Combining Test-Based and Finite Element-Based Models in NASTRAN

Components often exist within critical load paths of complex systems that are not readily modeled with conventional finite element techniques. Furthermore, the owner of the system model often has no design authority or interest in some components other than their effects on the remaining system. Frequency dependent stiffness and damping for these components can also significantly add to the modeling difficulty. This article describes a process for combining test-based and finite element-based models in NASTRAN that circumvents many of these limitations. Advantages of including test-based models within a complex system model include: (1) It is generally faster and more accurate to develop a test-based model than a finite element-based model; (2) Computer run times and computer resources are reduced; and (3) Minimizing errors, which are frequently present in complex system models, is possible. In this combined analysis approach, test-based models are determined using admittance modeling. A test-based model for the component’s dynamics is derived at the locations where it interfaces with the system finite element model. This model is then converted into a NASTRAN readable format and analytically coupled to the finite element model, enabling prediction of the combined system response. Several examples are presented to demonstrate the efficacy of this approach. A brief introduction to admittance modeling 1 is presented as background for the work referenced in this article. Admittance modeling is a mathematical technique where subsystems can be combined or separated in a building-block approach by using accelerance (acceleration over force) frequency response functions (FRFs). An example is shown in Figure 1, where we have two structures (A and B) joined at a single point. The desired subsystem FRFs are H B , the base structure. The FRFs for the add-on structure are H A and represent all of the required test fixtures. The combined structure, H C , is the total system. It is straightforward to derive the relationships between driving-point FRFs where each FRF is the ratio of the acceleration response to the input force at the connection point of each structure. At a given frequency, H A , H B and H C are 6 ¥ 6 matrices of complex numbers that are the ratio of the six acceleration responses (three translational and three rotational) at the connection point due to each of the six input forces (three forces and three moments) applied at the connection point. For an applied force (f C ) at the connection point, force equilibrium requires that f C = f A + f B , where f A and f B are the forces on structures A and B at the connection point. Since compatibility at the connection point requires that a A = a B = a C , we can divide the force equation by acceleration to rewrite it in terms of FRFs (H = a/f) as