TIKHONOV REGULARIZATION FOR THE MODIFIED MAPPING-COLLOCATION METHOD APPLIED TO CIRCUMFERENTIAL CRACK IN A CURVED BEAM

2014-07-25
Amireghbali, A.
Çöker, Demirkan
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.
Citation Formats
A. Amireghbali and D. Çöker, “TIKHONOV REGULARIZATION FOR THE MODIFIED MAPPING-COLLOCATION METHOD APPLIED TO CIRCUMFERENTIAL CRACK IN A CURVED BEAM,” 2014, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/54688.