| Summary: | 博士 === 國立成功大學 === 航空太空工程學系 === 88 === In this dissertation, the modified differential quadrature method (MDQM) and modified differential quadrature element method (MDQEM) are presented for structural analysis.
In MDQM, modified relationships are developed for dealing with boundary conditions so as to overcome the numerical error induced by using the -method in the original DQM, and a new formulation process is proposed to incorporate the modified relationships for deriving the discretized governing equations. The present method is applied to various structural problems, such as: static, free vibration and buckling analyses of beams and plates, vibration analysis of turbomachinery blades with classical or elastic supports based on the beam or shell models. Numerical results of the present method are shown to have excellent accuracy. The MDQM is proven to be efficient and convenient for analyses of single structural elements.
By following the concept of MDQM and the domain decomposition technique, the modified differential quadruatre element method (MDQEM) is developed for structural analysis. The representative algebraic equations will be furnished with consideration of boundary conditions in each element. The global system equations are assembled from the element equations with consideration of compatibility and continuity conditions. Multiple boundary conditions can be satisfied at one boundary point. Computational scheme of this approach is easily implemented. An Euler beam element and a classical plate element are developed. Static and free vibration analyses of beams and plates having discontinuities in material, geometry, loading and boundary conditions are examined. Results obtained by the present approach are shown to have high accuracy and good convergence. The MDQEM can be used for a wide range of applications.
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