A STRESS RECOVERY METHOD FOR CRACKS IN KIRCHHOFF PLATE BASED ON THE SYMPLECTIC EIGENSOLUTIONS NEAR THE CRACK TIPS

For a plate structure with through cracks, the calculation accuracy of the stress field and the stress intensity factor near the crack tips has important influence on the safety evaluation of the plate. Based on the analytical symplectic eigen-solutions of the crack tip field in the Kirchhoff plate bending problem with cracks, a finite element stress recovery method is proposed to improve the calculation accuracy of the stress field near the crack tips. Firstly, the bending problem of the cracked plate is analyzed by using the conventional finite element program, and the nodal displacements near the crack tip are obtained. Secondly, the undetermined coefficients in the symplectic eigen-solutions are determined by using nodal displacements, and the explicit expression of the stress field near the crack tip is obtained. The numerical results show that the present approach can present the stress results with more precision and has good numerical stability.