A semi-analytical approach for stress concentration of cantilever beams with circular holes under bending 半解析法求解懸臂梁受彎矩之應力集中問題

Po-Yuan Chen and Jeng-Tzong Chen Graduate Student, Department of Harbor and River Engineering 2 Distinguished Professor, Department of Harbor and River Engineering National Taiwan Ocean University Abstract In the paper, the degenerate kernels and Fourier series expansions are adopted in the null-field integral equation to solve bending problems of a circular beam with circular holes. The main gain of using degenerate kernels in integral equations is free of calculating the principal values for singular integrals. An adaptive observer system is addressed to fully employ the property of degenerate kernels for circular boundaries in the polar coordinate. After moving the null-field point to the boundary and matching the boundary conditions, a linear algebraic system is obtained without boundary discretization. The present method is treated as a “semi-analytical” since analytical expressions as much as possible before numerical implementation. Finally, an example, including four holes, is given to demonstrate the validity of the proposed method. The present formulation can be extended to handle beam problems with arbitrary number and various positions of circular holes.