An Iterative Finite Element Procedure for the Analysis of Piezoelectric Continua

Abstract

In this paper an iterative finite element procedure is presented for the analysis of twoand three-dimensional piezoelectric continua. The procedure is applied to the steady-state analysis of two-dimensional media subjected to mechanical and electrical loading.

Computational modeling of rate-dependent domain switching in piezoelectric materials

“…For the computation of the initial unit-cell orientation m, which also determines the initial polarization vector P s as well as the initial spontaneous strains ε s , commonly applied Eulerian angles (Φ, Θ, Ψ ) are adopted; see for instance the monograph by Goldstein et al (2002) for detailed background information. To be specific, Φ, Ψ ∈ [0, 2π) and sin(Θ − π 2 ) ∈ [−1, 1] are generated by random.…”

“…Fundamentals for the problem at hand have been addressed by Allik and Hughes (1970), wherein use of variational principles has been made. Subsequently, (nonlinear) finite element formulations have been investigated in different contexts; see for instance the coupled formulations in Gaudenzi and Bathe (1995) and Schröder and Gross (2004) or, for an overview, the monograph by Silvester and Ferrari (1996). In general, finite element techniques can be used to simulate both micro-and macromechanically motivated models, see for instance McMeeking (1998a, 1998b) or Kamlah and Böhle (2001).…”

Nonlinear dynamic response of piezolaminated smart beams

“…A formulation on laminated composite plates with integrated sensors and actuators including large deformations was presented by Reddy [7]. An iterative finite element procedure for the analysis of piezoelectric continua including electromechanical coupling is also solved by Gaudenzi and Bathe [8]. Icardi and Sciuva [9] presented large deflection and stress analysis of multilayered plates with induced strain actuators.…”

Characterization of Properties and Damage in Piezoelectrics

“…In Gaudenzi & Bathe (1995) an iterative (stagger) formulation was proposed, which iteratively solves the mechanical and the electric problems. On the other hand, elastic, coupling and dielectric properties have different orders of magnitude, making extremely ill-conditioned to the stiffness matrix.…”