A cell-based smoothed discrete shear gap method (CS-DSG3) using triangular elements for static and free vibration analyses of shell structures

Abstract

Keywords:Reissner-Mindlin shell Shear locking Cell-based smoothed discrete shear gap technique (CS-DSG3) Smoothed finite element method Strain smoothing technique a b s t r a c t A cell-based smoothed discrete shear gap method (CS-DSG3) for static and free vibration analyses of Reissner-Mindlin shells is formulated by combining the cell-based strain smoothing technique with the discrete shear gap method (DSG3) using three-node triangular elements. In the CS-DSG3, each triangular element will be divided into three sub-triangles, and in each sub-triangle, the stabilized DSG3 is used to compute the strains and to avoid the transverse shear locking. Then the strain smoothing technique on whole of the triangular element is used to smooth the strains on these three sub-triangles. The CS-DSG3 hence not only overcomes the drawback of the DSG3 but also improves the accuracy as well as the stability of the DSG3. The numerical examples demonstrated that the CS-DSG3 is free of shear locking and achieves the high accuracy compared to other existing shell elements.

Efficient Co-Rotational 3-Node Shell Element

“…Firstly, an overview of the DSG3 formulation (Bletzinger et al, 2000) is given, followed by the further development (Nguyen- Thoi et al, 2013) which leads to the CS-DSG3 element formulation.…”

“…Then is the rotational degree of freedom totally free to spin and corresponding stiffness has a zero stiffness. In order to avoid this rotational singularity in the stiffness matrix the zero values corresponding to drilling degree of freedom r zi are replaced by an approximated value of 10 -3 times of maximal diagonal value in the element stiffness matrix (Nguyen- Thoi et al, 2013):…”

“…Afterwards, in order to smooth the strains in the sub-triangles, strain smoothing technique on the whole triangular element is applied. As a result the CS-DSG3 overcomes the drawback of the DSG3 element which depends on the sequence of node numbering and improves the accuracy and stability of the DSG3 element (Nguyen- Thoi et al, 2013).…”

“…In its nature, this requirement is contrary to the requirements for high accuracy and reliability, so the short overview of available elements should focus only to high quality elements that offer a good compromise and therewith a conciliation of the requirements. The low-order shell elements that particularly stand out among numerous candidates are the "Discrete Kirchhoff Theory-Constant Strain Triangular element" (DKT-CST) and the Cell Smoothed Discrete Shear Gap triangular shell element (CS-DSG3) (Nguyen- Thoi et al, 2013). The DKT-CST shell element represents a superposition of the CST membrane element and the DKT plate element.…”

Piezoelectric Co-Rotational 3-Node Shell Element

“…In the CS-DSG3 formulation, the element domain is divided into three DSG3 (Nguyen- Thoi et al, 2013) sub-triangle elements by connecting the triangle central point with the element nodes. The DSG formulation is applied in each of the sub-triangles.…”