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Research Papers

Component Mode Synthesis Order-Reduction for Dynamic Analysis of Structure Modeled With NURBS Finite Element

[+] Author and Article Information
K. Zhou

Department of Mechanical Engineering,
University of Connecticut,
191 Auditorium Road, Unit 3139,
Storrs, CT 06269

G. Liang

Associate Professor
Laboratory Management Division,
Shanghai Maritime University,
Shanghai 201306, China

J. Tang

Professor
Department of Mechanical Engineering,
University of Connecticut,
191 Auditorium Road, Unit 3139,
Storrs, CT 06269
e-mail: jtang@engr.uconn.edu

1Corresponding author.

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received September 9, 2015; final manuscript received December 5, 2015; published online February 3, 2016. Assoc. Editor: Michael Leamy.

J. Vib. Acoust 138(2), 021016 (Feb 03, 2016) (15 pages) Paper No: VIB-15-1371; doi: 10.1115/1.4032516 History: Received September 09, 2015; Revised December 05, 2015

Nonuniform rational B-splines (NURBS) finite element has advantages in analyzing the structure with curved surface geometry. In this research, we develop a component mode synthesis (CMS) based order-reduction technique which can be applied to large-scale NURBS finite element dynamic analysis. In particular, we establish a new substructure division scheme. The underlying idea is to optimally construct interface between adjacent substructures that can maximize the geometry consistency between the original structure and the divided substructures and at the meantime facilitate the compatibility conditions needed in mode synthesis. Case studies are carried out to validate the performance of the order-reduction formulation.

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Figures

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Fig. 1

Substructure division illustration: (a) conventional finite element model with existing interface (: nodal point); (b) NURBS finite element model with arbitrarily constructed interface (: control point; : inserted control point); and (c) NURBS finite element model with optimized interface (: control point; : inserted control point)

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Fig. 2

Two types of curves: (a) type 1 curve and (b) type 2 curve (: control point)

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Fig. 3

Geometry comparison when inserted control point is close to the original second control point: (a) inserted control point with nonoptimal coordinates and (b) inserted control point with optimized coordinate

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Fig. 4

Geometry comparison when control point is inserted between the second and third original control points

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Fig. 5

Flowchart of substructure division procedure

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Fig. 6

NURBS geometry of wind turbine blade

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Fig. 7

yz-planar view: airfoil cross section (: control point)

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Fig. 8

xz-planar view and interface definition (: control point and : existing interface)

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Fig. 9

xy-planar view and inserted control points with uniformly selected x coordinates (: control point; : inserted control point; and : constructed interface)

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Fig. 10

(a) Illustration of constructed interface in a zoom in view and (b) projection of concerned geometry onto the xz-plane with an M×N grid. The y-coordinates of the surface at grid points describe the geometry.

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Fig. 11

Comparison of first three z-direction bending mode shapes: (a) full-scale analysis and (b) order-reduced analysis with optimal interface construction (S2)

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Fig. 12

Absolute errors of first three z-direction bending mode shapes under different interface constructions: (a) S1, (b) S2, and (c) S3

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Fig. 13

Absolute errors at interface cross section of the second mode shape under different interface constructions (: S1; : S2; and : S3)

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Fig. 14

Comparison of first three z-direction modal stresses: (a) full-scale analysis and (b) order-reduced analysis with optimal interface construction (S2)

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Fig. 15

Comparison of first three z-direction modal stresses under different interface constructions: (a) S1, (b) S3, and (c) extreme case

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Fig. 16

Modal stresses at interface cross section for the third mode shape under different interface constructions (: S1; : S2; : S3; *: extreme case)

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Fig. 17

Natural frequency truncation error in log-scale with respect to different numbers of kept modes (: 10 kept modes; : 20 kept modes; : 30 kept modes; and : 40 kept modes)

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