Mixed Formulation Based Three-Node Flat Triangular Shell Elements for Nonlinear Dynamics

Abstract

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.

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