Determining the Stress Intensity Factor in a Cracked Plate Under Tensile Stresses using the Finite Element Method

Numerical methods, especially the Finite Element method, are increasingly being used for solving different problems. Due to fact that these methods are approximate, having a good understanding and judgment about the errors and their distribution is very important. Hence education of users of engineering analysis and design software is necessary and inattention to it may result in catastrophe.  As regards this issue, the problem of determining the stress intensity factor in a cracked plate under tensile stresses, by using the finite element method together with error estimation and adaptivity, is the subject of this article. For this purpose, an academic FORTRAN code has been developed which is able to estimate the finite element solution error by using the superconvergent patch stress recovery method. In addition, an adaptive solution with remeshings in each step is carried out to improve the quality of the employed finite element mesh. Comparing the obtained results with the analytical solution, as well as the ANSYS commercial software, it is observed that the employed algorithm for error estimation has a better performance and can be used for determination of the stress intensity factor in complex structures with arbitrary cracks.