Two-dimensional Thermal Stress Analysis using X-FEM

Abstract

Conventional FEM requires that the boundary of the element just matches the crack line to perform stress analyses of structures containing cracks in the field of fracture mechanics. These modeling processes are rather complicated and cannot be performed easily even if the automatic mesh generation technique is utilized. Recently, Belytschko et al. proposed the extended finite element method (X-FEM) based on the concept of partition of unity, and applied this method to the evaluation of the stress intensity factors and perfoming the crack extension simulation. The X-FEM can be used to simplify the modeling of continua containing several cracks and hence perform effective stress analyses related to fracture mechanics. This paper describes the two-dimensional thermal stress analysis of structures containing cracks. Stress intensity factors having mixed modes coupled with mode-I and mode-II are evaluated by M1-integral method in conjunction with X-FEM. This method is examined in numerical examples of elastic and thermo elastic analyses. The numerical results show that X-FEM is an effective method for performing thermal stress analyses and evaluating stress intensity factors.