New generalized plane strain FE formulation for the buckling analysis of piezocomposite beam

In this paper, a novel, simple, yet useful, generalized plane strain finite element formulation for the analysis of piezocomposite beam has been presented. This finite element formulation is a 2D formulation with improved accuracy in predicting the buckling behavior of the piezocomposite beam when compared to the conventional 2D piezofinite element formulation. Though the present formulation has the same computational cost as of a conventional 2D piezofinite element formulation, the buckling results predicted by this formulation are close to 3D piezofinite element formulation. This generalized plane strain formulation is similar to the plane strain formulation that reduces a 3D stress–strain relation to 2D stress–strain relation and does not include out of plane degrees of freedom, which is included in most of the formulations available for generalized plane strain. In the present formulation, the reduced 2D stress–strain relationship incorporates the effect of allowed/applied strain ε0 in the third direction (the direction that is not included in the 2D FE model). This paper reveals an important concept that the variation of buckling results predicted by plane stress, plane strain and 3D piezofinite element formulations for a piezocomposite beam varies very significantly in contrast to the elastic finite element formulation (or closed circuit condition of a piezofinite element formulation) where there are no such significant variations.