Effect of Elastic Supports on Lengthwise Fracture in Functionally Graded Beams under Changing Twist Angle

There are many engineering applications in which various structures are supported by different elastic supports. On the other hand, usage of functionally graded materials for making of load-carrying structures in various sectors of current engineering is growing constantly. The safety and reliability of these structures relay in high extent on their fracture behavior. In view of this, the present paper is focused on analyzing of lengthwise fracture in beam structures that are functionally graded along the radius of the crosssection. The right-hand end of the beam is rigidly fixed, while the left-hand end is supported by a circular elastic spring. The beam is under changing twist angle. The circular spring support acts on the beam by a twist moment. The beam hosts a lengthwise crack representing a circular surface. The functionally graded material has viscoelastic behavior under changing shear strains due to the twist. One of the primary motives for developing of this analysis is to evaluate the effect of the elastic spring support on the lengthwise fracture. In this relation, the strain energy release rate is determined. The solutions accounts for the circular spring support. The solution is verified upon methods known from the scientific literature. It is clarified how the circular elastic spring support influences the strain energy release rate under changing twist angle.