An Inhomogeneous Cell‐Based Smoothed Finite Element Method for Free Vibration Calculation of Functionally Graded Magnetoelectroelastic Structures

Abstract

To overcome the overstiffness and imprecise magnetoelectroelastic coupling effects of finite element method (FEM), we present an inhomogeneous cell-based smoothed FEM (ICS-FEM) of functionally graded magnetoelectroelastic (FGMEE) structures. Then the ICS-FEM formulations for free vibration calculation of FGMEE structures were deduced. In FGMEE structures, the true parameters at the Gaussian integration point were adopted directly to replace the homogenization in an element. The ICS-FEM provides a continuous system with a close-to-exact stiffness, which could be automatically and more easily generated for complicated domains, thus significantly decreasing the numerical error. To verify the accuracy and trustworthiness of ICS-FEM, we investigated several numerical examples and found that ICS-FEM simulated more accurately than the standard FEM. Also the effects of various equivalent stiffness matrices and the gradient function on the inherent frequency of FGMEE beams were studied.

Free vibration analysis of functionally graded magneto-electro-elastic plates with in-plane material heterogeneity

“…Depended on the FEM, Xie et al (2016) conducted the sensitivity analysis of the dynamic behaviors for functionally graded magneto-electro-elastic square plates with clamped boundary condition. Cai et al (2018) and Zhou et al (2019) utilized the inhomogeneous cell-based smoothed FEM to examine the free vibration and non-linear transient behaviors of functionally graded smart magneto-electro-elastic beams under various boundary constraints. Meanwhile, a series of numerical methodologies including the asymptotic approach associated with the multiple scales method (Tsai and Wu, 2008; Wu and Tsai, 2010), Legendre orthogonal polynomial series expansion method (Wu et al, 2008; Yu and Ma, 2010), the propagator matrix incorporated with the successive approximation approach (Wu and Lu, 2009), the power series approach (Cao et al, 2012), Chebyshev spectral element approach (Xiao et al, 2016), and the polynomial expansions (Zhang et al, 2018) are also employed to investigate the dynamic responses of functionally graded magneto-electro-elastic plates.…”