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Multi-objective isogeometric integrated optimization for shape control of piezoelectric functionally graded plates. (English) Zbl 1506.74323

Summary: This paper presents a novel multi-objective integrated optimization method for static shape control of piezoelectric functionally graded plates (FGPs). The new method combines isogeometric analysis (IGA) and an effective multi-objective non-gradient algorithm which has not been applied to the integrated design of piezoelectric FGPs. Mechanical behavior of the FGPs with surface bonded piezoelectric layers is derived using the IGA associated with a third-order shear deformation theory (TSDT). The high-order continuity of NURBS basis functions in IGA meets the demand of \(C^1\)-continuity of the TSDT. In optimal design problem, material layout of the FGPs and control voltages of piezoelectric layers are simultaneously optimized under the conditions of minimum static shape error and maximum first-order natural frequency. The B-spline control points for describing ceramic volume fraction distribution of the FGPs and the applied voltages are taken as design variables. In addition, an improved multi-objective particle swarm optimization algorithm is used as an optimization solver. The validity and applicability of this combination of innovative method are demonstrated through several numerical examples in integrated design.

MSC:

74P20 Geometrical methods for optimization problems in solid mechanics
74F15 Electromagnetic effects in solid mechanics
74K20 Plates
74S05 Finite element methods applied to problems in solid mechanics
74S22 Isogeometric methods applied to problems in solid mechanics
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[1] Wu, C. C.; Kahn, M.; Moy, W., Piezoelectric ceramics with functional gradients: a new application in material design, J. Am. Ceram. Soc., 79, 3, 809-812 (1996)
[2] Zhang, L.; Song, Z.; Liew, K., Optimal shape control of CNT reinforced functionally graded composite plates using piezoelectric patches, Composites B, 85, 140-149 (2016)
[3] Irschik, H., A review on static and dynamic shape control of structures by piezoelectric actuation, Eng. Struct., 24, 1, 5-11 (2002)
[4] Frecker, M., Recent advances in optimization of smart structures and actuators, J. Intell. Mater. Syst. Struct., 14, 4-5, 207-216 (2003)
[5] Chee, C.; Tong, L.; Steven, G., Static shape control of composite plates using a curvature-displacement based algorithm, Int. J. Solids Struct., 38, 36-37, 6381-6403 (2001) · Zbl 0981.74513
[6] Sun, D.; Tong, L., Design optimization of piezoelectric actuator patterns for static shape control of smart plates, Smart Mater. Struct., 14, 6, 1353 (2005)
[7] Wang, C. M.; Ang, K. K.; Ajit, A., Shape control of laminated cantilevered beams with piezoelectric actuators, J. Intell. Mater. Syst. Struct., 10, 2, 164-175 (1999)
[8] Nguyen, Q.; Tong, L.; Gu, Y., Evolutionary piezoelectric actuators design optimisation for static shape control of smart plates, Comput. Methods Appl. Mech. Engrg., 197, 1-4, 47-60 (2007) · Zbl 1169.74524
[9] Nguyen, Q.; Tong, L., Voltage and evolutionary piezoelectric actuator design optimisation for static shape control of smart plate structures, Mater. Des., 28, 2, 387-399 (2007)
[10] Liew, K.; He, X.; Meguid, S., Optimal shape control of functionally graded smart plates using genetic algorithms, Comput. Mech., 33, 4, 245-253 (2004) · Zbl 1067.74547
[11] Liew, K.; He, X.; Ray, T., On the use of computational intelligence in the optimal shape control of functionally graded smart plates, Comput. Methods Appl. Mech. Engrg., 193, 42-44, 4475-4492 (2004) · Zbl 1112.74459
[12] da Mota Silva, S.; Ribeiro, R.; Rodrigues, J. D.; Vaz, M.; Monteiro, J., The application of genetic algorithms for shape control with piezoelectric patches—an experimental comparison, Smart Mater. Struct., 13, 1, 220 (2004)
[13] Khorsand, A.-R.; Akbarzadeh-T, M.-R.; Moin, H., Genetic quantum algorithm for voltage and pattern design of piezoelectric actuator, (2006 IEEE International Conference on Evolutionary Computation (2006), IEEE), 2593-2600
[14] Kang, Z.; Tong, L., Topology optimization-based distribution design of actuation voltage in static shape control of plates, Comput. Struct., 86, 19-20, 1885-1893 (2008)
[15] Liu, S.; Tong, L.; Lin, Z., Simultaneous optimization of control parameters and configurations of PZT actuators for morphing structural shapes, Finite Elem. Anal. Des., 44, 6-7, 417-424 (2008)
[16] Wang, X.; Zhou, W.; Wu, Z.; Zhang, X., Integrated design of laminated composite structures with piezocomposite actuators for active shape control, Compos. Struct., 215, 166-177 (2019)
[17] Yang, K.; Zhu, J.; Wu, M.; Zhang, W., Integrated optimization of actuators and structural topology of piezoelectric composite structures for static shape control, Comput. Methods Appl. Mech. Engrg., 334, 440-469 (2018) · Zbl 1440.74140
[18] Bendine, K.; Boukhoulda, F.; Haddag, B.; Nouari, M., Active vibration control of composite plate with optimal placement of piezoelectric patches, Mech. Adv. Mater. Struct., 26, 4, 341-349 (2019)
[19] Wang, C.; Yu, T.; Curiel-Sosa, J. L.; Xie, N.; Bui, T. Q., Adaptive chaotic particle swarm algorithm for isogeometric multi-objective size optimization of FG plates, Struct. Multidiscip. Optim., 1-22 (2019)
[20] Correia, V. M.F.; Madeira, J. F.A.; Araújo, A. L.; Soares, C. M.M., Multiobjective design optimization of laminated composite plates with piezoelectric layers, Compos. Struct., 169, 10-20 (2017)
[21] Dhuri, K.; Seshu, P., Multi-objective optimization of piezo actuator placement and sizing using genetic algorithm, J. Sound Vib., 323, 3-5, 495-514 (2009)
[22] Kudikala, R.; Kalyanmoy, D.; Bhattacharya, B., Multi-objective optimization of piezoelectric actuator placement for shape control of plates using genetic algorithms, J. Mech. Des., 131, 9, Article 091007 pp. (2009)
[23] Lezgy-Nazargah, M.; Vidal, P.; Polit, O., An efficient finite element model for static and dynamic analyses of functionally graded piezoelectric beams, Compos. Struct., 104, 71-84 (2013)
[24] Hughes, T. J.; Cottrell, J. A.; Bazilevs, Y., Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement, Comput. Methods Appl. Mech. Engrg., 194, 39-41, 4135-4195 (2005) · Zbl 1151.74419
[25] Chen, T.; Mo, R.; Wan, N., NURBS based isogeometric finite element method for analysis of twodimensional piezoelectric device, Procedia Eng., 15, 3562-3566 (2011)
[26] Willberg, C.; Gabbert, U., Development of a three-dimensional piezoelectric isogeometric finite element for smart structure applications, Acta Mech., 223, 8, 1837-1850 (2012) · Zbl 1401.74278
[27] Chen, M.; Chen, H.; Ma, X.; Jin, G.; Ye, T.; Zhang, Y.; Liu, Z., The isogeometric free vibration and transient response of functionally graded piezoelectric curved beam with elastic restraints, Results Phys., 11, 712-725 (2018)
[28] Phung-Van, P.; Tran, L. V.; Ferreira, A. J.M.; Nguyen-Xuan, H.; Abdel-Wahab, M., Nonlinear transient isogeometric analysis of smart piezoelectric functionally graded material plates based on generalized shear deformation theory under thermo-electro-mechanical loads, Nonlinear Dynam., 87, 2, 1-16 (2016)
[29] Thanh, C.-L.; Tran, L. V.; Bui, T. Q.; Nguyen, H. X.; Abdel-Wahab, M., Isogeometric analysis for size-dependent nonlinear thermal stability of porous FG microplates, Compos. Struct., 221, Article 110838 pp. (2019)
[30] Tseng, P.; Yun, S., A coordinate gradient descent method for nonsmooth separable minimization, Math. Program., 117, 1-2, 387-423 (2009) · Zbl 1166.90016
[31] Pfrommer, B.; Cote, M.; Louie, S.; Cohen, M., Relaxation of crystals with the quasi-Newton method, J. Comput. Phys., 131, 1, 233-240 (1997) · Zbl 0868.65088
[32] Deb, K.; Pratap, A.; Agarwal, S.; Meyarivan, T., A fast and elitist multiobjective genetic algorithm: NSGA-II, IEEE Trans. Evol. Comput., 6, 2, 182-197 (2002)
[33] Sun, S.; Yu, T.; Nguyen, T.-T.; Atroshchenko, E.; Bui, T. Q., Structural shape optimization by IGABEM and particle swarm optimization algorithm, Eng. Anal. Bound. Elem., 88, 26-40 (2018) · Zbl 1403.74234
[34] Thanh, C.-L.; Phung-Van, P.; Thai, C. H.; Nguyen-Xuan, H.; Wahab, M. A., Isogeometric analysis of functionally graded carbon nanotube reinforced composite nanoplates using modified couple stress theory, Compos. Struct., 184, 633-649 (2018)
[35] Thanh, C.-L.; Ferreira, A.; Wahab, M. A., A refined size-dependent couple stress theory for laminated composite micro-plates using isogeometric analysis, Thin-Walled Struct., 145, Article 106427 pp. (2019)
[36] Wang, C.; Koh, J.; Yu, T.; Xie, N.; Cheong, K., Material and shape optimization of bi-directional functionally graded plates by GIGA and an improved multi-objective particle swarm optimization algorithm, Comput. Methods Appl. Mech. Engrg., 366, Article 113017 pp. (2020) · Zbl 1442.74161
[37] Vel, S. S.; Batra, R., Exact solution for thermoelastic deformations of functionally graded thick rectangular plates, AIAA J., 40, 7, 1421-1433 (2002)
[38] Lieu, Q. X.; Lee, J., Modeling and optimization of functionally graded plates under thermo-mechanical load using isogeometric analysis and adaptive hybrid evolutionary firefly algorithm, Compos. Struct., 179, 89-106 (2017)
[39] Reddy, J. N., Mechanics of Laminated Composite Plates and Shells: Theory and Analysis (2004), CRC Press · Zbl 1075.74001
[40] Thanh, C.-L.; Tran, L. V.; Vu-Huu, T.; Abdel-Wahab, M., The size-dependent thermal bending and buckling analyses of composite laminate microplate based on new modified couple stress theory and isogeometric analysis, Comput. Methods Appl. Mech. Engrg., 350, 337-361 (2019) · Zbl 1441.74082
[41] Yin, S.; Hale, J. S.; Yu, T.; Bui, T. Q.; Bordas, S. P., Isogeometric locking-free plate element: a simple first order shear deformation theory for functionally graded plates, Compos. Struct., 118, 121-138 (2014)
[42] Piegl, L.; Tiller, W., The NURBS Book (2012), Springer Science & Business Media
[43] Luo, Q.; Tong, L., High precision shape control of plates using orthotropic piezoelectric actuators, Finite Elem. Anal. Des., 42, 11, 1009-1020 (2006)
[44] Y. Narita, Layerwise optimization for the maximum fundamental frequency of laminated composite plates, J. Sound Vib. 263 (5) 1005-1016.
[45] Farsangi, M. A.; Saidi, A., Levy type solution for free vibration analysis of functionally graded rectangular plates with piezoelectric layers, Smart Mater. Struct., 21, 9, Article 094017 pp. (2012)
[46] He, X.; Ng, T.; Sivashanker, S.; Liew, K., Active control of FGM plates with integrated piezoelectric sensors and actuators, Int. J. Solids Struct., 38, 9, 1641-1655 (2001) · Zbl 1012.74047
[47] 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)
[48] Moita, J. S.; Araújo, A. L.; Correia, V. F.; Soares, C. M.M.; Herskovits, J., Material distribution and sizing optimization of functionally graded plate-shell structures, Composites B, 142, 263-272 (2018)
[49] Tzou, H., Development of a light-weight robot end-effector using polymeric piezoelectric bimorph, (Proceedings, 1989 International Conference on Robotics and Automation (1989), IEEE), 1704-1709
[50] Li, S.; Huang, L.; Jiang, L.; Qin, R., A bidirectional B-spline finite point method for the analysis of piezoelectric laminated composite plates and its application in material parameter identification, Compos. Struct., 107, 346-362 (2014)
[51] Phung-Van, P.; Nguyen-Thoi, T.; Le-Dinh, T.; Nguyen-Xuan, H., Static and free vibration analyses and dynamic control of composite plates integrated with piezoelectric sensors and actuators by the cell-based smoothed discrete shear gap method (CS-FEM-DSG3), Smart Mater. Struct., 22, 9, Article 095026 pp. (2013)
[52] Li, K.; Wu, D.; Gao, W., Spectral stochastic isogeometric analysis for static response of FGM plate with material uncertainty, Thin-Walled Struct., 132, 504-521 (2018)
[53] Boor, C., On calculating with B-splines, J. Approx. Theory, 6, 1, 50-62 (1972) · Zbl 0239.41006
[54] Piegl, L. A.; Tiller, W., The NURBS Book (1997), Springer Berlin Heidelberg · Zbl 0868.68106
[55] Hosseini, S. F.; Moetakef-Imani, B.; Hadidi-Moud, S.; Hassani, B., The effect of parameterization on isogeometric analysis of free-form curved beams, Acta Mech., 227, 7, 1983-1998 (2016) · Zbl 1344.74038
[56] Hu, L.; Zhang, W., NSGA-II approach for proper choice of nodes and knots in B-spline curve interpolation, Comput. Aided Des., 127, Article 102885 pp. (2020)
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