Determine the stress intensity factor in a plate with a center crack under thermal and mechanical loading using isogeometric method based on the Bezier extraction operator

In this research, an analysis of the stress and stress intensity factor in a cracked plate under thermal and mechanical loading is done. For this purpose, using MATLAB coding, a plate with a center crack was modeled by the isogeometric method (IGA) based on the Bezier extraction operator. In this method, NURBS basis functions are generated as a linear combination of Bernstein polynomials using the Bezier extraction operator. Using this operator Bezier elements with Co continuity (similar to elements of the finite element method) were produced and Bernstein polynomials are defined on these elements. In order to model the crack, the extended isogeometric method (XIGA) was used. In this method, the control points that exist along the crack and at the tip of the crack are identified and extracted using the proper level set functions. Therefore, there is no need to re-meshing or modify the elements. By enriching the extracted control points with appropriate enrichment functions and applying boundary conditions, the analysis process was carried out and the strains and stresses were calculated. Finally, the value of the first mode stress intensity factor was obtained based on the interaction integral method. To check the accuracy of the obtained results, a similar analysis was performed using the finite element method and the results obtained from both methods were compared. These studies showed that the considered isogeometric method provides more accurate solutions with a much smaller number of elements and computational costs.