Vibration and Nonlinear Dynamics of Plates and Shells - Applications of Flat Triangular Finite Elements

This e-book focuses on the vibrational and nonlinear aspects of plate and shell structure dynamics by applying the finite element model. Specifically, shell finite elements employed in the ...
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Mixed Formulation Based Three-Node Flat Triangular Shell Elements for Nonlinear Dynamics

Pp. 111-148 (38)

Meilan Liu and Cho W. S. To


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.


Mixed formulation, three-node shell elements, dynamics, nonlinear, elastic and elasto-plastic.


Department of Mechanical Engineering Lakehead University Thunder Bay Ontario Canada