We develop a generalized plane strain (GPS) finite element formulation to predict
the critical buckling voltage and temperature of a piezo composite beam in
more generality than the cases characterized by plane strain and plane stress
assumptions.
This generalized plane strain formulation represents the two-dimensional
finite element model as closely as possible to the three-dimensional finite
element model. It is similar to the plane strain formulation that reduces a
three-dimensional stress-strain relation to a two-dimensional one, but in contrast
with most GPS formulations in the literature, it does not include out of
plane degrees of freedom. In our formulation the reduced two-dimensional
stress-strain relation incorporates the effect of allowed/applied strain
in the
dimension not included in the two-dimensional model. Further, since the goal is to
deal with thermal and electrical buckling analysis, an initial strain vector is
incorporated in the formulation.
A finite element solver based on an eight-node quadrilateral element
was developed under the new formulation, and its results show good
agreement with those reported by Varelis and Saravanos (2004) and those
obtained with ANSYS. The critical electrical and thermal buckling loads for
examples other than those characterized by plane stress and plane strain
were analyzed, and it was found that they are significantly influenced by
, the
parameter controlling the out-of-plane strains.