Modal Substructuring of Geometrically Nonlinear FiniteElement Models
The efficiency of a modal substructuring method depends on the component modes used to reduce each subcomponent model. Methods such as Craig–Bampton have been used extensively to reduce linear finiteelement models with thousands or even millions of degrees of freedom down orders of magnitude while maintaining acceptable accuracy. A novel reduction method is proposed here for geometrically nonlinear finiteelement models using the fixedinterface and constraint modes of the linearized system to reduce each subcomponent model. The geometric nonlinearity requires an additional cubic and quadratic polynomial function in the modal equations, and the nonlinear stiffness coefficients are determined by applying a series of static loads and using the finiteelement code to compute the response. The geometrically nonlinear, reduced modal equations for each subcomponent are then coupled by satisfying compatibility and force equilibrium. This modal substructuring approach is an extension of the Craig–Bampton method and is readily applied to geometrically nonlinear models built directly within commercial finiteelement packages. The efficiency of this new approach is demonstrated on two example problems: one that couples two geometrically nonlinear beams at a shared rotational degree of freedom, and another that couples an axial spring element to the axial degree of freedom of a geometrically nonlinearmore »
 Authors:

^{[1]};
^{[2]};
^{[3]}
 Sandia National Lab. (SNLNM), Albuquerque, NM (United States)
 Univ. of Wisconsin, Madison, WI (United States)
 Air Force Research Lab. (AFRL), WrightPatterson AFB, OH (United States)
 Publication Date:
 Report Number(s):
 SAND20158622J
Journal ID: ISSN 00011452; 619965
 Grant/Contract Number:
 AC0494AL85000
 Type:
 Accepted Manuscript
 Journal Name:
 AIAA Journal
 Additional Journal Information:
 Journal Volume: 54; Journal Issue: 2; Journal ID: ISSN 00011452
 Publisher:
 AIAA
 Research Org:
 Sandia National Lab. (SNLNM), Albuquerque, NM (United States)
 Sponsoring Org:
 USDOE; US Air Force Office of Scientific Research (AFOSR)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 97 MATHEMATICS AND COMPUTING
 OSTI Identifier:
 1339293
Kuether, Robert J., Allen, Matthew S., and Hollkamp, Joseph J.. Modal Substructuring of Geometrically Nonlinear FiniteElement Models. United States: N. p.,
Web. doi:10.2514/1.J054036.
Kuether, Robert J., Allen, Matthew S., & Hollkamp, Joseph J.. Modal Substructuring of Geometrically Nonlinear FiniteElement Models. United States. doi:10.2514/1.J054036.
Kuether, Robert J., Allen, Matthew S., and Hollkamp, Joseph J.. 2015.
"Modal Substructuring of Geometrically Nonlinear FiniteElement Models". United States.
doi:10.2514/1.J054036. https://www.osti.gov/servlets/purl/1339293.
@article{osti_1339293,
title = {Modal Substructuring of Geometrically Nonlinear FiniteElement Models},
author = {Kuether, Robert J. and Allen, Matthew S. and Hollkamp, Joseph J.},
abstractNote = {The efficiency of a modal substructuring method depends on the component modes used to reduce each subcomponent model. Methods such as Craig–Bampton have been used extensively to reduce linear finiteelement models with thousands or even millions of degrees of freedom down orders of magnitude while maintaining acceptable accuracy. A novel reduction method is proposed here for geometrically nonlinear finiteelement models using the fixedinterface and constraint modes of the linearized system to reduce each subcomponent model. The geometric nonlinearity requires an additional cubic and quadratic polynomial function in the modal equations, and the nonlinear stiffness coefficients are determined by applying a series of static loads and using the finiteelement code to compute the response. The geometrically nonlinear, reduced modal equations for each subcomponent are then coupled by satisfying compatibility and force equilibrium. This modal substructuring approach is an extension of the Craig–Bampton method and is readily applied to geometrically nonlinear models built directly within commercial finiteelement packages. The efficiency of this new approach is demonstrated on two example problems: one that couples two geometrically nonlinear beams at a shared rotational degree of freedom, and another that couples an axial spring element to the axial degree of freedom of a geometrically nonlinear beam. The nonlinear normal modes of the assembled models are compared with those of a truth model to assess the accuracy of the novel modal substructuring approach.},
doi = {10.2514/1.J054036},
journal = {AIAA Journal},
number = 2,
volume = 54,
place = {United States},
year = {2015},
month = {12}
}