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A new concept of applying smoothed finite element method (S-FEM) to
multi-physical coupling issues is presented. Among all SFEM members, CS-FEM was first proposed and CS-FEM is the closest to standard FEM. Specifically, the CS-FEM can be implemented on existing FEM codes, and has been implanted in the framework of the commercial software package ABAQUS. Magneto-electro-elastic (MEE) materials display high degree of magneto-electric coupling effects, and the distinctive advantage in converting energy among elastic, electric and magnetic fields has attracted attentions. The multi-physical coupling characteristic of MEE material is affected by the thermal environment. Current research on the MEE structure proprieties remains the use of deterministic finite element (FE) simulations. Hence, we proposed the multi-physical cell-based smoothed finite element method (MCS-FEM) to investigate the nonlinear vibration performance of MEE system under thermal circumstance. Numerical experiments explored the accuracy, convergence and efficiency of the MCS-FEM. The thermal impacts on the MEE systems were demonstrated by presenting the variation of generalized displacements. Combining the Newmark scheme with Rayleigh damping assumption, the damping effects on the MEE systems was discussed. The presented methods and simulation results will benefit researches in investigating the coupled multi-physical problem, and further contribute to the design of intelligence structures in service.

Cell-based smoothed finite element method, Magneto-electro-elastic material, Nonlinear vibration, Newmark scheme