An Improved Quadrilateral Flat Element with Drilling Degrees of Freedom for Shell Structural Analysis
H. Nguyen-Van1, N. Mai-Duy1and T. Tran-Cong; 

Source CMES: Computer Modeling in Engineering & Sciences, Vol. 49, No. 2, pp. 81-112, 2009
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Keywords flat shell, strain smoothing method, shear-locking free, first-order shear deformation theory, drilling degrees of freedom.
Abstract This paper reports the development of a simple and efficient 4-node flat shell element with six degrees of freedom per node for the analysis of arbitrary shell structures. The element is developed by incorporating a strain smoothing technique into a flat shell finite element approach. The membrane part is formulated by applying the smoothing operation on a quadrilateral membrane element using Allman-type interpolation functions with drilling DOFs. The plate-bending component is established by a combination of the smoothed curvature and the substitute shear strain fields. As a result, the bending and a part of membrane stiffness matrices are computed on the boundaries of smoothing cells which leads to very accurate solutions, even with distorted meshes, and possible reduction in computational cost. The performance of the proposed element is validated and demonstrated through several numerical benchmark problems. Convergence studies and comparison with other existing solutions in the literature suggest that the present element is efficient, accurate and free of lockings.
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