11th World Congress on Computational Mechanics (WCCM) / 5th European Conference on Computational Mechanics (ECCM) / 6th European Conference on Computational Fluid Dynamics (ECFD), Barcelona, Spain, 20 - 25 July 2014, pp.1604-1611
The modified mapping-collocation (MMC) method is applied to the problem of an isotropic curved beam with a circumferential crack under pure bending moment. Using least squares method to solve the overdetermined system of boundary condition equations causes numerical difficulties. Alternatively zeroth-order Tikhonov regularization is applied to solve the system. The regularization technique appears brilliantly helpful in eliminating the convergence problems associated with ill-posedness of the problem. The boundary condition satisfaction is examined. The results of stress analysis are in good agreement with that of the finite element method.