PROJECTION METHOD IN STRUCTURAL DYNAMICS IN APPLICATION TO SHOCK PROPAGATION SIMULATION FOR TRUSS COUPLED SHELL STRUCTURES

摘要

The projection method is known as a mathematical method to couple dynamical systems by algebraic constraints. Therewith it is used as a substructure coupling technique. Furthermore it is derived consistently from the Lagrange multipliers technique, which has been already used successfully in structural dynamics. The common and conventional technique in structural dynamics for the coupling of large mathematical models is the application of model reduction combined with a following component mode synthesis. Those provide matrices for the important modes and physical degrees of freedom at the interfaces. A considerable engineering and numerical effort to establish the reduced models and running the solution is necessary. In addition the models information is reduced and redoing the engineers modelling work is required, if the quality needs to be improved or if a new interface has to be established. Despite of this disadvantage, this approach is sensible, because it is embedded in a successful and global solution strategy. The new technique takes advantage from the use of the projection method, based on the DRAZIN inverse. In contrast to the application of reduction methods, the projection method keeps the original matrices. Therefore optimized algorithms for band matrix models - or other efficient mathematical model presentation - are retained for the solution. In addition no model information will be lost and no engineering effort to establish reduced models is necessary. An algorithm well suited for this technique is implemented in SYSTEM V. System V is a tool used at EADS in-house in the past for European and International launcher projects. It serves for the prediction of wave propagation and vibration induced by mechanical or pyrotechnical shock in axis-symmetrical shell structures. The fact that SYSTEM V works with Fourier degrees of freedom on axi-symmetrical structures delivers small decoupled band matrix systems, which are solved very efficiently, even for a very fine grid. Therewith shock analysis up to a frequency of 20 kHz is possible. The new and the conventional technique has been implemented in SYSTEM V for first numerical tests on a generic launcher tank-truss-tank structure. The first experience with this method will be communicated herewith. It shall be noted that with this development tank fluid has been added to the simulation by a Navier-Stokes model in moving least square particle approximation [3]. This will be subject to an accompanying paper. This paper introduces to the projection method and presents first results. An outlook will be given for future application.