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Research Papers

Reducing Dynamic Response Variation Using NURBS Finite Element-Based Geometry Perturbation

[+] Author and Article Information
K. Zhou

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

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 November 1, 2014; final manuscript received June 16, 2015; published online July 23, 2015. Assoc. Editor: Michael Leamy.

J. Vib. Acoust 137(6), 061008 (Jul 23, 2015) (11 pages) Paper No: VIB-14-1421; doi: 10.1115/1.4030902 History: Received November 01, 2014

The uncertainties in real structures usually lead to variations in their dynamic responses. In order to reduce the likelihood of unexpected failures in structures, it is necessary to reduce the response variations. Among various design manipulations, the modification of surface geometry could be a viable option to achieve performance robustness against uncertainties. However, such design modification is difficult to achieve based on conventional finite element methods, primarily due to the inevitable discrepancy between the conventional finite element mesh and the corresponding surface geometry. This issue may become even more severe in design optimization, as an optimized mesh based on conventional finite element analysis may yield nonsmooth surface geometry. In this research, we adopt the nonuniform rational B-splines (NURBS) finite element method to facilitate the robust design optimization (RDO), where the fundamental advantage is that the NURBS finite element mesh is conformal to the underlying NURBS geometry. Furthermore, this conformal feature ensures that, upon finite element-based optimization, the resulting surface geometry is smooth. Taking advantage of that both the uncertainties and the design modifications are small, we formulate a sensitivity-based algorithm to rapidly evaluate the response variations. Based on the direct relation between the response variations and design parameters, the optimal surface geometry that yields the minimal response variation can be identified. Systematic case analyses are carried out to validate the effectiveness and efficiency of the proposed approach.

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Figures

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Fig. 1

(a) Response distribution under structural uncertainties; (b) design objective illustration (left: before design modification and right: after design modification); and (c) design constraint illustration (left: before design modification and right: after design modification)

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Fig. 3

Quadratic NURBS basis functions in x-direction

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Fig. 4

(a) Mesh (120 elements) and (b) control net (528 control points)

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Fig. 5

Original bottom geometry (: fixed control or nodal point and : adjustable control or nodal point—design variable)

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Fig. 6

Modified bottom geometry using (a) NURBS FEM (: fixed control point and : control point moved) and (b) conventional FEM (: fixed nodal point and : nodal point moved)

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Fig. 7

Optimized bottom geometry (zoom-in view)

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Fig. 8

Comparison of displacement response standard deviation versus excitation frequency: (a) before design modification and (b) after design modification (: sensitivity based and : Monte Carlo based)

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Fig. 9

NURBS geometry of wind turbine blade

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Fig. 10

Wind turbine blade model in SolidWorks

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Fig. 11

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

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Fig. 12

xy-planar view (: control point)

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Fig. 13

xz-planar view (: control point)

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Fig. 14

(a) Control points and mesh of cross section in physical space (: control point selected as design variable) and (b) mesh of cross section in parametric space

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Fig. 15

Design objective function versus design parameters (α and A)

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Fig. 16

Optimized cross section geometry (: control points and resulted geometry before design modification and : control points and resulted geometry after design modification)

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Fig. 17

Comparion of stress response standard deviation versus excitation frequency: (a) before design modification and (b) after design modification (: sensitivity based and : Monte Carlo based)

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Fig. 18

Comparison of mean of stress response versus excitation frequency (: before design modification and : after design modification)

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