Abstract: Using the governing equations of plane elasticity for sectorial domain in Hamiltonian form, the methods of separation of variables and eigenfunction expansion are developed for solving the elastic-plastic finite element analytically for the Dugdale model solutions, so that such kind of analytical element can be installed into FEM program systems. This semi-analytical finite element method can be used for Dugdale model solutions for cracked plates of arbitrary shape and load. Numerical results indicate that the method of the paper is efficient for such kind of problem and is in high precision.
Keywords: hamiltonian system, dugdale model, plastic zone size, crack opening displacement, semi-analytical finite element method.