×

A geometrically nonlinear piezoelectric solid shell element based on a mixed multi-field variational formulation. (English) Zbl 1146.74052

Summary: This paper is concerned with a geometrically nonlinear solid shell element to analyse piezoelectric structures. The finite element formulation is based on a variational principle of Hu-Washizu type and includes six independent fields: displacements, electric potential, strains, electric field, mechanical stresses and dielectric displacements. The element has eight nodes with four nodal degrees of freedoms, three displacements and the electric potential. A bilinear distribution through the thickness of independent electric field is assumed to fulfill the electric charge conservation law in bending dominated situations exactly. The presented finite shell element is able to model arbitrary curved shell structures and incorporates a 3D material law. A geometrically nonlinear theory allows for large deformations and includes stability problems. Linear and nonlinear numerical examples demonstrate the ability of the proposed model to analyse piezoelectric devices.

MSC:

74S05 Finite element methods applied to problems in solid mechanics
74K25 Shells
74F15 Electromagnetic effects in solid mechanics
74G65 Energy minimization in equilibrium problems in solid mechanics
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Smart Materials and Structures with Control and Design Applications. CISM Courses and Lectures No. 429. Springer: Wien/New York, 2001; 1-26.
[2] Microsystem Design. Kluwer Academic Publishers: Boston/Dordrecht/London, 2001.
[3] Si, Journal of Magnetism and Magnetic Materials 270 pp 167– (2004)
[4] Pines, Smart Materials and Structures 7 pp 581– (1998)
[5] Allik, International Journal for Numerical Methods in Engineering 2 pp 151– (1970)
[6] Saravanos, Applied Mechanics Review 52 pp 305– (1999)
[7] Benjeddou, Computers and Structures 76 pp 347– (2000)
[8] . Locking-free piezoelectric MITC shell elements. In Computational Fluid and Solid Mechanics, (ed.). Elsevier Science: Oxford, 2003; 392-395.
[9] Bernadou, Computer Methods in Applied Mechanics and Engineering 192 pp 4003– (2003)
[10] Bernadou, Computer Methods in Applied Mechanics and Engineering 192 pp 4045– (2003)
[11] Bernadou, Computer Methods in Applied Mechanics and Engineering 192 pp 4075– (2003)
[12] Wang, International Journal for Numerical Methods in Engineering 53 pp 1477– (2002)
[13] Lammering, Smart Materials and Structures 12 pp 904– (2003)
[14] Lammering, Computers and Structures 41 pp 1101– (1991)
[15] Zheng, Smart Materials and Structures 13 pp n43– (2004)
[16] Sze, International Journal for Numerical Methods in Engineering 48 pp 545– (2000)
[17] Sze, International Journal for Numerical Methods in Engineering 48 pp 565– (2000)
[18] Sze, Journal of Sound and Vibration 253 pp 495– (2000)
[19] Tzou, AIAA Journal 1 pp 110– (1996)
[20] Tzou, Journal of Vibration and Acoustics 116 pp 489– (1994)
[21] Tzou, Journal of Vibration and Acoustics 119 pp 374– (1997)
[22] Tzou, Journal of Vibration and Acoustics 119 pp 382– (1997)
[23] Pai, International Journal of Solids and Structures 30 pp 1603– (1993)
[24] Zhou, International Journal of Solids and Structures 37 pp 1663– (2000)
[25] Tzou, Journal of Sound and Vibration 188 pp 189– (1995)
[26] Varelis, Smart Materials and Structures 11 pp 330– (2002)
[27] Yang, Smart Materials and Structures 8 pp 73– (1999)
[28] Gopinathan, Smart Materials and Structures 9 pp 24– (2000)
[29] Benjeddou, Thin-Walled Structures 40 pp 573– (2002)
[30] . Consistency analysis of electroelastic finite element models. Proceedings of the 2nd European Conference on Computational Mechanics, Cracow, 2001 (pages CD-Version).
[31] Sze, Journal of Sound and Vibration 226 pp 519– (1999)
[32] Zeng, International Journal for Numerical Methods in Engineering 56 pp 13– (2003)
[33] Dvorkin, Engineering Computations 1 pp 77– (1984)
[34] Betsch, Communications in Numerical Methods in Engineering 11 pp 899– (1995)
[35] Simo, International Journal for Numerical Methods in Engineering 29 pp 1595– (1990)
[36] Continuum mechanics of electromagnetic solids. In Applied Mathematics and Mechanics, , , , (eds), vol. 33. North-Holland Series: Amsterdam, 1988. · Zbl 0652.73002
[37] Nichtlineares piezoelektrisches Finite-Elemente-Verfahren zur Modellierung piezokeramis-cher Aktoren. Ph.D. Thesis, Universität Erlangen-Nürnberg, 2002.
[38] Klinkel, Computer Methods in Applied Mechanics and Engineering (2005)
[39] Loikkannen, International Journal for Numerical Methods in Engineering 20 pp 523– (1983)
[40] Feap–manual. http://www.ce.berkeley/rlt/feap/manual.pdf
[41] MacNeal, Finite Elements in Analysis and Design 1 pp 3– (1985)
[42] Development of a light-weight robot end-effector using polymeric piezoelectric bimorph. Conference on Robotics and Automation. IEEE: New York, 1989; 1704-1709.
[43] Yoon, Smart Materials and Structures 13 pp 459– (2004)
[44] Yoon, Smart Materials and Structures 11 pp 163– (2002)
[45] Goo, Smart Materials and Structures 9 pp 24– (2000)
[46] Hilber, Earthquake Engineering and Structural Dynamics 5 pp 283– (1977)
[47] Structural analysis of laminated anisotropic plates. Ph.D. Thesis. Technomic: Lancaster, PA, 1987.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.