Comparing the Identification Methods for a Finite Element Mass Matrix of the Axisymmetric Shell Restricted by Rigid Ends

Abstract

The paper deals with comparison of various algorithms to obtain mass-inertial characteristics of the finite element (FE) of revolution shell restricted by rigid ends.Such shells are widely used in engineering, for example, as body parts of gas turbine plants. When solving the problems of linear statics and modal analysis for complex structures containing such shells, a method of replacing a complex section of the structure by a single generalized element with previously calculated characteristics is used.In case of stiffness properties everything is obvious, since with using a numerical integration of the system of differential equations of a revolution shell, the stiffness matrix elements can be found exactly, while to obtain mass-inertial characteristics a standalone consideration is necessary.The paper considers different algorithms to build a matrix of the shell FE mass, limited by rigid ends, with an arbitrary form of the generatrix:consistent/inconsistent formulation;frequency identification algorithm;natural frequency identification and that of free element shapes.When performing numerical experiments it was found that a classical approach that uses form functions obtained from statics is inappropriate for constructing the mass matrix of the generalized element. Therefore, other algorithms were proposed to obtain mass-inertial characteristics. But those of have some restrictions too:the frequency identification algorithm requires large computational efforts and can be successfully used only in the cases of securing, which involve identification;natural frequency identification and that of free element shapes can be successfully used only in the case of free FE.Thus, when replacing the extended section by one generalized element in solving dynamics problems, it is necessary to be clearly aware of requirements imposed on the generalized element and on this basis choose one or another algorithm for obtaining mass-inertial characteristics, since the result significantly depends on the chosen identification method.

Keywords

• mass matrix
• finite element
• natural frequency
• form function
• mode
• identification
• axisymmetric shell