Efficient mixed Timoshenko-Mindlin shell elements

The precise representation of rigid body motions in the displacement patterns of curved Timoshenko– Mindlin (TM) shell elements is considered. This consideration requires the development of the strain– displacement relationships of the TM shell theory with regard to their consistency with the rigid body motions. For this purpose a re ned TM theory of multilayered anisotropic shells is elaborated. The e ects of transverse shear deformation and bending-extension coupling are included. The fundamental unknowns consist of ve displacements and eight strains of the face surfaces of the shell, and eight stress resultants. On the basis of this theory the simple and e cient mixed models are developed. The elemental arrays are derived using the Hu–Washizu mixed variational principle. Numerical results are presented to demonstrate the high accuracy and e ectiveness of the developed 4-node shell elements and to compare their performance with other nite elements reported in the literature