| Summary: | 碩士 === 國立臺灣海洋大學 === 河海工程學系 === 103 === This study is to develop a new approach to derive the geometrically nonlinear strain energy of a thin shell element based on the rigid body motion rule and the incremental force equilibrium condition. In this research, we derive the incremental virtual work done by boundary forces and boundary moments in deformed state when an incremental rigid body displacement is superimposed by using the rigid body motion rule. Using the equilibrium condition for the incremental virtual work, the geometrically nonlinear strain energy of the thin shell element can be obtained by a set of given incremental rigid body displacements. This strain energy derived by following this procedure has obeyed the rigid body motion rule. Furthermore, the incremental virtual work done by the boundary forces and moments for the shell element can be obtained by considering the force equilibrium conditions for the shells at the initial state and the deformed state by superimposing a virtual rigid body displacement. Similarly, the geometrically nonlinear strain energy for the thin shell element can be obtained by superimposing a virtual rigid body displacement by using the virtual work equilibrium conditions. The strain energy obtained by this procedure satisfy the incremental force equilibrium rule. By combining the above-mentioned two procedures for deriving the geometrically nonlinear strain energies, one can find the complete geometrically nonlinear strain energy based on the arbitrary nature of incremental and virtual displacement. The present procedure proposed in this study only requires simple integration and comparison between the strain energies obtained from the two rules, which can avoid cumbersome derivation. In addition, the geometrically nonlinear strain energy obtained from this method can satisfy both the rigid body motion rule and the incremental force equilibrium conditions.
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