For Libraries For Publication Open Access Downloads About Us Contact Us
Paper Titles
Selected Aspects of Current Challenges in Composite Product Development for Automotive and Aerospace Industry
p.51
Fatigue Properties of Aerospace Z-Pinned Composites
p.67
Some Examples of “Multi-Physical” Fatigue of Organic Matrix Composites for Aircraft Applications
p.79
Post-Buckling Analysis of Damaged Multilayered Composite Stiffened Plates by Rayleigh-Ritz Method
p.99
A Promising Way to Model Damage in Composite and Dry Fabrics Using a Discrete Element Method (DEM)
p.119
A Thermal Stress Analysis of Three-Dimensional Beams by Refined One-Dimensional Models and Strong Form Solutions
p.139
High-Fidelity and Computationally Efficient Component-Wise Structural Models: An Overview of Applications and Perspectives
p.175
Reduced Order Models for Static and Dynamic Analysis of Composite Panels Based on a Perturbation Approach
p.199
Shell Finite Elements for the Analysis of Multifield Problems in Multilayered Composite Structures
p.215

Shell Finite Elements for the Analysis of Multifield Problems in Multilayered Composite Structures

Article Preview

Abstract:

This paper deals with the analysis of layered structures under thermal and electro-mechanical loads. Constitutive equations for multifield are considered and the Principle of Virtual Displacements (PVD) is employed to derive the governing equations. The MITC9 shell finite element based on the Carrera's Unified Formulation (CUF) has been applied for the analysis. The models grouped in the CUF have variable through-the-thickness kinematic and they provide an accurate distribution of displacements and stresses along the thickness of the laminate. The shell element has nine nodes and the Mixed Interpolation of Tensorial Components (MITC) method is used to contrast the membrane and shear locking phenomenon. The finite element analysis of multilayered plates and shells has been addressed. Variable kinematics, as well as layer-wise and equivalent single layer descriptions, have been considered for the presented FEs, according to CUF. A few problems are analyzed to show the effectiveness of the proposed approach. Various laminations, thickness ratios and curvature ratios are considered. The results, obtained with different theories contained in the CUF, are compared with both the elasticity solutions given in literature and the analytical solutions obtained using the CUF and the Navier's method.

You might also be interested in these eBooks
Composite Materials and Structures in Aerospace Engineering View Preview

Info:

Periodical:

Applied Mechanics and Materials (Volume 828)

Pages:

215-236

DOI:

https://doi.org/10.4028/www.scientific.net/AMM.828.215

Citation:

Cite this paper

Online since:

March 2016

Authors:

Maria Cinefra, Erasmo Carrera

Keywords:

Composite, Multifield Problems, Multilayered Structure, Shell Finite Elements, Unified Formulation, Variational Statements

Export:

RIS, BibTeX

Price:

Permissions CCC:

Request Permissions

Permissions PLS:

Request Permissions

Сopyright:

© 2016 Trans Tech Publications Ltd. All Rights Reserved

Share:

Citation:

References

[1] T. Ikeda, Fundamentals of piezoelectriticy, Oxford: University Press, (1996).

Google Scholar

[2] E. Carrera, Historical Review of Zig-Zag Theories for Multilayered Plates and Shells, Applied Mechanics Review. 56 (2003) 287-308.

DOI: 10.1115/1.1557614

Google Scholar

[3] E. Carrera, S. Brischetto, Piezoelectric Shell Theories with a priori continuous transverse electromechanical variables, Journal of Mechanics of Materials and Structures. 2(2) (2007) 377-399.

DOI: 10.2140/jomms.2007.2.377

Google Scholar

[4] E. Carrera, C. Fagiano, Mixed piezoelectric plate elements with continuous transverse electric displacements, Journal of Mechanics of Materials and Structures. 2(3) (2007) 421-438.

DOI: 10.2140/jomms.2007.2.421

Google Scholar

[5] R.D. Mindlin, Forced tickness-shear and flexural vibrations of piezoelectric crystal plates, Journal of Applied Physics. 22(1) (1952) 83-88.

DOI: 10.1063/1.1701983

Google Scholar

[6] H.F. Tiersten, R.D. Mindlin, Forced vibrations of piezoelectric crystal plates, Quarterly of Applied Mathematics. 20(2) (1962) 107-119.

DOI: 10.1090/qam/99964

Google Scholar

[7] E.P. EerNisse, Variational method for electroelastic vibration analysis, IEEE Trans. Ultrasonic. SU. 14(4) (1967) 153-160.

DOI: 10.1109/t-su.1967.29431

Google Scholar

[8] H.F. Tiersten, Linear piezoelectric plate vibrations, New York: Plenum, (1969).

Google Scholar

[9] H. Allik, T.J.R. Hughes, Finite element method for piezoelectric vibration, International Journal for Numerical Methods in Engineering. 14(4) (1970) 153-160.

Google Scholar

[10] R.D. Mindlin, Equation of high frequency vibration of thermopiezoelectric crystal plates, International Journal of Solids and Structures. 10 (1974) 625-637.

DOI: 10.1016/0020-7683(74)90047-x

Google Scholar

[11] M.C. Dokmeci, Theory of vibration of coated, thermopiezoelectric laminae, Journal of Mathematical Physics. 19(1) (1978) 109-126.

Google Scholar

[12] M. Cinefra, S. Valvano, E. Carrera, Heat conduction and Thermal Stress Analysis of laminated composites by a variable kinematic MITC9 shell element, Curved and Layered Structures. 2 (2015) 301-320.

DOI: 10.1515/cls-2015-0017

Google Scholar

[13] M. Cinefra, E. Carrera, S. Valvano, Variable kinematic shell elements for the analysis of electromechanical problems, SMART 2013 - Modelling and Analysis of Smart Structures, special issue of Mechanics of Advanced Materials and Structures. 22 (2015).

DOI: 10.1080/15376494.2014.908042

Google Scholar

[14] M. Cinefra, S. Valvano, E. Carrera, A Layer-Wise MITC9 Finite Element for the Free-Vibration Analysis of Plates with Piezo-Patches, International Journal of Smart and Nano Materials. 6(2) (2015) 85-104.

DOI: 10.1080/19475411.2015.1037377

Google Scholar

[15] E. Carrera, P. Nali, Multilayered plate elements for the analysis of multifield problems, Finite Elements in Analysis and Design. 46 (2010) 732-742.

DOI: 10.1016/j.finel.2010.04.001

Google Scholar

[16] A. Robaldo, E. Carrera, A. Benjeddou, A Unified Formulation for finite element analysis of piezoelectric plates, Computers & Structures. 84 (2006) 1494-1505.

DOI: 10.1016/j.compstruc.2006.01.029

Google Scholar

[17] E. Carrera, A. Robaldo, Hierarchic finite elements based on the Carrera Unified Formulation for the static analysis of shear actuated multilayered piezoelectric plates, Multidiscipline Modeling in Materials and Structures. 6 (2010) 45-77.

DOI: 10.1108/15736101011055266

Google Scholar

[18] E. Carrera, M. Boscolo, A. Robaldo, Hierarchic multilayered plate elements for coupled multifield problems of piezoelectric adaptive structures: Formulation and numerical assessment, Archives of Computational Methods in Engineering. 14 (2007).

DOI: 10.1007/s11831-007-9012-8

Google Scholar

[19] E. Carrera, P. Nali, Classical and mixed finite elements for the analysis of multifield problems and smart layered plates, Acta Mechanica Solida Sinica. 23 (2010) 115-121.

Google Scholar

[20] E. Carrera, M. Boscolo, Classical and mixed finite elements for static and dynamic analysis of piezoelectric plates, International Journal for Numerical Methods in Engineering. 70 (2007) 1135-1181.

DOI: 10.1002/nme.1901

Google Scholar

[21] E. Carrera, A. Buttner, P. Nali, Mixed Elements for the Analysis of Anisotropic Multilayered Piezoelectric Plates, Journal of Intelligent Material Systems and Structures. 21 (2010) 701-717.

DOI: 10.1177/1045389x10364864

Google Scholar

[22] E. Carrera, P. Nali, Mixed piezoelectric plate elements with direct evaluation of transverse electric displacement, International Journal for Numerical Methods in Engineering. 80(4) (2009) 403- 424.

DOI: 10.1002/nme.2641

Google Scholar

[23] A. Robaldo, E. Carrera, A. Benjeddou, Unified formulation for finite element thermoleastic analysis of multilayered anisotropic composite plates, Journal of Thermal Stresses. 28 (2005) 1031- 1064.

DOI: 10.1080/01495730590964963

Google Scholar

[24] P. Nali, E. Carrera, A. Calvi, Advanced fully coupled thermo-mechanical plate elements for multilayered structures subjected to mechanical and thermal loading, International Journal for Numerical Methods in Engineering. 85 (2011) 896-919.

DOI: 10.1002/nme.3006

Google Scholar

[25] E. Carrera, A. Robaldo, Mixed finite elements for thermoelastic analysis of multilayered anisotropic plates, Journal of Thermal Stresses. 30 (2007) 165-194.

DOI: 10.1080/01495730600897385

Google Scholar

[26] E. Carrera, M. Digifico, P. Nali, S. Brischetto, Refined multilayered plate elements for coupled magneto-electro-elastic analysis, Multidiscipline Modeling in Materials and Structures. 5 (2009) 119-138.

DOI: 10.1163/157361109787959859

Google Scholar

[27] E. Carrera, S. Brischetto, C. Fagiano, P. Nali, Mixed multilayered plate elements for coupled magneto-electro-elastic problems, Multidiscipline Modeling in Materials and Structures. 5 (2009) 251-256.

DOI: 10.1163/157361109789017050

Google Scholar

[28] K.J. Bathe, P.S. Lee, J.F. Hiller, Towards improving the MITC9 shell element, Computers and Structures. 81 (2003) 477-489.

DOI: 10.1016/s0045-7949(02)00483-2

Google Scholar

[29] C. Chinosi, L. Della Croce, Mixed-interpolated elements for thin shell, Communications in Numerical Methods in Engineering. 14 (1998) 1155-1170.

DOI: 10.1002/(sici)1099-0887(199812)14:12<1155::aid-cnm216>3.0.co;2-9

Google Scholar

[30] N.C. Huang, Membrane locking and assumed strain shell elements, Compunters and Structures. 27(5) (1987) 671-677.

DOI: 10.1016/0045-7949(87)90083-6

Google Scholar

[31] E. Carrera, A class of two-dimensional theories for anisotropic multilayered plates analysis, Accademia delle Scienze di Torino, Memorie Scienze Fisiche. 19-20 (1995) 1-39.

DOI: 10.5962/bhl.title.27479

Google Scholar

[32] E. Carrera, C0 z requirements - models for the two dimensional analysis of multilayered structures, Composite Structures. 37(3-4) (1997) 373-383.

DOI: 10.1016/s0263-8223(98)80005-6

Google Scholar

[33] P.M. Naghdi, The theory of shells and plates, Handbuch der Physic. 4 (1972) 425-640.

Google Scholar

[34] W.T. Koiter, On the foundations of the linear theory of thin elastic shell, Proc. Kon. Nederl. Akad. Wetensch. 73 (1970) 169-195.

Google Scholar

[35] H. Murakami, Laminated composite plate theory with improved in-plane responses, Journal of Applied Mechanics. 53 (1986) 661-666.

DOI: 10.1115/1.3171828

Google Scholar

[36] N.N. Rogacheva, The theory of piezoelectric Shells and Plates, Boca Raton, Florida (USA): CRC Press, (1994).

Google Scholar

[37] D. Chapelle, K.J. Bathe, The finite element analysis of shells. -Fundamentals, Berlin: Springer, (2003).

Google Scholar

[38] K. -J. Bathe, E. Dvorkin, A formulation of general shell elements - the use of mixed interpolation of tensorial components, International Journal for Numerical Methods in Engineering. 22 (1986) 697-722.

DOI: 10.1002/nme.1620220312

Google Scholar

[39] M.L. Bucalem, K. -J. Bathe, Higher-order MITC general shell elements, International Journal for Numerical Methods in Engineering. 36 (1993) 3729-3754.

DOI: 10.1002/nme.1620362109

Google Scholar

[40] M. Cinefra, E. Carrera, Shell finite elements with different through-the-thickness kinematics for the linear analysis of cylindrical multilayered structures, International Journal for Numerical Methods in Engineering. 93 (2013) 160-182.

DOI: 10.1002/nme.4377

Google Scholar

[41] J.N. Reddy, Mechanics of Laminated Composite Plates and Shells, Theory and Analysis CRC Press, (1997).

Google Scholar

[42] V. Tungikar, B.K.M. Rao, Three dimensional exact solution of thermal stresses in rectangular composite laminates, Composite Structures. 27(4) (1994) 419-430.

DOI: 10.1016/0263-8223(94)90268-2

Google Scholar

[43] S. Brischetto, E. Carrera, Heat conduction and thermal analysis in multilayered plates and shells, Mechanics Research Communications. 38 (2011) 449-455.

DOI: 10.1016/j.mechrescom.2011.05.016

Google Scholar

[44] A.N.S. Institute, Ieee standard on piezoelectricity, Technical Report NASA CR 4665, IEEE, March (1987).

Google Scholar

[45] D. Ballhause, M. D'Ottavio, B. Kroplin, E. Carrera, A unified formulation to assess multilayered theories for piezoelectric plates, Computer & Structures. 83 (2005) 1217-1235.

DOI: 10.1016/j.compstruc.2004.09.015

Google Scholar

[46] E. Carrera, S. Brischetto, P. Nali, Plates and Shells for Smart Structures Classical and Advanced Theories for Modeling and Analysis, New Delhi: Wiley, (2011).

DOI: 10.1002/9781119950004

Google Scholar

[47] M. Cinefra, S. Valvano, Temperature profile influence on layered plates response considering classical and advanced theories, Mechanics of Advanced Materials and Structures, in press, doi: 10. 1080/15376494. 2015. 1070304.

Google Scholar

[48] K. Bhaskar, T.K. Varadan, J.S.M. Ali, Thermoelastic solutions for orthotropic and anisotropic composite laminates, Composites: Part B. 27(B) (1996) 415-420.

DOI: 10.1016/1359-8368(96)00005-4

Google Scholar

[49] E. Carrera, , AIAA Journal, 40(9) (2002) 1885-1896.

Google Scholar

© 2025 Trans Tech Publications Ltd. All rights are reserved, including those for text and data mining, AI training, and similar technologies. For open access content, terms of the Creative Commons licensing CC-BY are applied.
Scientific.Net is a registered trademark of Trans Tech Publications Ltd.