# Application of finite element method in alloy centrifugal casting

Compared with the transfer matrix method, the main characteristic of the finite element method is that the expression is concise and standard. It has outstanding advantages in solving the problem of complex mechanical system composed of rotor and surrounding structure. However, when the model is too complex, this method will consume huge computational resources. The basic idea of the finite element method is: first, the continuous system is discretized, and the complex structure is divided into several elements which are only connected at the boundary nodes. Each element is an elastic body, and the element displacement is expressed by the interpolation function of the node displacement. Then, the element stiffness matrix and mass matrix are obtained by using the virtual work principle, and the element motion equation can be obtained Assemble the equations of motion of the whole system.

In the history, the finite element method was used to analyze the rotor dynamics in 1970. RUH applied the finite element method to the shaft system. He used a simple engineering beam model to study the bending vibration of the shaft with only translational inertia. Later, Nelson and mcvanugh introduced the gyroscopic effect and derived the finite element mass matrix and stiffness matrix of Rayleigh beam axis model, which expanded the finite element method. Nelson introduced Timoshenko beam theory into the finite element model of beam in 1980.

With the rapid development of computer technology, the dominant frequency of computer is higher and higher, and the memory capacity is larger and larger. The disadvantage of consuming computing resources of finite element method is gradually overcome. Finite element method has become a potential method for rotor dynamics analysis and calculation. Many famous companies in the world have developed their own special commercial finite element software, such as ANSYS, ABAQUS, Marc, NASTRAN, etc. However, due to the need to consider the gyroscopic effect and support anisotropy in rotor dynamics, for some special structures, these software sometimes can not be directly applied to the analysis of rotor dynamics, but need to be re developed to calculate rotor dynamics. 