A new accurate smoothed finite element formulation for dynamic explicit analyses of nearly incompressible solids using 10-node tetrahedral elements is proposed. Smoothed finite element method (S-FEM) is one of the next-generation FEMs; especially, the edge-based S-FEM using four-node tetrahedra (ES-FEM-T4) is an excellent FE formulation that avoids shear locking and has a superlinear mesh convergence rate as 2nd-order elements. However, ES-FEM-T4 is known to cause volumetric locking and pressure checkerboarding issues in nearly incompressible cases. ES-FEM-T4 also has a backward compatibility issue in its implementation to
existing standard FE codes due to the strain smoothing across multiple elements.

The author proposed a new concept of cell-based S-FEM using ten-node tetrahedra with selective reduced integration (SelectiveCS-FEM-T10) and overcame the above issues of ES-FEM-T4. Adopting selective reduced integration (SRI) technique, SelectiveCS-FEM-T10 does not suffer from volumetric locking and pressure checkerboarding. In contrast to ES-FEM, SelectiveCS-FEM-T10 can be implemented to existing standard FE codes because it only performs intra-element strain smoothing in the manner of CS-FEMs. Besides, the author recently proposed an optimal formulation of SelectiveCS-FEM-T10 that subdivides each T10 element
radially so that the accuracy and robustness was improved. The performance of the new SelectiveCS-FEM-T10 in static analysis has already been evaluated but not yet in dynamic analysis.

The new SelectiveCS-FEM-T10 is a pure displacement-based FEM, which does not require additional DOF such as pressure; thus, it has the advantage of applicability to dynamic explicit analysis, in contrast to mixed (hybrid) elements. This study confirms that the new SelectiveCS-FEM-T10 has good accuracy and robustness in dynamic explicit analysis. It also confirms that the new SelectiveCS-FEM-T10 has no spurious low-energy modes in modal analysis to guarantee the energetic stability in dynamic analysis.