STUDY ON AN INTEGRATION OF THE NODAL CONDENSATION METHOD INTO THE FINITE ELEMENTS ANALYSIS TOOLS

Abstract

The modern intertial navigation devices often utilize elastic suspension based sensitive elements. In general elastic suspension has a complicated structure, and its optimization requires numerous calculations for various parameters, such as stiffness characteristics. The major contribution to the solution of the above optimization problem is brought by highly effective nodal condensation method. This method however is often overcomplicated by difficulties in the analytical determinization of stiffness matrixes of the elastic elements. Furthermore, it is even impossible to perform exact calculations in some cases.On countrary to the nodal condensation method, the finite elements analysis tools provide inexact solutions to the optimization problems, and thus can be applied for elastic elements of even complicated structure. The disadvantages of the finite elements method is in large computational resourses required for the calculations, and in the absence of the preprocessing analytical structural analysis that might simplify the following calculations.Hence the research on the possible integration of the nodal condensation method into the finite-elements analysis tools is of the primary importance for the handling of the complicated designs.In this work, we investigate the results of the aformentioned integration for the stiffness characteristics analysis of the micromechanical tuning-fork gyroscopes.More precisely, stiffness characteristics and the computation of the loads on the individual elastic elements are proposed to compute using the equations of the nodal condensation method. After the individual characteristics are calculated, the finite-elements method is used to compute the optimal stiffness characteristics for the elastic element.Combination of the nodal condensation method and the finite elements method, was applied for the calculation of the stiffness characteristics of the micromechanical tuning-fork gyroscope. It showed better performance compare to their separate application, thus proving its effectiveness.Analysis of the results obtained in the conducted investigation provides a conclusion of the principal superiority of the proposed method. It allows to improve the precision of the obtained optimal solution, and to reduce the computational effort.In summary, proposed method gives an opportunity of utilizing strong sides of both nodal condensation method and finite elements method for the analysis of the application of different loads on the individual elements of the mechanical design.