Fourier Series Method for Plated Structures

• Main Authors: Jiann-Gang Deng, 鄧建剛
• Other Authors: Fu-Ping Cheng
• Format: Others
• Language: zh-TW
• Published: 1999
• Online Access: http://ndltd.ncl.edu.tw/handle/18575088009002482125

博士 === 國立交通大學 === 土木工程系 === 87 === This study presents a novel method based on edge function and corner function approach using the Fourier series for boundary value problems and applies it to polygonal domains. This method is also applied to (1).plane bi-axial stress,(2).plane elasticity problems, (3).plate bending problems,(4).plated structures assembled by bi-axial stress and plate bending,(5).plated structures assembled by plane elasticity and plate bending. In addition, analytical solutions for bi-axial stress, plane elasticity and plate bending for each edge serving as a set of fundamental functions, utilized coordinate transformation and boundary integral, the solution function of each edges are obtained. The problem can be solved by superimposing the solution functions and matching the Fourier harmonics of the prescribed boundary conditions. By this approach, a convex polygon can be solved with one element only; non-convex domain is divided into several convex sub-domains with appropriate continuity conditions at the interface. The process closely resembles the boundary element method, except that the unknowns are the amplitudes of Fourier harmonics. Similar to the boundary integral method, the proposed method does not involve any mesh generation. In addition, the number of elements and the degrees of freedom for the proposed method are significantly smaller than the finite element and finite difference methods. The proposed method also holds an advantage over boundary elements in that the matrices are directly integrated from an analytical solution instead of numerical integration. Combining bi-axial stress and plate bending element, or combining plane elasticity and plate bending element, allows us to readily extend the proposed method to plated structures.