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

Date

2014-07-25

Author

Amireghbali, A.
Çöker, Demirkan

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

144
views

0
downloads

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.

Subject Keywords

Fracture mechanics, Curved crack, Stress intensity factor, Modified mapping collocation method, Tikhonov regularization

URI

https://hdl.handle.net/11511/54688

Collections

Department of Aerospace Engineering, Conference / Seminar

Suggestions

OpenMETU
Core

Elastic analysis of a circumferential crack in an isotropic curved beam using the modified mapping-collocation method Amireghbali, Aydin; Çöker, Demirkan (2014-07-01) The modified mapping-collocation (MMC) method was applied to the boundary value problem (BVP) of a circumferential crack in an isotropic elastic curved beam subjected to pure bending moment loading. The stress correlation technique is then used to determine opening and sliding mode stress intensity factor (SIF) values based on the computed stress field near the crack tip. The MMC method aims at solving two-dimensional BVP of linear elastic fracture mechanics (LEFM) circumventing the need for direct treatmen...
Elastic analysis of a circumferential crack in an isotropic curved beam using modified mapping-collocation method Amireghbali, Aydın; Çöker, Demirkan; Department of Aerospace Engineering (2013) The modified mapping-collocation (MMC) method is applied to analyze a circumferential crack in an isotropic curved beam. Based on the method a MATLAB code was developed to obtain the stress field. Incorporating the stress correlation technique, the opening and sliding fracture mode stress intensity factors (SIF)s of the crack for the beam under pure bending moment load case are calculated. The MMC method aims to solve two-dimensional problems of linear elastic fracture mechanics (LEFM) by combining the powe...
Three dimensional analysis of periodic cracking in FGM coatings under thermal stresses Dağ, Serkan; Erdogan, Fazil (2006-10-18) A three dimensional finite element method is used to examine periodic surface cracking problem in a functionally graded coating subjected to transient thermal loads. The ceramic/metal FGM coating is assumed to contain periodic semi-elliptical cracks and to be perfectly bonded to a homogeneous substrate. The composite structure is subjected to transient residual/thermal stresses. Temperature and displacement fields are computed using a three dimensional finite element approach. Finite element models are crea...
Cracked infinite cylinder with two rigid inclusions under axisymmetric tension Toygar, M. Evren; Gecit, M. Rusen (2006-08-01) This paper considers the problem of an axisymmetric infinite cylinder with a ring shaped crack at z = 0 and two ring-shaped rigid inclusions with negligible thickness at z = +/- L. The cylinder is under the action of uniformly distributed axial tension applied at infinity and its lateral surface is free of traction. It is assumed that the material of the cylinder is linearly elastic and isotropic. Crack surfaces are free and the constant displacements are continuous along the rigid inclusions while the stre...
Surface cracking in an orthotropic medium subjected to frictional contact Sarikaya, Duygu; Dağ, Serkan (2016-07-01) This article presents an analytical method capable of resolving the coupled problem of surface cracking in an orthotropic elastic medium subjected to frictional contact by a rigid flat punch. Reciprocal influences between the surface crack and the flat punch are accounted for by establishing a fully coupled formulation. Governing partial differential equations involving the displacement components are derived in accordance with plane theory of orthotropic elasticity. General solutions corresponding to mode ...

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.