Abstract：A novel 2-dimensional hybrid stress finite element is proposed for stress analyses of plate with holes. The new element, which is a 4-node quadrilateral plane element, is denoted as P-HS4-8β. Firstly, a stress in polar coordinates is obtained by physical equations and geometric equations. Secondly, the obtained stress is introduced into energy functional of the Hellinger-Reissner variational principle for plane stress problem in polar coordinates. In the new energy functional, the number of the stress variables is 2. According to this, the hybrid stress finite element formation is established. A matrix for stress interpolation is obtained by the traction-free condition along the edge of hole and the compatibility equation, and is introduced into the hybrid stress finite element formation. Numerical results show that, the new method gives a good accuracy of the stress near the holes.
2015, Vol. 36 
