DOF Reduction Strategy for Large Order Finite Element Models Robert N. Coppolino, CTO Measurement Analysis Corporation 23850 Madison Street Torrance, California 90505 ABSTRACT State-of-the-art technologies in computation and software have led to ever increasing size of finite element models, simply because this is possible. While it is arguable that “degree-of-freedom” proliferation is unnecessary, there are some potential benefits to be realized, namely (1) commonality of stress and dynamic models and (2) employment of finite element models in the mid- and high-frequency ranges (normally the domain of statistical energy analysis). The conventional approach to Test Analysis Model (TAM) definition for modal testing is based on Guyan Reduction. The strategy encounters severe difficulties (due to Boussinesq type singularities) when shell and 3-D elasticity elements are used to build a finite element model (FEM). This paper describes a “load-patch” variation of Guyan Reduction that alleviates 3-D problematic singularities. Two illustrative examples are used to demonstrate advantages and benefits of the new TAM definition procedure. 1. INTRODUCTION Finite element models of modern structural systems, such as aircraft, spacecraft, and automobiles, are typically composed of thousands to millions of grid points due to the sophistication of commercial CAE software products and mechanical (static and dynamic) fidelity requirements[1,2]. During the 1960’s model order reduction methods, based on the Rayleigh-Ritz method[3] were introduced for computation of “large order” system normal modes. The two prominent reduction methods that are popular to this day are (1) Guyan Reduction[4] and the Craig-Bampton method[5]. In the decade that followed, iterative methods[6,7] that treated large, sparse eigenvalue problems, were developed and became widely accepted. While mathematical methods for treating very large order dynamic finite element models are quite mature, the need for reduced order models (commonly called Test-Analysis Models or TAMs) persists in modal testing applications[8]. This is due to the fact that models of an order consistent with modal test instrumentation are required (predominantly in aerospace applications) for test data quality evaluation and test-analysis correlation. The most widely accepted method employed for definition of TAMs is Guyan Reduction. For many years following the introduction of Guyan Reduction in 1965, finite element models were typically composed of one- and two-dimensional finite elements based upon technical theory (e.g., beams, plates and shells). Static deflection shape functions produced by application of point loads (the basis of Guyan Reduction) were typically smooth and “sensible”. Increasing utilization of three dimensional finite elements in structural dynamic models in recent years has led to a critical difficulty in the development of TAMs due to poorly defined shape functions. The present paper formally introduces a “new” model order reduction approach that is based upon application of distributed load patches to define reasonable deflection has been used by others in a variety of applications, without being “formalized” as a general reduction strategy). This “new” reduction procedure, while conceptually similar to Guyan Reduction, produces accurate, consistent TAMs when one-, twoand three-dimensional finite elements are employed to define the dynamic finite element model. T. Proulx (ed.), Linking Models and Experiments, Volume 2, Conference Proceedings of the Society for Experimental Mechanics Series 5, DOI 10.1007/978-1-4419-9305-2_25, © The Society for Experimental Mechanics, Inc. 2011 shape functions (Note that “new” is deliberately placed in quotes by the author, since it is believed that the load patch method 359
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