Hybrid Finite Element Formulation for Electrostrictive Materials: Dynamic Analysis of Beam

Abstract

A nonlinear electromechanical coupled dynamic finite element formulation for electrostrictive materials is proposed. This formulation includes the quadratic dependence of strain with polarization, valid at a constant temperature and excludes hysteresis. The present formulation uses linear finite element analysis along with the numerical solution of the nonlinear constitutive equation using Newton-Raphson technique only within each electrostrictive elements. Therefore this formulation is capable of handling nonlinearity only on the electrostrictive domain instead of making the whole finite element analysis as nonlinear. The Newton-Raphson technique is specially modified in order to guarantee the convergence of the solution. A simple technique for obtaining the initial guess of the solution for Newton-Raphson technique is also proposed which gives faster convergence of the solution. The assumption made in most of the finite element formulations, that polarization is approximately equal to electric displacement has been relaxed. The proposed finite element formulation is computationally very efficient than any other available nonlinear dynamic finite element formulation for electrostrictive materials and it proves its very high computational efficiency especially in case of electrostrictive patches embedded in large structures.

Keywords:

• Finite element method
• electrostriction
• Dynamic analysis
• electrostrictive beam