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Title: Modal Substructuring of Geometrically Nonlinear Finite Element Models with Interface Reduction

Abstract

Substructuring methods have been widely used in structural dynamics to divide large, complicated finite element models into smaller substructures. For linear systems, many methods have been developed to reduce the subcomponents down to a low order set of equations using a special set of component modes, and these are then assembled to approximate the dynamics of a large scale model. In this paper, a substructuring approach is developed for coupling geometrically nonlinear structures, where each subcomponent is drastically reduced to a low order set of nonlinear equations using a truncated set of fixedinterface and characteristic constraint modes. The method used to extract the coefficients of the nonlinear reduced order model (NLROM) is non-intrusive in that it does not require any modification to the commercial FEA code, but computes the NLROM from the results of several nonlinear static analyses. The NLROMs are then assembled to approximate the nonlinear differential equations of the global assembly. The method is demonstrated on the coupling of two geometrically nonlinear plates with simple supports at all edges. The plates are joined at a continuous interface through the rotational degrees-of-freedom (DOF), and the nonlinear normal modes (NNMs) of the assembled equations are computed to validate the models.more » The proposed substructuring approach reduces a 12,861 DOF nonlinear finite element model down to only 23 DOF, while still accurately reproducing the first three NNMs of the full order model.« less

Authors:
 [1];  [2];  [3]
  1. Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
  2. Univ. of Wisconsin, Madison, WI (United States). Dept. of Engineering Physics
  3. Air Force Research Lab. (AFRL), Wright-Patterson AFB, OH (United States)
Publication Date:
Research Org.:
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
Sponsoring Org.:
US Air Force Office of Scientific Research (AFOSR); USDOE National Nuclear Security Administration (NNSA)
OSTI Identifier:
1360796
Report Number(s):
SAND-2016-2065J
Journal ID: ISSN 0001-1452; 619965
Grant/Contract Number:
AC04-94AL85000; FA9550-11-1-0035
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
AIAA Journal
Additional Journal Information:
Journal Volume: 55; Journal Issue: 5; Journal ID: ISSN 0001-1452
Publisher:
AIAA
Country of Publication:
United States
Language:
English
Subject:
42 ENGINEERING; substructuring; component mode synthesis; geometric nonlinearity; interface reduction; nonlinear normal modes

Citation Formats

Kuether, Robert J., Allen, Matthew S., and Hollkamp, Joseph J. Modal Substructuring of Geometrically Nonlinear Finite Element Models with Interface Reduction. United States: N. p., 2017. Web. doi:10.2514/1.J055215.
Kuether, Robert J., Allen, Matthew S., & Hollkamp, Joseph J. Modal Substructuring of Geometrically Nonlinear Finite Element Models with Interface Reduction. United States. doi:10.2514/1.J055215.
Kuether, Robert J., Allen, Matthew S., and Hollkamp, Joseph J. Wed . "Modal Substructuring of Geometrically Nonlinear Finite Element Models with Interface Reduction". United States. doi:10.2514/1.J055215. https://www.osti.gov/servlets/purl/1360796.
@article{osti_1360796,
title = {Modal Substructuring of Geometrically Nonlinear Finite Element Models with Interface Reduction},
author = {Kuether, Robert J. and Allen, Matthew S. and Hollkamp, Joseph J.},
abstractNote = {Substructuring methods have been widely used in structural dynamics to divide large, complicated finite element models into smaller substructures. For linear systems, many methods have been developed to reduce the subcomponents down to a low order set of equations using a special set of component modes, and these are then assembled to approximate the dynamics of a large scale model. In this paper, a substructuring approach is developed for coupling geometrically nonlinear structures, where each subcomponent is drastically reduced to a low order set of nonlinear equations using a truncated set of fixedinterface and characteristic constraint modes. The method used to extract the coefficients of the nonlinear reduced order model (NLROM) is non-intrusive in that it does not require any modification to the commercial FEA code, but computes the NLROM from the results of several nonlinear static analyses. The NLROMs are then assembled to approximate the nonlinear differential equations of the global assembly. The method is demonstrated on the coupling of two geometrically nonlinear plates with simple supports at all edges. The plates are joined at a continuous interface through the rotational degrees-of-freedom (DOF), and the nonlinear normal modes (NNMs) of the assembled equations are computed to validate the models. The proposed substructuring approach reduces a 12,861 DOF nonlinear finite element model down to only 23 DOF, while still accurately reproducing the first three NNMs of the full order model.},
doi = {10.2514/1.J055215},
journal = {AIAA Journal},
number = 5,
volume = 55,
place = {United States},
year = {Wed Mar 29 00:00:00 EDT 2017},
month = {Wed Mar 29 00:00:00 EDT 2017}
}

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Free Publicly Available Full Text
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  • 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 amore » 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 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.« less
  • Hot bar heat loss in the transfer table, the rolling stage between rougher stands and finishing stands in a hot mill, is of major concern for reasons for energy consumption, metallurgical uniformity, and rollability. A mathematical model, as well as the corresponding numerical solution, is presented for the evolution of temperature in a coiling and uncoiling bar in hot mills in the form of a parabolic partial differential equation for a shape-changing domain. The space discretization is achieved via a computationally efficient geometrically adaptive finite element scheme that accommodates the change in shape of the domain, using a computationally novelmore » treatment of the resulting thermal contact problem due to coiling. Time is discretized according to a Crank-Nicolson scheme. Finally, some numerical results are presented.« less
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