Analysis of shell structures by an improved 3-node triangular flat shell element with a bubble function and cell-based strain smoothing

Abstract

An enhanced 3-node triangular flat shell element with 18 degrees of freedom according to the Reissner–Mindlin theory is presented in this paper. New cell-based smoothed (CS) bending strains were derived from the displacement approximations enriched by a cubic shape function for the rotations at the bubble node located at the centroid of the triangular element. The true drilling degrees of freedom of the proposed element, which is independent from user-defined coefficients, was achieved by cell-based smoothing the Allman’s membrane strains. The membrane and bending stiffness matrices were then efficiently determined by the line integration of the smoothing domains’ boundaries. The shear-locking removal MITC3+ technique was employed to interpolate the transverse shear strains. The outstanding performance of the developed 3-node triangular flat shell element, so-called the CS-MITC18+ shell element, was demonstrated through the static and free vibration analyses of several benchmark shell structures. Numerical results shown that the CS-MITC18+ flat shell element has the spatially isotropic and zero-energy mode properties, and provides competitive accuracy, convergence, and computational cost in comparison to other conventional and strain-smoothed 3-node triangular flat shell elements.