Free Vibration Analysis And Design Optimization Of Frame Structures Using Exact Finite Elements

The exact finite element method recently developed is very efficient and accurate forvibration and stability analysis problems of frame structures. This dissertation aims at furtherdevelopment of the related theory and its applications. New exact finite elements aredeveloped, and a new method for free vibration analysis of combined dynamic system isproposed. Further, the exact finite element is applied to design optimization of framestructures. The study shows that the exact finite element has wide application prospect.Firstly, the basic theory of the exact finite element, including the element formulation,discussion of shape functions and iterative algorithm, is introduced. And an exact spatialbeam element is then developed. Illustrative numerical examples are presented to show theaccuracy and efficiency of this element.Secondly, two exact Timoshenko beam elements for free vibration analysis of framestructures are developed, including one for the general case when the effect of axial force andelastic foundation are considered. Numerical examples are presented to demonstrate thevalidity and advantage of this new element. The effects of depth-to-length ratio, axial forceand elastic foundation on structural free vibration are also investigated.Thirdly, the exact finite element is applied to free vibration analysis of combineddynamical system. Numerical examples validate the method and show the effect of differentcomponents on the free vibration of combined dynamical systems.Fourthly, the design optimization problem of frame structures is considered to takeadvantage of the exact finite element. With the derived eigenvalue sensitivity based onexplicit expression of element stiffness matrix and mass matrix, the eigenvalue sensitivity canbe obtained efficiently and accurately, and a size optimization algorithm for frame structureswith natural frequency constraint is implemented and numerical examples presented.Fifthly, a summary of the present study is presented and future work suggested.In the appendix, a user graphic interface for free vibration analysis of combined dynamicsystem based on Matlab GUI is introduced briefly.