A superconvergent finite element for composite beams with embedded magnetostrictive patches

Abstract

A superconvergent finite element formulation for a composite beam with embedded magnetostrictive patches is presented in this paper. The element uses linear properties of magnetostrictive materials, which can act both as sensors and actuators. A refined 2-node beam element is derived based on the Euler–Bernoulli and First Order Shear Deformation Theory for axial–flexural-shear coupled deformation in asymmetrically stacked laminated composite beams with magnetostrictive patches. The element has an interpolating function, which is derived by solving the static part of the governing equations of motion exactly, where a general ply-stacking is considered. Thus, the element has superconvergent properties for static problems. The formulated consistent mass matrix, however, is approximate. Since the stiffness matrix is exact for static analysis, the formulated element predicts natural frequency to greater level of accuracy with smaller discretization compared to any other conventional finite elements. Numerical experiments are performed for static and natural frequency calculation and the superconvergent property of the formulated element is shown by comparing the solution with the standard 1-D FE beam element and 2-D FEM.