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 Vibration Analysis

Pp. 7-29 (23)

Meilan Liu and Cho W. S. To

Abstract

In order to investigate the vibration characteristics and dynamic responses of complicated shell structures with geometrical and material nonlinearities, it is essential to formulate shell finite elements that are easy to use, accurate, effective, and applicable to thin as well as moderately thick shells. This chapter presents the development of the mixed formulation or hybrid strain based three-node flat triangular shell elements, with a particular emphasis on the linear analysis of thin to moderately thick shells. Section 2.1 gives a brief introduction and an outline of the features of the shell elements. Section 2.2 deals with the derivation of consistent stiffness and mass matrices of a particular element. In Section 2.3, results and discussions pertaining to rigid-body modes, patch test, and mesh topology are presented. Concluding remarks are given in Section 2.4.

Keywords:

Mixed formulation, three-nodes, triangular, shell finite elements, vibration analysis.

Affiliation:

Department of Mechanical Engineering Lakehead University Thunder Bay Ontario Canada