Reduction of finite element models employing inclusion principle

The overlapping expansion/contraction method has been developed by Ikeda and Siljak[1] to simplify the decentralized control design. This method expands a given interconnected system to yield a larger model which now consists of disjointed subsystems - the expanded model is said to include the original model if certain conditions are satisfied. Recently, as an extension of the inclusion principle to matrix-second-order systems, the existence of an expanded system in a matrix-second-order form has been established by the authors[2]. The subsystems comprising this expanded system can then be obtained in standard matrix-second-order form. The aim of this paper is to show the applicability of these results to order(model) reduction of finite element models of flexible structures. Specifically, we will show that the above subsystems can be directly obtained from the elemental equations (requiring neither the expanded system nor the original assembled set of equations) of the structure. This naturally results in substantial saving in computations and computer memory.