×

Consistency and recovery in electroelasticity. II: Equilibrium and mixed finite elements. (English) Zbl 1096.74524

Summary: The first part of this paper [ibid. 192, No. 7-8, 831-850 (2003; Zbl 1025.74030)] establishes the concept of consistency for standard finite elements in electroelasticity. This has permitted to trace the origin of certain spurious oscillations affecting the finite element response in terms of stress and electric flux density. In this second part, the consistency analysis is generalized to models which directly involve stress and electric flux density as independent variables. The analysis shows that also these models can suffer from spurious outcomes. However, selecting the approximation functions on consistency basis allows to eliminate, or at least reduce, the undesired oscillations.

MSC:

74S05 Finite element methods applied to problems in solid mechanics
74F15 Electromagnetic effects in solid mechanics

Citations:

Zbl 1025.74030
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] de Miranda, S.; Ubertini, F., Consistency and recovery in electroelasticity. part I: standard finite elements, Comput. methods appl. mech. engrg., 192, 831-850, (2003) · Zbl 1025.74030
[2] Zhang, H.-L., On variational principles of a piezoelectric body, Acta acust., 10, 223-230, (1985), (in Chinese)
[3] Yang, J.S., Mixed variational principles for piezoelectric elasticity, (), II.1.31-II.1.38
[4] P. Bisegna, F. Maceri, Twenty-five functionals of linear piezoelectricity, Internal Report 51, Department of Civil Engineering, University of Rome “Tor Vergata”, Italy, 1998 (in Italian) · Zbl 1126.74392
[5] Sze, K.Y.; Pan, Y.S., Hybrid finite element models for piezoelectric materials, J. sound vib., 226, 519-547, (1999)
[6] Cannarozzi, A.A.; Ubertini, F., Some hybrid variational methods for linear electroelasticity problems, Int. J. solid struct., 38, 2573-2596, (2001) · Zbl 0977.74021
[7] Fraeijs de Veubeke, B.M., Displacement and equilibrium models in the finite element method, (), pp. 145-197 · Zbl 0359.73007
[8] Pian, T.H.H.; Tong, P., Finite element method in continuum mechanics, (), 1-58 · Zbl 0149.42802
[9] Brezzi, F.; Fortin, M., Mixed and hybrid finite element models, (1991), Springer-Verlag New York · Zbl 0788.73002
[10] Stolarski, H.; Belytschko, T., Limitation principles for mixed finite elements based on the hu – washizu variational formulation, Comput. methods appl. mech. engrg., 60, 195-216, (1987) · Zbl 0613.73017
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.