Finite element dynamic analysis of rotating tapered three dimensional Timoshenko beams

The equations of motion are derived for the three dimensional rotating tapered Timoshenko beam using a Lagrangian formulation in conjunction with the finite element technique. These equations include the effects of Coriolis forces, shear deformation and rotary inertia, hub radius, taper ratios and pre-cone and setting angle. A mixed set of generalized co-ordinates that accounts for inertia coupling between reference motions and local elastic deformations is employed. The shape functions of the three dimensional beam element are derived using Timoshenko beam theory. Explicit expressions of the element mass, stiffness, Coriolis and inertia terms matrices are derived in parametric form thus avoiding extensive numerical computations. The generalized eigenvalue problem is defined and cast into state space form using explicit expressions for the mass, stiffness and Coriolis matrices. Modal transformations from the space of nodal co-ordinates to the space of modal co-ordinates are invoked to alleviate the problem of large dimensionality resulting from the finite element discretization. Both planar and complex modal transformations are presented and implemented to obtain a reduced order model. The reduced order model form of equations of motion is computer generated, integrated forward in time and the system dynamic response is evaluated for different types of external loading conditions. Explicit expressions for Southwell coefficient for rotating tapered Timoshenko beams are obtained as a function of all parameter variations. The frequency spectrum of the forced time signal response is computed and plotted along with the response profiles for a wide range of parameter variation using the FFT algorithm.</p

The effect of loading history on unstable fracture of austenitic steel (304)

The present paper presents an analysis of the influence of loading history on unstable fracture of austenitic steel 304 (SS 304) using the J-integral and its applicability in situations where a loading history exists. A CT specimen is employed for the purpose. The loading history effect on the unstable fracture of SS 304 is studied by performing cyclic loading with different load histories at constant load range (ΔPi) and at constant stress intensity factor range (ΔKj). The results show that the plastic singularity is well described by the integral (J) for the different types of loadings used. Moreover, the real meaning of (JIC) as a representative of the maximum energy release rate is quite limited if it ignores the loading history. The experimental results show that the dissipated energy ΔJ is more active when the loading is done at constant ΔP. The evolution of ΔJ can be directly linked to the crack growth rate and to the extent of the plastic zone developed at the crack tip.</jats:p