Proceedings ArticleDOI
Hybrid finite element formulation for electrostrictive materials: static and buckling analysis of beam
TLDR
In this article, a nonlinear electromechanical coupled static finite element formulation for electrostrictive materials is proposed, which includes the quadratic dependence of strain with polarization, valid at a constant temperature and excludes hypersteresis.Abstract:
A nonlinear electromechanical coupled static finite element formulation for electrostrictive materials is proposed. This
formulation includes the quadratic dependence of strain with polarization, valid at a constant temperature and excludes
hysteresis. The present formulation uses linear finite element analysis for stress and strain evaluation along with the
numerical solution of the nonlinear constitutive equation using Newton - Raphson technique only within each
electrostrictive elements and hence this formulation is named as hybrid finite element formulation. Polarization is an
explicit independent variable in this formulation and the nonlinear equations at each electrostrictive elements are solved
for this variable. Since the nonlinear constitutive equation is a function of polarization and tends to infinity for certain
values of polarization, the Newton - Raphson technique is specially modified in order to guarantee the convergence of
the solution. A simple technique for obtaining the initial guess of the solution for Newton - Raphson technique is also
proposed which gives faster convergence of the solution. Since the polarization is an explicit independent variable in the
present formulation, the assumption, made in most of the finite element formulations [15, 16, 17, 18], that polarization is
approximately equal to electric displacement has been relaxed. The developed static finite element formulation has been
extended to solve buckling problems of electrostrictive beams. Analytical solutions have been developed for static and
buckling analysis of electrostrictive beams. The developed finite element formulation results are compared with that of
the analytical solution results and it has been found that the results are in very good agreement. The proposed finite
element formulation is computationally very efficient than any other available nonlinear finite element formulation for
electrostrictive materials. The proposed finite element formulation proves its very high computational efficiency
especially in case of buckling analyses as well as in case of electrostrictive patches embedded in large structures.read more
References
More filters
Book
Concepts and Applications of Finite Element Analysis
TL;DR: In this article, the authors present a formal notation for one-dimensional elements in structural dynamics and vibrational properties of a structural system, including the following: 1. Isoparametric Elements.
Book
An introduction to continuum mechanics
Morton E. Gurtin,W. J. Drugan +1 more
TL;DR: In this paper, the NavierStokes Equations are used to define linear elasticity for tensor analysis, and the invariance of material response is established. But the analysis is restricted to finite elasticity and cannot be extended to infinite elasticity.
Journal ArticleDOI
Finite element method for piezoelectric vibration
Henno Allik,Thomas J. R. Hughes +1 more
TL;DR: In this paper, a finite element formulation which includes the piezoelectric or electroelastic effect is given, a strong analogy is exhibited between electric and elastic variables, and a stiffness finite element method is deduced.
Journal ArticleDOI
Distributed piezoelectric sensor/actuator design for dynamic measurement/control of distributed parameter systems: A piezoelectric finite element approach
Horn-Sen Tzou,C.I. Tseng +1 more
TL;DR: In this paper, a new structure (shell or plate) containing an integrated distributed piezoelectric sensor and actuator is proposed, where the distributed sensing layer monitors the structural oscillation due to the direct PDE and the distributed actuator layer suppresses the oscillation via the converse PDE.