GEOMETRICALLY NONLINEAR ANALYSIS OF PIEZOELECTRIC ACTIVE LAMINATED SHELLS BY MEANS OF ISOGEOMETRIC FE FORMULATION

Predrag Milić, Dragan Marinković, Žarko Ćojbašić

DOI Number
10.22190/FUME050123059M
First page
Last page

Abstract


The topic of piezoelectric active thin-walled structures has attracted a great deal of attention over the previous couple of decades. Lightweight structures with piezoelectric material based active elements, sensors and actuators, offer numerous advantages over their passive counterparts. This explains the motivation of authors to dedicate their work to this enticing research field. Accurate and reliable numerical tools for modeling and simulation of this type of structures is still a hot topic in the research community. This paper offers an isogeometric finite element formulation for shell type of structures made of composite laminates including piezoelectric layers characterized by the electro-mechanical coupling. The shell kinematics is based on the Mindlin-Reissner assumptions, thus including the transverse shear effects. A few examples selected from the available literature are considered to demonstrate the applicability of the developed numerical tool and assess its performance.

Keywords

Isogeometric analysis, Laminated structure, Reissner-Mindlin kinematics, Shell, Piezoelectricity, Geometrically nonlinear analysis

Full Text:

PDF

References


Wang, K., Alaluf, D., Rodrigues, G., Preumont, A., 2021, Precision Shape Control of Ultra-thin Shells with Strain Actuators, Journal of Applied and Computational Mechanics, 7(Special Issue), pp. 1130-1137.

Todorov, T., Mitrev, R., Penev, I., 2020, Force analysis and kinematic optimization of a fluid valve driven by shape memory alloys, Reports in Mechanical Engineering, 1(1), pp. 61-76.

Preumont, A., 2018, Vibration Control of Active Structures, Springer Cham, 518 p.

Mitrev, R., Todorov, T., Fursov, A., Fomichev, V., Il'in, A., 2021, A Case Study of Combined Application of Smart Materials in a Thermal Energy Harvester with Vibrating Action, Journal of Applied and Computational Mechanics, 7(1), pp. 372-381.

Nguyen, X., Nguyen, H., 2022, Investigation of influences of fabrication tolerances on operational characteristics of piezo-actuated stick-slip micro-drives, Facta Universitatis-Series Mechanical Engineering, 20(1), pp. 109-126.

Shao, S., Song, S., Xu, M., Jiang, W., 2018, Mechanically reconfigurable reflector for future smart space antenna application, Smart Materials and Structures, 27(9), 095014.

Kulkarni, H., Zohaib, K., Khusru, A., Shravan-Aiyappa, K., 2018, Application of piezoelectric technology in automotive systems, Materials Today: Proceedings, 5(10, Part 1), pp. 21299-21304.

Nestorović, T., Marinković, D., Chandrashekar, G., Marinković, Z., Trajkov, M., 2012, Implementation of a user defined piezoelectric shell element for analysis of active structures, Finite Elements in Analysis and Design, 52, pp. 11-22.

Rama, G., Marinković, D., Zehn, M., 2018, Efficient three-node finite shell element for linear and geometrically nonlinear analyses of piezoelectric laminated structures, Journal of Intelligent Material Systems and Structures, 29(3), pp, 345-357.

Carrera, E., Valvano, S., Kulikov, G.M., 2018, Electro-mechanical analysis of composite and sandwich multilayered structures by shell elements with node-dependent kinematics, International Journal of Smart and Nano Materials, 9(1), pp. 1-33.

Rama, G., Marinkovic, D.Z., Zehn, M.W., 2017, Linear shell elements for active piezoelectric laminates, Smart Structures and Systems, 20(6), pp. 729-737.

Kulikov, G.M., Plotnikova, S.V., Carrera, E., 2018, Hybrid-Mixed Solid-Shell Element for Stress Analysis of Laminated Piezoelectric Shells through Higher-Order Theories, in: Altenbach, H., Carrera, E., Kulikov, G. (Eds), Analysis and Modelling of Advanced Structures and Smart Systems, Advanced Structured Materials, vol 81. Springer, Singapore.

Reddy, J.N., 2003, Mechanics of Laminated Composite Plates and Shells: Theory and Analysis, Second Edition. CRC Press, 858 p.

Gabbert, U., Koppe, H., Seeger, F., Berger, H., 2002, Modelling of smart composite shell structures, Journal of Theoretical and Applied Mechanics, 3(40), pp. 575-593.

Rama, G., Marinkovic, D., Zehn, M., 2018, A three-node shell element based on the discrete shear gap and assumed natural deviatoric strain approaches, Journal of the Brazilian Society of Mechanical Sciences and Engineering, 40(7), 356.

Petrolo, M., Carrera, E., 2021, Selection of element-wise shell kinematics using neural networks, Computers & Structures, 244, 106425.

Carrera, E., Zozulya, V.V., 2022, Carrera unified formulation (CUF) for the micropolar plates and shells. I. Higher order theory, Mechanics of Advanced Materials and Structures, 29(6), pp. 773-795.

Li, G., Carrera, E., Hou, Y., Kulikov, G.M., 2021, Multi-layered plate finite element models with node-dependent kinematics for smart structures with piezoelectric components, Chinese Journal of Aeronautics, 34(8), pp. 164-175.

Rama, G., Marinkovic, D., 2018, High performance 3-node shell element for linear and geometrically nonlinear analysis of composite laminates, Composites Part B: Engineering, 151, pp. 118-126.

Katariya, P.V., Hirwani, C.K., Panda, S.K., 2019, Geometrically nonlinear deflection and stress analysis of skew sandwich shell panel using higher-order theory, Engineering with Computers, 35, pp. 467–485.

Liguori, F.S., Madeo, A., 2021, A corotational mixed flat shell finite element for the efficient geometrically nonlinear analysis of laminated composite structures, International Journal for Numerical Methods in Engineering, 122(17), pp. 4575-4608.

Marinković, D., Rama, G., Zehn, M., 2019, Abaqus implementation of a corotational piezoelectric 3-node shell element with drilling degree of freedom, Facta Universitatis-Series Mechanical Engineering, 17(2), pp. 269- 283.

Hughes, T.J.R., Cottrell, J.A., Bazilevs, Y., 2005, Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement, Computer Methods in Applied Mechanics and Engineering, 194(39-41), pp. 4135- 4195.

Nguyen-Thanha, N., Valizadehb, N., Nguyenc, M.N., Nguyen-Xuand, H., Zhuange, X., Areiasf, P., Zih, G., Bazilevsg, Y., De Lorenzisa, L., Rabczukb, T., 2015, An extended isogeometric thin shell analysis based on Kirchhoff-Love theory, Computer Methods in Applied Mechanics and Engineering, 284, pp. 265-291.

Milić, P., Marinković, D., 2015, Isogeometric FE analysis of complex thin-walled structures, Transactions of FAMENA, 39(1), pp. 15-26.

Benson, D.J., Bazilevs, Y., Hsu, M.C., Hughes, T.J.R., 2010, Isogeometric shell analysis: The Reissner-Mindlin shell, Computer Methods in Applied Mechanics and Engineering, 199(5-8), pp. 276-289.

Echter, R., Oesterle, B., Bischoff, M., 2013, A hierarchic family of isogeometric shell finite elements, Computer Methods in Applied Mechanics and Engineering, 254, pp. 170-180.

Yujie, G., Martin, R., 2015, A layerwise isogeometric approach for NURBS-derived laminate composite shells, Composite Structures, 124, pp. 300-309.

Hosseini, S., Remmers, J.J., Verhoosel, C.V., de Borst, R., 2015, Propagation of delamination in composite materials with isogeometric continuum shell elements, Int. J. Numer. Methods Eng., 102(3), pp. 159-179.

Milić, P., Marinković, D., Klinge, S., Ćojbašić, Ž., 2023, Reissner-Mindlin based isogeometric finite element formulation for piezoelectric active laminated shells, Tehnički Vjesnik, 30(2), pp. 416-425.

Adam, C., Bouabdallah, S., Zarroug, M., Maitournam, H., 2015, Improved numerical integration for locking treatment in isogeometric structural elements, Part II: Plates and shells, Computer Methods in Applied Mechanics and Engineering, 284, pp. 106-137.

Marinković, D., Köppe, H., Gabbert, U., 2007, Accurate modeling of the electric field within piezoelectric layers for active composite structures. Journal of Intelligent Material Systems and Structures, 18(5), pp. 503-513.

Bathe, K.J., 1996, Finite Element Procedures, Prentice Hall, New York.

Marinković, D., Koppe, H., Gabbert, U., 2008, Degenerated shell element for geometrically nonlinear analysis of thin-walled piezoelectric active structures, Smart materials and structures, 17(1), 015030.

Tzou, H.S., Ye, R., 1996, Analysis of piezoelastic structures with laminated piezoelectric triangle shell elements, AIAA J, 34(1), pp. 110–115.

Zhang, S., 2014, Nonlinear FE Simulation and Active Vibration Control of Piezoelectric Laminated Thin-Walled Smart Structures, PhD Thesis, Fakultat fur Maschinenwesen der Rheinisch-Westfalischen Technischen Hochschule Aachen, Germay, 210 p.


Refbacks

  • There are currently no refbacks.


ISSN: 0354-2025 (Print)

ISSN: 2335-0164 (Online)

COBISS.SR-ID 98732551

ZDB-ID: 2766459-4