| Abstract: | An implementation of the Ahmad Thick Shell element using vector manipulation, reduced integration and the incorporation of the missing term in the approximating polynomial is presented. The first two aspects are merely applications. The theory is presented elsewhere6,7,11,18 and will not be repeated for the sake of conciseness. The third aspect was achieved by adding to the original nodal configuration a central node having only one degree-of-freedom. That node is then eliminated to preserve the original number of degrees-of-freedom. The Ahmad thick shell element is adequately presented in finite element literature.1-3 The co-ordinate definition and the displacement field are retained and will not be dealt with henceforth. However, a different concept of the strain definition due to Irons is used and the bending terms are included in the modulus matrix. The element like all second generation isoparametric elements is easily implemented through a shape function subroutine suitable for quadrilaterals. It reproduces exactly rigid body motion for any combination of elements of any geometry even for elements withcurved sides and variable thickness. Although Ahmad's thick shell element passed the patch test for unequal parallelograms but not for quadrilaterals the version presented passes that test for quadrilaterals. In spite of its credentials, the new version denoted by A has a major setback. the presence of one too many spurious mechanism is reported. |
