Introduction to Aircraft Aeroelasticity and Loads

D

Model Condensation

The idea of model condensation is that the size of a static or dynamic model in either physical or modal space may be reduced in size and a faster solution obtained with a limited penalty in accuracy. In this appendix, the basic ideas will be illustrated primarily for a physical model (see Chapter 22 for application), but the concept extends to a modal model and this will be commented upon.

D.1 INTRODUCTION

For complex structures such as aircraft, the FE model can be extremely large; a static solution may be readily carried out, but a dynamic solution, such as determining eigenvalues or response, is often preceded by some form of physical ‘condensation’, or model order reduction.

Firstly, consider the physical equations of motion for an FE model of order N:

where M, K are the mass and the stiffness matrices (N × N), r is the displacement vector and R is the vector of applied forces. Now consider dividing the displacements into ‘master’ (N_m) and ‘slave’ (N_s) degrees of freedom r_m, r_s, where normally . The master DoFs are those that are to be retained in the analysis, while the slave DoFs are to be removed by physical condensation for the initial analysis, but estimates of the slave DoFs can be recovered later. There are two types of condensation, static and dynamic. ...