#### Vol. 3, No. 9, 2008

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Generalized plane strain finite-element formulation for thermal and electrical buckling analysis of piezo composite beam

### R. Jerome and N. Ganesan

Vol. 3 (2008), No. 9, 1625–1640
##### Abstract

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 ${\epsilon }_{0}$ 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 $\alpha$, the parameter controlling the out-of-plane strains.

##### Keywords
generalized plane strain, finite element, piezo composite, beam, electrical buckling, thermal buckling