Dynamic of flat shell elements

Shell structures are frequently used in marine, mechanical, aerospace, and civil engineering applications due to efficient load carrying capability relative to material costs; aesthetical considerations also may be a governing factor for using shells. For this reason, finite element analysis of shells has been receiving continuous attention since the early days of the development of the method.

Several types of shell elements have been developed. One possibility, which gives simple but accurate and efficient elements, is to use three node flat shell elements. These elements have three translations and three rotations at each node and are obtained by the superposition of a membrane element and a plate element. Several alternatives may be used both for the membrane and the plate part of the element. For most of them, only stiffness matrices have been developed and therefore only static analyses have been performed.

The purpose of this Master thesis is to investigate the dynamic of these elements. The main objective is to derive and test the consistent and lumped mass matrices of some of these elements. The accuracy of the obtained elements will be assessed using benchmark examples implemented in MATLAB, and comparisons with results obtained using ANSYS with other types of shell elements, will be performed.

This project, which is a part of an on-going research project on non-linear corotational finite shell elements, should lead to a conference article.

One or two students interested in finite elements, MATLAB programming, and mathematics are sought for this project.