Vibration of structures by hybrid strain-based three-node flat triangular shell elements

Finite elements that are capable of representing vibration behaviour of general plate and shell structures have been developed and presented in this paper. The formulations and derivation of the explicit stiffness matrices of the elements have already been proposed and obtained earlier by the authors. These three-node 18-d.o.f. flat triangular shell elements have proved to be accurate and reliable for general shell structures under static loads. In the present paper, explicit expressions for corresponding consistent mass matrices are derived. The shell elements are of the hybrid strain type and degenerate in nature. This degenerate nature allows for applications to thin as well as to moderately thick to thick shells and makes extension to non-linear analysis simple. The hybrid strain feature, however, provides continuity of displacements and strains. Efforts are also directed to address the issue of normal rotation. The presented elements are capable of reflecting true normal rotation as well as desirable membrane and bending behaviour. Computed results of several problems that were considered in the obstacle course of the static analysis are included to demonstrate the accuracy and capability of the elements.