Finite element formulation for active functionally graded thin-walled structures

Hanen Jrad; Hanen Mallek; Mondher Wali; Fakhreddine Dammak

doi:10.1016/j.crme.2018.07.010

Finite element formulation for active functionally graded thin-walled structures

Hanen Jrad ¹ ; Hanen Mallek ¹ ; Mondher Wali ¹ ; Fakhreddine Dammak ¹

¹ Engineering Production Mechanics and Materials Unit (UGPM2), National Engineering School of Sfax, B.P. W3038, Sfax, University of Sfax, Tunisia

Comptes Rendus. Mécanique, Volume 346 (2018) no. 12, pp. 1159-1178.

Résumé

For the analysis and design process of smart structures with integrated piezoelectric patches, the finite element method provides an effective simulation approach. In this paper, an attempt on modeling and simulation of the behavior of hybrid active structures is carried out using developed Kirchhoff-type-four-node shell element.

The finite element results are compared with reference solutions taking into account the electromechanical responses of smart structures with various geometries, and the results show very high agreement. The main aspect of the application of the proposed element is to predict the behavior of FGM shells containing piezoelectric layers. A set of numerical analyses is performed in order to highlight the applicability and effectiveness of the present finite element model, notably for smart FGM structures. A comprehensive parametric study is conducted to show the influence of material composition, the placement and the thickness of the piezoelectric layers on the deformation of the laminated structure.

Reçu le : 2018-03-13
Accepté le : 2018-07-23
Publié le : 2018-08-27

DOI : 10.1016/j.crme.2018.07.010

Mots clés : Active functionally graded shells, Finite element analysis, Smart structures, Thin-walled hybrid composite, Piezoelectric sensors/actuators

Affiliations des auteurs :

Hanen Jrad ¹ ; Hanen Mallek ¹ ; Mondher Wali ¹ ; Fakhreddine Dammak ¹

¹ Engineering Production Mechanics and Materials Unit (UGPM2), National Engineering School of Sfax, B.P. W3038, Sfax, University of Sfax, Tunisia

@article{CRMECA_2018__346_12_1159_0,
     author = {Hanen Jrad and Hanen Mallek and Mondher Wali and Fakhreddine Dammak},
     title = {Finite element formulation for active functionally graded thin-walled structures},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {1159--1178},
     publisher = {Elsevier},
     volume = {346},
     number = {12},
     year = {2018},
     doi = {10.1016/j.crme.2018.07.010},
     language = {en},
}

TY  - JOUR
AU  - Hanen Jrad
AU  - Hanen Mallek
AU  - Mondher Wali
AU  - Fakhreddine Dammak
TI  - Finite element formulation for active functionally graded thin-walled structures
JO  - Comptes Rendus. Mécanique
PY  - 2018
SP  - 1159
EP  - 1178
VL  - 346
IS  - 12
PB  - Elsevier
DO  - 10.1016/j.crme.2018.07.010
LA  - en
ID  - CRMECA_2018__346_12_1159_0
ER  -

%0 Journal Article
%A Hanen Jrad
%A Hanen Mallek
%A Mondher Wali
%A Fakhreddine Dammak
%T Finite element formulation for active functionally graded thin-walled structures
%J Comptes Rendus. Mécanique
%D 2018
%P 1159-1178
%V 346
%N 12
%I Elsevier
%R 10.1016/j.crme.2018.07.010
%G en
%F CRMECA_2018__346_12_1159_0

Hanen Jrad; Hanen Mallek; Mondher Wali; Fakhreddine Dammak. Finite element formulation for active functionally graded thin-walled structures. Comptes Rendus. Mécanique, Volume 346 (2018) no. 12, pp. 1159-1178. doi : 10.1016/j.crme.2018.07.010. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2018.07.010/

Bibliographie
Cité par

[1] M.V. Gandhi; B.S. Thompson Smart Materials and Structures, Chapman & Hall, London, 1992

[2] U. Gabbert Research activities in smart materials and structures and expectations to future developments, J. Theor. Appl. Mech., Volume 3 (2002) no. 43, pp. 549-574

[3] W.M. Zhang; G. Meng; D. Chen Stability, nonlinearity and reliability of electrostatically actuated MEMS devices, Sensors, Volume 7 (2007) no. 5, pp. 760-796

[4] M.A. Foda; A.A. Almajed; M.M. ElMadany Vibration suppression of composite laminated beams using distributed piezoelectric patches, Smart Mater. Struct., Volume 19 (2010) no. 11

[5] J.M. Dietl; A.M. Wickenheiser; E.A. Garcia Timoshenko beam model for cantilevered piezoelectric energy harvesters, Smart Mater. Struct., Volume 19 (2010) no. 5

[6] S. Chesne; C. Pezerat Distributed piezoelectric sensors for boundary force measurements in Euler–Bernoulli beams, Smart Mater. Struct., Volume 20 (2011) no. 7

[7] W.M. Zhang; O. Tabata; T. Tsuchiya; G. Meng Noise-induced chaos in the electrostatically actuated MEMS resonators, Phys. Lett. A, Volume 375 (2011) no. 32, pp. 2903-2910

[8] N. Kammoun; H. Jrad; S. Bouaziz; M.B. Amar; M. Soula; M. Haddar Thermo-electro-mechanical vibration characteristics of graphene/piezoelectric/graphene sandwich nanobeams, J. Mech. (2017), pp. 1-15 | DOI

[9] W. Pompea; H. Worch; M. Epple; W. Friess; M. Gelinsky; P. Greil; U. Hempele; D. Scharnweber; K. Schulte Functionally graded materials for biomedical applications, Mater. Sci. Eng. A, Volume 362 (2003), pp. 40-60

[10] E. Müller; C. Drašar; J. Schilz; W.A. Kaysser Functionally graded materials for sensor and energy applications, Mater. Sci. Eng., Volume 362 (2003), pp. 17-30

[11] A. Kidane; A. Shukla Dynamic constitutive behavior of Ti/TiB FGM under thermo mechanical loading, J. Mater. Sci., Volume 43 (2008), pp. 2771-2777

[12] J.N. Reddy; C.F. Liu A higher-order shear deformation theory of laminated elastic shells, Int. J. Eng. Sci., Volume 23 (1985) no. 3, pp. 319-330

[13] L. Dozio On the use of the trigonometric Ritz method for general vibration analysis of rectangular Kirchhoff plates, Thin-Walled Struct., Volume 49 (2011) no. 1, pp. 129-144

[14] J.N. Reddy; D.H. Robbins Theories and computational models for composite laminates, Appl. Mech. Rev., Volume 47 (1994) no. 6, pp. 147-169

[15] A.J.M. Ferreira; G.E. Fasshauer; R.C. Batra; J.D. Rodrigues Static deformations and vibration analysis of composite and sandwich plates using a layerwise theory and RBF-PS discretizations with optimal shape parameter, Compos. Struct., Volume 86 (2008) no. 4, pp. 328-343

[16] E. Carrera; S. Brischetto; P. Nali Plates and Shells for Smart Structures: Classical and Advanced Theories for Modeling and Analysis, John Wiley and Sons, Ltd, 2011

[17] M. Cinefra; E. Carrera; L. Della Croce; C. Chinosi Refined shell elements for the analysis of functionally graded structures, Compos. Struct., Volume 94 (2012) no. 2, pp. 415-422

[18] E. Viola; F. Tornabene; N. Fantuzzi Static analysis of completely doubly-curved laminated shells and panels using general higher-order shear deformation theories, Compos. Struct., Volume 101 (2013), pp. 59-93

[19] E. Viola; F. Tornabene; N. Fantuzzi General higher-order shear deformation theories for the free vibration analysis of completely doubly-curved laminated shells and panels, Compos. Struct., Volume 95 (2013), pp. 639-666

[20] F. Tornabene; E. Viola Static analysis of functionally graded doubly-curved shells and panels of revolution, Meccanica, Volume 48 (2013) no. 4, pp. 901-930

[21] J.N. Reddy; A.R. Srinivasa Non-linear theories of beams and plates accounting for moderate rotations and material length scales, Int. J. Non-Linear Mech., Volume 66 (2014), pp. 43-53

[22] Y.Q. Tang; Z.H. Zhou; S.L. Chan Geometrically nonlinear analysis of shells by quadrilateral at shell element with drill, shear, and warping, Int. J. Numer. Methods Eng., Volume 108 (2016) no. 10, pp. 1248-1272

[23] J. Mars; S. Koubaa; M. Wali; F. Dammak Numerical analysis of geometrically non-linear behavior of functionally graded shells, Lat. Am. J. Solids Struct., Volume 14 (2017) no. 11, pp. 1952-1978

[24] A. Frikha; M. Wali; A. Hajlaoui; F. Dammak Dynamic response of functionally graded material shells with a discrete double directors shell element, Compos. Struct., Volume 154 (2016), pp. 385-395

[25] A. Frikha; F. Dammak Geometrically nonlinear static analysis of functionally graded material shells with a discrete double directors shell element, Comput. Methods Appl. Mech. Eng., Volume 315 (2017), pp. 1-24

[26] S. Zghal; A. Frikha; F. Dammak Free vibration analysis of carbon nanotube-reinforced functionally graded composite shell structures, Appl. Math. Model., Volume 53 (2018), pp. 132-155

[27] S. Zghal; A. Frikha; F. Dammak Static analysis of functionally graded carbon nanotube-reinforced plate and shell structures, Compos. Struct., Volume 176 (2017), pp. 1107-1123

[28] C. Miehe A theoretical and computational model for isotropic elastoplastic stress analysis in shells at large strains, Comput. Methods Appl. Mech. Eng., Volume 155 (1998) no. 3–4, pp. 193-233

[29] S. Klinkel; F. Gruttmann; W. Wagner A robust non-linear solid shell element based on a mixed variational formulation, Comput. Methods Appl. Mech. Eng., Volume 195 (2006), pp. 179-201

[30] M. Schwarze; S. Reese A reduced integration solid-shell finite element based on the EAS and the ANS concept-large deformation problems, Int. J. Numer. Methods Eng., Volume 85 (2011) no. 3, pp. 289-329

[31] K. Rah; W. Van Paepegem; A.M. Habraken; J. Degrieck; R.J. Alves de Sousa; R.A.F. Valente Optimal low-order fully integrated solid-shell elements, Comput. Methods Appl. Mech. Eng., Volume 51 (2013) no. 3, pp. 309-326

[32] A. Hajlaoui; E. Triki; A. Frikha; M. Wali; F. Dammak Nonlinear dynamics analysis of FGM shell structures with a higher order shear strain enhanced solid-shell element, Lat. Am. J. Solids Struct., Volume 14 (2017) no. 1, pp. 72-91

[33] A. Hajlaoui; A. Jarraya; I. Kallel-Kammoun; F. Dammak Buckling analysis of a laminated composite plate with delaminations using the enhanced assumed strain solid shell element, J. Mech. Sci. Technol., Volume 26 (2012) no. 10, pp. 3213-3221

[34] D. Marinković; H. Köppe; U. Gabbert Accurate modeling of the electric field within piezoelectric layers for active composite structures, J. Intell. Mater. Syst. Struct., Volume 18 (2007) no. 5, pp. 503-513

[35] D. Marinković; H. Köppe; U. Gabbert Aspects of modeling piezoelectric active thin-walled structures, J. Intell. Mater. Syst. Struct., Volume 20 (2009) no. 15, pp. 1835-1844

[36] V. Balamurugan; S. Narayanan A piezolaminated composite degenerated shell finite element for active control of structures with distributed piezosensors and actuators, Smart Mater. Struct., Volume 17 (2008) no. 3

[37] D. Marinković; M. Zehn Finite element formulation for active composite laminates, Am. J. Eng. Appl. Sci., Volume 8 (2015) no. 3, p. 328

[38] R. Lammering; S. Mesecke-Rischmann Multi-field variational formulations and related finite elements for piezoelectric shells, Smart Mater. Struct., Volume 12 (2003) no. 6, p. 904

[39] D. Marinković; H. Köppe; U. Gabbert Numerically efficient finite element formulation for modeling active composite laminates, Mech. Adv. Mat. Struct., Volume 13 (2006) no. 5, pp. 379-392

[40] T. Nestorović; D. Marinković; G. Chandrashekar; Z. Marinković; M. Trajkov Implementation of a user defined piezoelectric shell element for analysis of active structures, Finite Elem. Anal. Des., Volume 52 (2012), pp. 11-22

[41] T. Nestorović; D. Marinković; S. Shabadi; M. Trajkov User defined finite element for modeling and analysis of active piezoelectric shell structures, Meccanica, Volume 49 (2014) no. 8, pp. 1763-1774

[42] A. Frikha; S. Zghal; F. Dammak Finite rotation three and four nodes shell elements for functionally graded carbon nanotubes-reinforced thin composite shells analysis, Comput. Methods Appl. Mech. Eng., Volume 329 (2018), pp. 289-311

[43] G. Bao; L. Wang Multiple cracking in functionally graded ceramic/metal coatings, Int. J. Solids Struct., Volume 32 (1995), pp. 2853-2871

[44] Y.S. Touloukian; R.K. Kirby; E.R. Taylor; T.Y.R. Lee Thermophysical Properties of Matter, Vol. 13. Thermal Expansion-Nonmetallic Solids, TPRC Data Series, Thermophysical and Electronic Properties Information Analysis Center, Lafayette, LA, USA, 1977

[45] X.Q. He; T.Y. Ng; S. Sivashanker; K.M. Liew Active control of FGM plates with integrated piezoelectric sensors and actuators, Int. J. Solids Struct., Volume 38 (2001) no. 9, pp. 1641-1655

[46] E.F. Crawley; K.B. Lazarus Induced strain actuation of isotropic and anisotropic plates, AIAA J., Volume 29 (1991) no. 6, pp. 944-951

Cité par Sources :

Commentaires - Politique