A quadrilateral membrane hybrid stress element with drilling degrees of freedom

A new kind of quadrilateral assumed stress hybrid membrane element with drilling degrees of freedom and a traction-free inclined side has been developed based on an extended Hellinger-Reissner principle which is established by expanding the essential terms of the assumed stress field as polynomials in the natural coordinates of the element. The homogeneous equilibrium equations are imposed in a variational sense through the internal displacements which are also expanded in the natural coordinates, while the tractionfree conditions along the inclined side are satisfied exactly. The use of such special element in the finite element solution is shown to be highly accurate when only a very coarse element mesh is used for plates with V-shaped rounded notches or inclined sides.