A new one-point quadrature, quadrilateral shell element with drilling degrees of freedom Original Research Article

In this paper we discuss the development of a new four-node general shell element with single point quadrature used for the analysis of non-linear geometrical and material problems. One of the main features of the present development is the implementation of a rotation component around the shell normal (i.e. drilling rotation) to Belytschkoʹs family of shell elements. Thus, at each node, six degrees of freedom (i.e. three translations and three rotations) make the element easy to connect to space beams, stiffeners or intersecting shells. A projection scheme for warping correction is proposed so that the element is accurate for both flat and warped configurations. All locking phenomena (such as transverse shear, in-plane shear and membrane locking) are controlled by an assumed strain method. Also, a physical stabilization approach for control of spurious zero-energy modes is proposed without requiring any artificial stabilization parameters. This approach is inexpensive and accurate because it updates and stores hourglass stresses only at the mid-surface rather than at all the integration points through the shell thickness.