A critical survey of the 9-node degenerated shell element with special emphasis on thin shell application and reduced integration

Since the publication of Ahmad's degenerated thick shell element in 1970, a large number of authors have studied this simple type of element and made their proposals for improving its behaviour. Special emphasis was placed on thin plate and shell applications. The present paper discusses special aspects of the 9-node Lagrangian element. Interesting facts are presented-in particular, a mathematical explanation of why reduced shear integration leads to improved results. Another topic deals with thin plate and shell applications. A modification of the stiffness is proposed which allows the application of the element like a Kirchhoff-type model to any plate problem. In the final section a case study of a variety of proposed element models is presented, and the accuracy is shown for various plate and shell problems.