A novel hybrid stress meshless method for two-dimension elastic structure with a traction-free circular boundary

To increase the use of the meshless method, a hybrid stress method is introduced into the meshless method.

The method is based on the radial point interpolation method (RPIM). According to the Hellinger Reissner principle, stress functions are introduced into the solution procedure. Finite elements are used as background cells for integration. All cells are divided into two types – the H cells, which are around the traction-free circular boundary, and the G cells. For the H cells, stress functions in polar coordinates are created. For the G cells, 12-parameter stress functions in Cartesian coordinates are used. Stress functions are based on equilibrium equations and stress compatible equation.

Numerical results show that this method is reliable.

Hybrid stress methods have been applied to finite element methods, but the finite element methods have not been applied into meshless methods.