【摘要】 将R-函数理论用于分析具有任意形状截面的各向异性杆弹性扭转问题.首先引入坐标变换将扭转问题的应力函数方程化成拉普拉斯算子方程,再利用拉普拉斯算子的基本解、边界方程及R-函数构造一个准Green函数,其满足了齐次边界条件.后再应用Green公式将各向异性杆弹性扭转问题的拉普拉斯算子方程转化为积分方程,应用R-函数理论选择适当的边界方程来消除积分方程的奇异性.数值算例表明,此方法是一种有效的数值方法.更多还原

【Abstract】 In this paper,the R-function theory is applied to solve the torsion problem of anisotropic bar with arbitrary shape cross section.Firstly,the stress function equation of the problem is transformed into the Laplace operator equation through coordinate transformation.Then,the fundamental solution of the Laplace operator,the boundary equation and the R-function are used to construct the quasi-Green’s function,which satisfies the homogeneous boundary condition of the problem.Finally,the Laplace operator differential equation of the problem is reduced to the Fredholm integral equation of the second kind by Green’s formula.The singularity of the kernel of the integral equation is overcome by choosing a suitable form of the normalized boundary equation by the R-function.Numerical examples show that this method is an effective numerical method.更多还原