0
Research Papers

Large Amplitude Free Flexural Vibration of Stiffened Plates Using Superparametric Element

[+] Author and Article Information
Saleema Panda

Department of Civil Engineering,
National Institute of Technology,
Rourkela 769008, India
e-mail: saleema.panda@gmail.com

Manoranjan Barik

Department of Civil Engineering,
National Institute of Technology,
Rourkela 769008, India
e-mail: manoranjanbarik@yahoo.co.in

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received May 27, 2016; final manuscript received August 27, 2016; published online December 5, 2016. Assoc. Editor: Javier Cuadrado.

J. Comput. Nonlinear Dynam 12(3), 031013 (Dec 05, 2016) (9 pages) Paper No: CND-16-1251; doi: 10.1115/1.4034679 History: Received May 27, 2016; Revised August 27, 2016

The present paper studies the nonlinear free flexural vibration of stiffened plates. The analysis is performed using a superparametric element. This element consists of an ACM plate-bending element along with in-plane displacements to represent the displacement field, and cubic serendipity shape function is used to define the geometry. The element can accommodate any arbitrary geometry, and the stiffeners either straight or curvilinear are modeled such that these can be placed anywhere on the plate. A number of numerical examples are presented to show its efficacy.

FIGURES IN THIS ARTICLE
<>
Copyright © 2017 by ASME
Your Session has timed out. Please sign back in to continue.

References

Prathap, G. , and Varadan, T. K. , 1978, “ Large Amplitude Flexural Vibration of Stiffened Plates,” J. Sound Vib., 57(4), pp. 583–593. [CrossRef]
Varadan, T. K. , and Pandalai, K. A. V. , 1979, “ Large Amplitude Flexural Vibration of Eccentrically Stiffened Plates,” J. Sound Vib., 67(3), pp. 329–340. [CrossRef]
Khalil, M. R. , Olson, M. D. , and Anderson, D. L. , 1988, “ Nonlinear Dynamic Analysis of Stiffened Plates,” Comput. Struct., 29(6), pp. 929–941. [CrossRef]
Rao, S. R. , Sheikh, A. H. , and Mukhopadhyay, M. , 1993, “ Large-Amplitude Finite Element Flexural Vibration of Plates/Stiffened Plates,” J. Acoust. Soc. Am., 93(6), pp. 3250–3257. [CrossRef]
Sheikh, A. H. , and Mukhopadhyay, M. , 1996, “ Large Amplitude Free Flexural Vibration of Stiffened Plates,” AIAA J., 34(11), pp. 2377–2383. [CrossRef]
Sheikh, A. H. , and Mukhopadhyay, M. , 2000, “ Geometric Nonlinear Analysis of Stiffened Plates by the Spline Finite Strip Method,” Comput. Struct., 76(6), pp. 765–785. [CrossRef]
Sheikh, A. H. , and Mukhopadhyay, M. , 2002, “ Linear and Nonlinear Transient Vibration Analysis of Stiffened Plate Structures,” Finite Elem. Anal. Des., 38(6), pp. 477–502. [CrossRef]
Kolli, M. , and Chandrashekhara, K. , 1997, “ Non-Linear Static and Dynamic Analysis of Stiffened Laminated Plates,” Int. J. Non-Linear Mech., 32(1), pp. 89–101. [CrossRef]
Kim, Y. , Jung, S.-K. , and White, D. W. , 2007, “ Transverse Stiffener Requirements in Straight and Horizontally Curved Steel I-Girders,” J. Bridge Eng., 12(2), pp. 174–183. [CrossRef]
Mitra, A. , Sahoo, P. , and Saha, K. , 2011, “ Mechanics of Materials and Structures,” J. Mech. Mater. Struct., 6(6), pp. 883–914. [CrossRef]
Abdelali, H. M. , Bikri, K. E. , and Benamar, R. , 2012, “ The Effects of Large Vibration Amplitudes on the Mode Shapes and Natural Frequencies of Thin Isotropic Skew Plates,” MATEC Web of Conferences, Vol. 1, p. 10004.
Ma, N. , Wang, R. , and Li, P. , 2012, “ Nonlinear Dynamic Response of a Stiffened Plate With Four Edges Clamped Under Primary Resonance Excitation,” Nonlinear Dyn., 70(1), pp. 627–648. [CrossRef]
Saheb, A. K. M. , and Rao, B. G. V. , 2014, “ Large Amplitude Free Vibrations of Mindlin Square Plates: A Novel Formulation,” Int. J. Curr. Eng. Technol., 2, pp. 544–548. [CrossRef]
Askari, H. , Saadatnia, Z. , Esmailzadeh, E. , and Younesian, D. , 2014, “ Multi-Frequency Excitation of Stiffened Triangular Plates for Large Amplitude Oscillations,” J. Sound Vib., 333(22), pp. 5817–5835. [CrossRef]
Adini, A. , and Clough, R. W. , 1961, “ Analysis of Plate Bending by the Finite Element Method,” National Science Foundation, Report No. G7337.
Melosh, R. J. , 1963, “ Basis for Derivation of Matrices for the Direct Stiffness Method,” AIAA J., 1(7), pp. 1631–1637. [CrossRef]
Zienkiewich, O. C. , and Taylor, R. L. , 1989, The Finite Element Method, 4th ed., McGraw-Hill, London.
Barik, M. , and Mukhopadhyay, M. , 1998, “ Finite Element Free Flexural Vibration Analysis of Arbitrary Plates,” Finite Elem. Anal. Des., 29(2), pp. 137–151. [CrossRef]
Mukhopadhyay, M. , and Sheikh, A. H. , 2004, Matrix and Finite Element Analyses of Structures, Ane Books, New Delhi, Chap. 17.
Mallet, R. , and Marcal, P. , 1968, “ Finite Element Analysis of Nonlinear Structures,” J. Struct. Div. ASCE, 94(9), pp. 2081–2105. http://cedb.asce.org/CEDBsearch/record.jsp?dockey=0015755
Barik, M. , and Mukhopadhyay, M. , 2002, “ A New Stiffened Plate Element for the Analysis of Arbitrary Plates,” Thin-Walled Struct., 40(7–8), pp. 625–639. [CrossRef]
Han, W. , and Petyt, M. , 1997, “ Geometrically Nonlinear Vibration Analysis of Thin, Rectangular Plates Using the Hierarchical Finite Element Method-I: The Fundamental Mode of Isotropic Plates,” Comput. Struct., 63(2), pp. 295–308. [CrossRef]
Corr, R. B. , and Jennings, E. , 1976, “ A Simultaneous Iteration Algorithm for Solution of Symmetric Eigenvalue Problem,” Int. J. Numer. Methods Eng., 10(3), pp. 647–663. [CrossRef]
Sheikh, A. H. , 1992, “ Linear and Nonlinear Analysis of Stiffened Plates Under Static and Dynamic Loading by the Finite Strip Method,” Ph.D., thesis, Indian Institute of Technology, Kharagpur, India.

Figures

Grahic Jump Location
Fig. 1

Mapping of arbitrary geometry into a square domain in s–t plane

Grahic Jump Location
Fig. 2

Mapping of element into a square domain in ξ−η plane

Grahic Jump Location
Fig. 3

Coordinate axes at any point of a curved stiffener

Grahic Jump Location
Fig. 4

Coordinate axes at any point of an elastically restrained curved boundary

Grahic Jump Location
Fig. 5

A typical 8 × 8 mesh discretization with boundary nodes of cross-stiffened square plate

Grahic Jump Location
Fig. 6

Cross section of type 1 stiffener

Grahic Jump Location
Fig. 7

A typical 4 × 4 mesh discretization with boundary nodes of straight stiffened rectangular plate

Grahic Jump Location
Fig. 8

A typical 8 × 8 mesh discretization with boundary nodes of curved stiffened rectangular plate

Grahic Jump Location
Fig. 9

Cross section of type 2 stiffener

Grahic Jump Location
Fig. 10

A typical 8 × 8 mesh discretization with boundary nodes of straight stiffened skew plate

Grahic Jump Location
Fig. 11

A typical 8 × 8 mesh discretization with boundary nodes of arbitrary stiffened circular plate

Grahic Jump Location
Fig. 12

A typical 8 × 8 mesh discretization with boundary nodes of annular stiffened plate

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In