By Using Bounday Integral Equation Method to Solve The Direct Euler-Bernoulli Beam Problem

• Main Authors: Bo-Jun Chang, 張博竣
• Other Authors: Chein-Shan Liu
• Format: Others
• Language: zh-TW
• Published: 2016
• Online Access: http://ndltd.ncl.edu.tw/handle/68160082120270051341

碩士 === 國立臺灣大學 === 土木工程學研究所 === 104 === In this thesis we numerically solve the direct Euler-Bernoulli beam problems by using a boundary integral equation method(BIEM) which is based on the generalized Green’s second identity and the self-adjoint operators. In the BIEM, we choose a set of adjoint Trefftz test functions which can be obtained by the method of separation of variables. In the numerical algorithm, we can expand a trial solution by using the bases satisfying the homogeneous governing equation and the boundary conditions simultaneously. To satisfy the above two properties of the bases, we use the adjoint Trefftz test functions as the bases and impose the specified boundary condition. By using these bases, moreover, we can eliminate the Gibbs phenomenon and avoid the matrix computations. Finally, there are several numerical examples to validate the effectiveness of the proposed scheme in this thesis and the results show that the BIEM is a highly accurate numerical method.