Elastic Torsion Bar with Arbitrary Cross-Section Using the Fredholm Integral Equations

By using a meshless regularized integral equation method (MRIEM), the solution of elastic torsion problem of a uniform bar with arbitrary cross-section is presented by the first kind Fredholm integral equation on an artificial circle, which just encloses the bar's cross-section. The termwise separable property of kernel function allows us to obtain the semi-analytical solutions of conjugate warping function and shear stresses. A criterion is used to select the regularized parameter according to the minimum principle of Laplace equation. Numerical examples show the effectiveness of the new method in providing very accurate numerical solutions as compared with the exact ones.