LEM for twisted re-entrant angle sections

• Extension of numerical method LEM to section with re-entrant angles under torsion.
• Shear stress field or Prandtl function for any kind of domain with arbitrary contour.
• Solution is obtained developing line integrals only, no need of any discretization.
• The method is robust in the sense that returns exact solution if this exists.
• Numerical implementation of the LEM has been developed using Mathematica software.

In this paper an innovative numerical method named as line element-less method, LEM, for finding solution of torsion problem has been extended to all shaped sections, including sections possessing re-entrant angles at their boundary. The response solution in terms of shear stress field or Prandtl function or warping function in all domain and for any kind of domain with arbitrary contour, may be performed quickly, calculating line integrals only. The method takes full advantage of the theory of analytic complex function and is robust in the sense that returns exact solution if this exists. Numerical implementation of LEM has been developed using Mathematica software without resorting to any discretization neither in the domain nor in the boundary. The latter means that you can use the same program for all sections just by changing the first few lines of program where you declare the geometry of the section. Some numerical applications have been reported to demonstrate the efficiency and accuracy of the method.