Analytic stress intensity factors for finite elastic disk using symplectic expansion

An analytic method to determine the stress intensity factors of finite elastic disk in polar coordinates is introduced with extension to various geometric domains using least-square method. It first finds the symplectic eigenfunctions after expressing the governing equilibrium equations in a Hamiltonian form for variable separation. The displacements and stresses are expanded by the symplectic eigenfunctions with coefficients determined from the boundary conditions. The stress intensity factors are actually the first two coefficients of the series and no post-processing is required. The higher coefficient gives the T-stress. Examples for discontinuous boundary conditions are included and new results are given.