Laminated smart shell structures; theory and analysis

摘要

Modeling of shells integrated with smart lamina and taking account of thermo-magneto-electro-elastic fields represents a challenge to be formulated and solved. In the present work, analytical model is proposed based on Hamilton's variational principle linked with Gibbs free energy functions. The model is casted according to the first-order shear deformation shell theory. The exact solution is derived for linearly constitutive properties, simply supported, shallow shell having rectangular plane-form under static loadings. The effects of the material properties, lay-ups of the constituent layers, and shell parameters on the free vibration behavior are investigated and analyzed. The accurate treatment of thermal, magnetic, electric, and elastic energies that are taken into account in this smart shell yields rather sophisticated equations for magnetic inductions, electric displacements and stress resultants. Therefore, the introduced model is expected to provide a foundation to investigate the interactive effects among the thermal, magnetic, electric, and elastic fields in smart shell structures.