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Title: Modal Substructuring of Geometrically Nonlinear Finite-Element 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 finite-element 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 finite-element models using the fixed-interface 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 finite-element 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 finite-element 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 » 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.« less
Authors:
 [1] ;  [2] ;  [3]
  1. Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
  2. Univ. of Wisconsin, Madison, WI (United States)
  3. Air Force Research Lab. (AFRL), Wright-Patterson AFB, OH (United States)
Publication Date:
OSTI Identifier:
1259510
Report Number(s):
SAND--2015-8622J
Journal ID: ISSN 0001-1452; 607377
Grant/Contract Number:
AC04-94AL85000
Type:
Accepted Manuscript
Journal Name:
AIAA Journal
Additional Journal Information:
Journal Volume: 54; Journal Issue: 2; Journal ID: ISSN 0001-1452
Publisher:
AIAA
Research Org:
Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States)
Sponsoring Org:
AFSOR; USDOE
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING