| Summary: | 博士 === 國立臺灣海洋大學 === 河海工程學系 === 94 === The rigid body rule and the force and moment equilibrium are basically two fundamental conditions for analysis of mechanics; therefore, the geometric nonlinear incremental virtual work equation, governing equation, boundary conditions and the geometric stiffness matrix of the plate structure should obey the basic two conditions. In this dissertation, applications of the rigid body rule and the incremental force and moment equilibrium with the geometric nonlinear theorem on the plate and shell structure are presented and main concerns are presented in three parts: the first, based on the update Lagrange formulation method, the incremental virtual work equation can be derived by using the virtual principle. In the deriving process, by considering the six terms of the nonlinear virtual strain energy arising from the virtual strains, the virtual work, produced from the incremental bending moment owing to the rotation of the plate after the deformed 2C state, can be reached and such virtual work has never been proposed in the literature. It should be noted that the derived geometric nonlinear incremental virtual work equation can fully pass both the rigid body rule and the force and moment equilibrium conditions; the second, a simple derivation for the nonlinear virtual strain energy is firstly proposed such that it can avoid the tedious derivation when the conventional virtual work method is adopted. The proposed simple method firstly constructs the incremental virtual work equation, which satisfies the rigid body rule and incremental force and moment equilibrium conditions and then, the geometric nonlinear virtual strain energy can be determined by simple integral calculation; the third and the last, the condition equation, for which the geometric stiffness matrix of the plate element satisfies the rigid body rule and the incremental force equilibrium conditions, is constructed and thus, a simple method for deriving the external geometric stiffness matrix of a reliable three-node triangular plate element is presented. It should be noted that this simple derivation method only needs some simple matrix operations and can avoid the tedious deriving process as compared with the finite element method. This geometric stiffness matrix of the element only relates with the nodal coordinates, nodal force and moment and actually is a simple explicit formulation. By adopting the stiffness matrix to conduct the geometric nonlinear analysis, the internal force of the plate element is not necessary to calculate and can further be presented in the global coordinate system. Besides, the skew-symmetric parts of the derived geometric stiffness matrix can be canceled out once they are merged into the global stiffness matrix of the structure. In this regard, this structural stiffness matrix becomes a symmetric one and thus, enhances its effectiveness.
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