NEW METHODS FOR ELASTIC TORSION OF BAR WITH ARBITRARY SHAPE OF CROSS-SECTION

Abstract

The solutions of the torsion problem of uniform bars with arbitrary cross-section are presented by the first kind Fredholm integral equation along a selected circle. Then we consider the Lavrentiev regularization and Tikhonov regularization to treat the ill-posed problem. The termwise separable property of kernel function allows us to obtain a two-point boundary value solution. Numerical examples show the effectiveness of the new methods in providing excellent estimates of the unknown data from the given boundary conditions.