A study on the plane problems of elastic mechanics using complex-variables BEM.

• Main Authors: Jiang , Pin Zhao, 江品昭
• Other Authors: Kuo , S.R.
• Format: Others
• Language: zh-TW
• Published: 2002
• Online Access: http://ndltd.ncl.edu.tw/handle/62942505955995296835

碩士 === 國立海洋大學 === 河海工程學系 === 90 === Abstract When dealing with the plane of elastic mechanics, the traditional CVBEM can only derive the kernel functions of real variable form from the real part of stress functions, with establishing singular and hyper-singular equations to solve the problems of degenerated boundaries. But in this article, we consider the real and the imaginary part of the stress function at the same time to establish a new CVBEM. Through the traditionally reciprocal-work theorem, we can derive the integral equations of coefficient matrix after the divergence of boundary quantities directly by integrating the variables we considered. Therefore, the original problems in the plane of elastic mechanics and the degenerated boundaries will be resolved by the multi-variable kernel functions, including real and imaginary part, in the new CVBEM. In our model, the imaginary part of the multi-variable kernel functions exists the problem of path diverging, which will cause the kernel functions unsolvable by BEM directly when them pass through the domain of objectives. Therefore, we use the method of relative angles, with the definitions of argument in computer software, to suggest some ways defined specifically to find the multi-variable kernel functions out of the objective domain. Finally, we extended this method with some numerical examples including the patch test, cantilever beams, simple beams, and two-dimensional crack problems in infinite region are considered to verify the validity of the proposed formulation.