engleski

A Study of the Surface Share Stress in Saint-Venant’s Torsion by the Boundary Element Method

Components of stress in Saint-Venant's torsion are determined as gradients of so-called Prandtl's stress function that satisfies Poisson's differential equation. Partial integration performed on the Poisson's differential equation results in integral equation that express Prandtl's stress function as a function of surface share stress, and in integral equation of equilibrium which solution is surface share stress. By application of boundary element method, the integral equation of equilibrium is approximated with set of linear equations, which solution are approximated values of surface share stress on the chosen number of boundary points. Once when surface share stress is determined, it is easy to calculate Prandtl's stress function and its gradients (i.e. stresses) in the arbitrary point of the cross section. The proposed method can be applied to any prismatic solid with uniform cross section, such as shafts, prismatic thin-wall shells, etc.

Saint-Venant’s torsion; share stress; boundary element method

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