A parametrized variational principle of nonlinear piezoelectricity

  • Ji-Huan He Donghua University

Abstract

The variational theory is the theoretical basis of the finite element method, meshfree particle methods and other modern numerical techniques. The present paper establishes a family of variational principles for nonlinear piezoelectricity. A new constitutive relation is suggested, which is deduced as a stationary condition of a generalized variational principle.

Keywords

variational theory, piezoelectricity, constitutive equations.,

References

[1] F. Ashida, T.R. Tauchert. An inverse problem for determination of transient surface temperature from piezoelectric sensor measurement. ASME J. App. Mech., 65: 367- 373, 1998.
[2] D.S . Chandrasekharaiah. A generalized linear thermo-elasticity theory for piezoelectric media. ACTA Mechanica, 71: 39-49, 1998.
[3] T.Y. Chen. Further correspondences between plane piezoelectricity and generalized plane strain in elasticity. Proc. R . Soc. Lond., A454: 873- 884, 1971 .
[4] W.Z. Chien. Method of high-order Lagrange multiplier and generalized variational principles of elasticity with more general forms of functionals. Applied Math. & Mech., 4(2): 137-150, 1983.
[5] S.I. Chizhikov, N.G. Sorokin and V.S. Petrakov. The elastoelectric effect in the non-centrosymmetric crystals. In: Piezoelectricity, eds. G. W. Taylor et al., Gordon & Breach Science Publishers, New York, 75- 91 , 1985.
Published
Jan 27, 2023
How to Cite
HE, Ji-Huan. A parametrized variational principle of nonlinear piezoelectricity. Computer Assisted Methods in Engineering and Science, [S.l.], v. 10, n. 3, p. 263-269, jan. 2023. ISSN 2956-5839. Available at: <https://cames.ippt.pan.pl/index.php/cames/article/view/1074>. Date accessed: 17 may 2024.
Section
Articles