To further theobjective of investigating the vibration characteristics and
dynamic responses of complicated shell structures with geometrical and material
nonlinearities, this chapter presents the development of mixed formulation based threenode
flat triangular shell elements suitable for the general nonlinear analysis of thin to
moderately thick shells. Section 7.1 gives a brief outline of the features of the shell
elements. Section 7.2 presents the incremental variational principle and its linearization.
The derivations of the consistent element stiffness matrices and the consistent element
mass matrices are dealt with in Sections 7.3 and 7.4. The constitutive relations of elastic
and elasto-plastic materials with small as well as finite strain deformations are given in
Section 7.5. The last two sections, Sections 7.6 and 7.7, respectively, are concerned
with configuration and stress updating, and numerical algorithms.
Keywords: Mixed formulation, three-node shell elements, dynamics, nonlinear,
elastic and elasto-plastic.
