A superconvergent alpha finite element method (SαFEM) for static and free vibration analysis of shell structures

Abstract

A superconvergent alpha finite element method (SαFEM) based on triangular mesh is presented for static and free vibration analysis of shell structures. In the SαFEM model, a linear strain field is re-constructed from the standard FEM piecewise constant strain field by devising a unique procedure with a tunable parameter α. The discretized system equations are then established based on the re-constructed strain field and the Hellinger-Reissner variational principle. By changing the value of the parameter α, our SαFEM can provide a proper softer stiffness leading to a “nearly exact” solution in strain energy norm. To avoid the transverse shear locking (caused by the Hellinger-Reissner theory), the discrete shear gap technique for triangular element (DSG3) is employed. From several typical numerical examples, it is demonstrated that the proposed Sα-FEM-DSG3 (or Sα-DSG3) possesses supercovergence property and can provide very accurate solutions for shell structures.