THE WILSON FLAT SHELL ELEMENT BASED ON PLANE ELASTICITY-PLATE BENDING ANALOGY

The effectiveness of formulating thin plate and shell finite elements by the analogy theory between plane elasticity and plate bending has been verified. With this method, plane elasticity elements can be transformed to plate bending elements. In this paper, the Wilson element QM6 is transformed to a new four node, eight D.O.F (degree of freedom) plate bending element, and then a new sixteen D.O.F flat shell element is presented by the combination of QM6 and the new plate bending element. The most important characteristic of the formulation is that the stretching part and the bending part of the flat shell element use the same interpolation in displacement space and stress function space. So the shell element possesses the relative balance between the quality of the stretching part and that of the bending part. The element has no fictitious D.O.F. Numerical results of typical problems with the new element show very good convergence and high precision.