Free vibration analysis of isotropic cylindrical shells using a new four node discrete Kirchhoff flat shell element based on Reddy´s third order theory

The four node discrete Kirchhoff quadrilateral element based on Reddy´s third order theory (DKTOT) developed earlier by the first author for the analysis of composite plates is modified in this work for the free vibration analysis of thick to thin isotropic clamped cylindrical shells. The modified four node element has seven local degrees of freedom namely, three displacements, two rotations and two transverse shear strains at the mid surface. Globally the element has nine degrees of freedom which is the result of transformation from local system to global system. The additional degrees are rotations about z axis. The finite element results of natural frequencies obtained with the modified flat shell element for thick to thin clamped cylindrical shells are compared with the results available in literature and also with the 3D finite element results of ABAQUS. It is observed that the performance of the developed flat shell element is quite satisfactory.