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

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 strain0 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. Finite element analysis of smart structures has attracted much attention in recent years due to its wide range of applications. A significant amount of research has gone into the analysis of piezo composite structures. A number of finite element (FE) models have been proposed for the analysis of smart structures; and a detailed survey is given in [Benjeddou 2000]. One of the main problems addressed is the buckling analysis of smart structures. Three-dimensional beam models can be simulated using two-dimensional in-plane elements by considering only the longitudinal cross-section of the three-dimensional beam model. The boundary conditions and the loading conditions can be simulated more accurately in this two-dimensional model than in the one-dimensional beam element model. Still, the two-dimensional analysis of the beam is based on either the plane stress or plane strain assumption, and cases outside these assumptions cannot be handled by two-dimensional in-plane elements. The generalized plane strain formulation can be used to model cases other than plane stress and plane strain at the cost of additional degrees of freedom. The generalized plane strain formulation has been discussed extensively in the literature and has been used for several applications. Most composite problems are generalized plane strain in nature, and they