Analysis of Mindlin Plates by the Moving Trefftz Method

• Main Authors: Chang-ChingLiu, 劉昶慶
• Other Authors: Yung-Ming Wang
• Format: Others
• Language: zh-TW
• Published: 2018
• Online Access: http://ndltd.ncl.edu.tw/handle/gqehtv

碩士 === 國立成功大學 === 土木工程學系 === 106 === In this thesis, we derive a numerical method named Moving Trefftz Method to simulate the mechanical behavior of Mindlin Plates. In order to incorporate the essential and natural boundary conditions into the variational principle, we adopt the Hellinger-Reissner variational principle. The characteristic of this method is adopting the concept of the Trefftz Method. We choose the functions that satisfy the differential equations as the basis of the local approximation function. By using the moving approximation of the Meshless Method in the modified H-R variational principle, we set nodes to construct the relationship between variables. Then, we can use the relationship to form simultaneous equations and solve the displacement field and the resultant stress field. In view of the convenience of using polynomial expressions in numerical analysis, we use the computational properties of polynomials to establish a systematic method to obtain the particular solutions and the bases required in the moving approximation. In numerical examples, we simulate the responses of the plate with different loads and boundary conditions. By changing the number of nodes and the order of bases, we compare the numerical solutions with the analytical solutions to validate the accuracy and the convergence of this method.