh, T.: A novel quadrilateral element for analysis of functionally graded porous plates/shells reinforced by graphene platelets. Arch. Appl. Mech. 91, 2435–2466 (2021)10.1007/s00419-021-01893-6 ↗
64. Tran, H.-Q., Vu, V.-T., Tran, M.-T.: Free vibration analysis of piezoelectric functionally graded porous plates with graphene platelets reinforcement by pb-2 Ritz method. Compos. Struct. 305, 116535 (2023)10.1016/j.compstruct.2022.116535 ↗
65. Van Do, V.N., Lee, Y.-K., Lee, C.-H.: Isogeometric analysis of FG-CNTRC plates in combination with hybrid type higher-order shear deformation theory. Thin-Walled Struct. 148, 106565 (2020)10.1016/j.tws.2019.106565 ↗
66. Van Ke, T., Van Minh, P., Dung, N.T., Thai, L.M., Van Thom, D.: Flexoelectric effect on bending and free vibration behaviors of piezoelectric sandwich FGP nanoplates via nonlocal strain gradient theconory. J. Vib. Eng. Technol. 12, 6567–6596 (2024)10.1007/s42417-023-01270-3 ↗
67. Van Minh, P., Van Ke, T.: A comprehensive study on mechanical responses of non-uniform thickness piezoelectric nanoplates taking into account the flexoelectric effect. Arab. J. Sci. Eng. 48, 11457–11482 (2022)10.1007/s13369-022-07362-8 ↗
68. Wang, B., Li, X.-F.: Free vibration of circular and annular nanoplates with surface and flexoelectric effects. Mech. Adv. Mater. Struct. 29, 6705–6717 (2021)10.1080/15376494.2021.1983898 ↗
69. Wang, S.Y., Quek, S.T., Ang, K.K.: Vibration control of smart piezoelectric composite plates. Smart Mater. Struct. 10, 637–644 (2001)10.1088/0964-1726/10/4/306 ↗
70. Wang, C., Song, Z., Fan, H: Novel evidence theory-based reliability analysis of functionally graded plate considering thermal stress behavior. Aerosp. Sci. Technol. 146, 108936 (2024)10.1016/j.ast.2024.108936 ↗
71. Xiao, Y., Wu, Z.: Non-linear bending analysis and control of graphene-platelets-reinforced porous sandwich plates with piezoelectric layer subjected to electromechanical loading. Appl. Math. Model. 137, 115708 (2025)10.1016/j.apm.2024.115708 ↗
72. Xu, J.W., Wang, P., Liu, Z.H.: Electromechanical coupling in piezoelectric nanoplate due to the flexoelectric effect. Acta Mech. 235, 479–492 (2023)10.1007/s00707-023-03764-3 ↗
73. Yang, J., Kitipornchai, S., Liew, K.M.: Large amplitude vibration of thermo-electro-mechanically stressed FGM laminated plates. Comput. Methods Appl. Mech. Eng. 192, 3861–3885 (2003)10.1016/S0045-7825(03)00387-6 ↗
74. Yang, J., Kitipornchai, S., Liew, K.M.: Non-linear analysis of the thermo-electro-mechanical behaviour of shear deformable FGM plates with piezoelectric actuators. Int. J. Numer. Methods Eng. 59, 1605–1632 (2004)10.1002/nme.932 ↗
75. Yang, W., Liang, X., Shen, S.: Electromechanical responses of piezoelectric nanoplates with flexoelectricity. Acta Mech. 226, 3097–3110 (2015)10.1007/s00707-015-1373-8 ↗
76. Yang, J., Chen, D., Kitipornchai, S.: Buckling and free vibration analyses of functionally graded graphene reinforced porous nanocomposite plates based on Chebyshev–Ritz method. Compos. Struct. 193, 281–294 (2018)10.1016/j.compstruct.2018.03.090 ↗
77. Yee, K., Ghayesh, M.H.: A review on the mechanics of graphene nanoplatelets reinforced structures. Int. J. Eng. Sci. 186, 103831 (2023)10.1016/j.ijengsci.2023.103831 ↗
78. Yin, S., Hale, J.S., Yu, T., Bui, T.Q., Bordas, S.P.A.: Isogeometric locking-free plate element: a simple first order shear deformation theory for functionally graded plates. Compos. Struct. 118, 121–138 (2014)10.1016/j.compstruct.2014.07.028 ↗
79. Zhang, S.-Q., Zhao, G.-Z., Zhang, S.-Y., Schmidt, R., Qin, X.-S.: Geometrically nonlinear FE analysis of piezoelectric laminated composite structures under strong driving electric field. Compos. Struct. 181, 112–120 (2017)10.1016/j.compstruct.2017.08.052 ↗
80. Zhang, Y., Zhuang, X., Lackner, R.: Stability analysis of shotcrete supported crown of NATM tunnels with discontinuity layout optimization. Int. J. Numer. Anal. Methods Geomech. 42, 1199–1216 (2018)10.1002/nag.2775 ↗
81. Zhao, X., Zheng, S., Li, Z.: Size-dependent nonlinear bending and vibration of flexoelectric nanobeam based on strain gradient theory. Smart Mater. Struct. 28, 075027 (2019)10.1088/1361-665X/ab1cfc ↗
82. Zhao, Y., Xing, S., Jin, Q., Yang, N., He, Y., Zhang, J.: Excellent angular and electrical performance damage tolerance of wave-absorbing laminate via gradient A-T-A design. Compos. Commun. 46, 101838 (2024)10.1016/j.coco.2024.101838 ↗
83. Zheng, S., Wang, X., Chen, W.: The formulation of a refined hybrid enhanced assumed strain solid shell element and its application to model smart structures containing distributed piezoelectric sensors/actuators. Smart Mater. Struct. 13, N43–N50 (2004)10.1088/0964-1726/13/4/N02 ↗
84. Zheng, S.J., Dai, F., Song, Z.: Active control of piezothermoelastic FGM shells using integrated piezoelectric sensor/actuator layers. Int. J. Appl. Electromagn. Mech. 303233, 107–124 (2009)10.3233/JAE-2009-1040 ↗
85. Zheng, S., Zhao, X., Wang, H.: Theoretical and finite element modeling of piezoelectric nanobeams with surface and flexoelectricity effects. Mech. Adv. Mater. Struct. 26, 1261–1270 (2019)10.1080/15376494.2018.1432799 ↗
86. Zheng, S., Zhang, N., Zhao, X., Chen, D., Wang, H.T.: Size-dependent mechanical analysis of porous functionally graded piezoelectric micro/nanoscale structures: a literature review. Smart Mater. Struct. 33, 093002 (2024)10.1088/1361-665X/ad5809 ↗
87. Zhou, S., Li, A., Zhang, R., Qi, L., Ren, F., Zheng, Z., Qiao, J., Sun, Y., Zhou, S.: Electro-mechanical responses of flexoelectric bilayer circular nano-plate with surface effect. Int. J. Mech. Mater. des. 20, 209–231 (2023)10.1007/s10999-023-09672-7 ↗