A unified formulation for triangular and quadrilateral flat shell finite elements with six nodal degrees of freedom

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Abstract
The flat shell elements presented herein are obtained by superposing discrete Kirchhoff plate bending elements and the membrane elements with drilling degrees of freedom. A simple formulation is presented which allows a 4‐node quadrilateral thin shell element to degenerate into the 3‐node triangular element. Therefore it can easily be used in mesh refinement and to solve other modelling problems. With a trivial modification, the discrete Kirchhoff quadrilateral plate bending element reduces to the standard discrete Kirchhoff triangular element when two nodes are coalesced. For the membrane elements this modification need not be performed, since we use reduced quadrature to avoid membrane locking. The shell elements possess six degrees of freedom per node, which allows easy modelling of complex shell surface intersections and compatibility with other elements with rotational degrees of freedom. Both the quadrilateral and triangular elements produce a 24 × 24 stiffness matrix. The direct stiffness addition of the terms associated with the coalesced nodes, performed in the finite‐element assembly process, produces the 18 × 18 triangular element stiffness. Several numerical examples are presented which illustrate the accuracy of the element.

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