An 8-Node Solid-Shell Finite Element based on Assumed Bending ‎Strains and Cell-Based Smoothed Membrane Strains for Static Analysis of Plates and Shells

Abstract

In this paper, a new 8-node solid-shell finite element is proposed. The transverse shear strains and transverse normal strains of the element are separately interpolated and related to the C0-displacement approximation at tying points to overcome the shear- and trapezoidal-locking phenomena. From the bending strain approximation suggested for degenerated shell elements, the assumed bending strains for the solid-shell element are firstly established. The membrane strains of the element are smoothed on domains defined by dividing the middle surface's element into 1, 2, 3 or 4 sub-cells in accordance with the cell-based strain smoothing (CS) technique. The formulations of the membrane stiffness matrices are explicitly integrated on the boundary lines of the smoothing sub-cells. The proposed CSn-Q8 element, in which n is the number of smoothing sub-cells, is verified through static analysis of several benchmark plate and shell problems. Numerical results show the improved performance of the CSn-Q8 element in comparison with other references.