Line element-less method (LEM) for beam torsion solution (truly no-mesh method)

In this paper a new numerical method for finding approximate solutions of the torsion problem is proposed. The method takes full advantage of the theory of analytic complex functions. A new potential function directly in terms of shear stresses is proposed and expanded in the double-ended Laurent series involving harmonic polynomials. A novel element-free weak form procedure, labeled line element-less method (LEM), has been developed imposing that the square of the net flux across the border is minimal with respect to coefficients expansion. Numerical implementation of the LEM results in systems of linear algebraic equations involving symmetric and positive-definite matrices without resorting to any discretization neither in the domain nor in the boundary. Some numerical applications are reported to demonstrate the efficiency and accuracy of the method.