A 3D cracked beam model with unilateral contact. Application to rotors

Abstract

Abstract The paper describes the derivation of a lumped cracked beam model from the tridimensional formulation of the general problem of elasticity with unilateral contact conditions on the cracks lips. Properties of the potential energy of this problem are established and exploited in order to reduce the amount of computation needed in its determination for the case of a beam containing cracks which shape and number can be general. Convex analysis is also used to derive the final form of the energy that determines the nonlinear “constitutive equation” of the section of the beam which can be incorporated in a FE analysis. Although the approach is very general, the applications aimed are specialized in cracked rotors analysis so that flexion dominant loading is more particularly investigated. A comparison with experimental results is given for four points bending test. Attention is also paid to others aspects of the behavior of cracked beam as the modeling of fatigue cracks, the coupling of the different components of internal forces in the constitutive equation of the cracked beam and finally local 3D loading encountered in rotor applications.