Residual stress analysis of thick-walled spherical pressure vessels using a complex variable finite element method

The complex variable finite element method, ZFEM, was applied to structures containing residual stresses. A thick-walled sphere model was subjected to an autofrettage process to induce the residual stress field which was analyzed using ZFEM. The stress results from ZFEM were compared to analytical solution and standard finite element results. ZFEM was used to calculate partial derivatives with respect to material parameters, geometry and the applied load. The ZFEM partial derivative results were shown to provide excellent accuracy when compared with derivatives of the analytical solution and finite differencing of standard finite element results. The variability of processes that contribute to the residual stresses creates uncertainty in the residual stress calculations. The level of uncertainty associated with a residual stress field must be quantified to accurately predict the service life of a structure. Traditional computation methods used to quantify the uncertainty are cumbersome and time consuming due to the computation time required for a residual stress analysis. A method to quantify the uncertainty of the residual stress fields using a first order Taylor approximation employing ZFEM partial derivative results was developed and resulted in significant computation time savings.