Implementation of automated multilevel substructuring for frequency response analysis of structures
Kaplan, Matthew Frederick
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In the design of vehicles, such as automobiles, aircraft, spacecraft, or submarines, it is important to be able to accurately predict dynamic behavior of the structure. With the extremely high cost of building physical prototypes of these vehicles, there is a growing emphasis on analysis of computer models. In this dissertation, a method known as Automated Multilevel Substructuring (AMLS) is presented for accurately solving frequency response problems involving large, complex models with millions of degrees of freedom. Conventional methods for addressing these problems, such as mode superposition using a Lanczos eigensolver or model reduction using component mode synthesis, are reviewed. The Automated Multilevel Substructuring (AMLS) method partitions finite element models into substructures, similar to component mode synthesis methods, but uses an automated partitioning procedure that reduces the burden on the analyst. The finite element matrices are projected onto a reduced subspace, on which the frequency response is computed. Two frequency response algorithms are presented. Both methods require the solution of a global eigenvalue problem on the reduced subspace. The first method uses straightforward mode superposition. The second method employs a new iterative approach in which the modal frequency response leads to a residual problem that is solved using an iterative splitting method. The global eigensolution and frequency response algorithms are specifically designed to take advantage of the properties of the reduced subspace. Numerical examples are presented for models with millions of degrees of freedom. The performance and accuracy of the AMLS method are compared to the standard commercial software package for large-scale linear dynamic analysis. These examples establish that AMLS can be used to accurately obtain the response of very large models with significantly less computational resources than competing methods. In comparison to the modal frequency response obtained with the standard commercial software package using a shifted block Lanczos algorithm, AMLS ran up to 6.4 times faster, used less memory, and required an order of magnitude less data transfer. Thus, the AMLS method makes it possible to do frequency response analysis of large, complex structures at higher frequencies than was previously practical.