Numerical calculation of the shear stresses in torsion problem of prismatic bars using collocated discrete least squares method

Collocated Discrete Least Squares (CDLS) meshfree method, is used for the numerical simulation of the Sain-Venant torsion problem and obtaining the shear stresses in the sections with irregular and complex boundaries. In this paper a matrix formulation is applied in discretizing the governing equations, which make the procedure easy to code and efficient in calculation. In the applied method, a limited number of neighbor nodes are considered in the producing radial basis shape functions, which make the matrices sparse and prepare a suitable condition for sparse matrices algebra and applying available subroutine in this case. In order to validate the proposed method in the analyzing stresses due to torsion, firstly an elliptic section is considered , which in this case, there is an analytical solution. In the second problem, a thin walled section is considered and solved by the theory of Saint-Venant in torsion and results are compared with the closed solution obtaining from the theory of the torsion of thin walled sections. In the third problem, torsion in a hollow elliptical section is solved. Finally, the torsion stresses in sections with more complex geometry is considered.