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TRANSIENT FINITE ELEMENT ANALYSIS OF
NON-LINEAR PIEZOELECTRIC MATERIAL
Primary Researchers:
Robert
L. Mullen
Department of
Civil Engineering
Case Western Reserve University,
Cleveland,
OH 44106, USA
E-mail: rlm@po.cwru.edu,
Tel. (216) 368-2423
Uday Kumar Dikshit
Department of Mechanical and Aerospace Engineering
Case Western Reserve University,
Cleveland,
OH 44106, USA
E-mail: rlm@po.cwru.edu,
Tel. (216) 368-2423
Abstract: Piezoelectric materials produce electric
charge when mechanically deformed. Conversely, an electric potential causes
a mechanical deformation. This property makes piezoelectric materials suitable
for sensor, actuator and transducer applications. The understanding of
the electroelastic behavior of piezoelectric materials is critical to predicting
the response of a structure with embedded piezoelectric material.
A transient analysis, using
the finite element method, is developed to study the equations of piezoelectricity,
including the plasticity effects. The analysis involves the development
of an elastic-plastic constitutive law for piezoelasticity. An implicit-explicit
scheme is constituted to solve the equations so as to exploit the highlights
of both the methods. An implicit scheme is numerically stable
and is required for the electric field steps while an explicit scheme is
inexpensive per time step, especially for non-linear problems, and requires
no stiffness matrix calculations resulting in an economy of the combined
scheme.
A program for the new implicit-explicit
scheme was written using rectangular, quadratic, Lagrangian
elements to determine the stress, displacement and potential fields for
two dimensional domains for comparison with analytic predictions. Two dimensional
linear and non-linear results are calculated for a simple actuator design.
CWRU Department of Civil Engineering
Communication
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