Flexural stability analysis of stiffened plates using the finite element method

  • Saleema Panda National Institute of Technology
  • Manoranjan Barik National Institute of Technology

Abstract

A four-noded stiffened plate element has been developed which has all the advantages and efficiency of an isoparametric element to model arbitrary shaped plates, but without the disadvantage of the shear-locking problem inherent in the isoparametric element. Another unique feature is that the arbitrary placement of the stiffener inside the plate element is without any restriction of its orientation. The boundary conditions have been incorporated in a general manner so as to accommodate the curved as well as the straight-edged boundaries. The element has been used for stability analysis of arbitrary shaped stiffened plates.


Novelty: In this work, a plate bending element is proposed, which can model any arbitrary shape as efficiently as an isoparametric element. As it does not include the shear deformation, thin plate problems can be considered without any numerical difficulties as observed in isoparametric elements. This element is generalized to accommodate any arbitrary shapes of the plate geometry. The mesh divisions for plates with irregular boundaries using the finite element method are sometimes difficult. However, this element eliminates such complexities as the mesh divisions are done in the mapped square plate. The stiffener is modeled so that it can be of any shape, dispositions and be arbitrarily placed on the plate.

Keywords

arbitrary shape, finite element method, thin plate, stability analysis,

References

[1] A. Adini, R.W. Clough. Analysis of Plate Bending by the Finite Element Method. Report submitted to the National Science Foundation. G7337, 1961.
[2] R.J. Melosh. Basis for derivation of matrices for the direct stiffness method. AIAA Journal, 1: 1631–7, 1963.
[3] M. Barik, M. Mukhopadhyay. Free flexural vibration analysis of arbitrary plates with arbitrary stiffeners. Journal of Vibration and Control, 5: 667–683, 1999.
[4] M. Barik, M. Mukhopadhyay. Finite element free flexural vibration analysis of arbitrary plates. Finite Elements in Analysis and Design, 29: 137–151, 1998.
[5] M. Barik. Finite element static, dynamic and stability analyses of arbitrary stiffened plates. Ph.D. Thesis, Ocean Engineering and Naval Architecture Department, Indian Institute of Technology, Kharagpur, 1999.
[6] O.K. Bedair. A contribution to the stability of stiffened plates under uniform compression. Computers & Structures, 66(5): 535–570, 1998.
[7] C.J. Brown, A.L. Yettram. The elastic stability of stiffened plates using the conjugate load/displacement method. Computers & Structures, 23(3): 385–391, 1986.
[8] B.H. Coburn, Z.Wu, P.M.Weaver. Buckling analysis of stiffened variable angle tow panels. Composite Structures, 111: 259–270, 2014.
[9] P.E. Fenner, A. Watson. Finite element buckling analysis of stiffened plates with filleted junctions. Thin-Walled Structures, 59: 171–180, 2012.
[10] M.W. Guo, I.E. Harik, W.X. Ren. Buckling behavior of stiffened laminated plates. International Journal of Solids and Structures, 39(11): 3039–3055, 2002.
[11] C. Mittelstedt. Closed-form buckling analysis of stiffened composite plates and identification of minimum stiffener requirements. International Journal of Engineering Science, 46(10): 1011–1034, 2008.
[12] T. Mizusawa, T. Kajita, M. Naruoka. Buckling of skew plate structures using B-spline functions. International Journal for Numerical Methods in Engineering, 15(1): 87–96, 1980.
[13] M. Mukhopadhyay. Vibration and stability analysis of stiffened plates by semi-analytic finite difference method, part I: consideration of bending displacements only. Journal of Sound and Vibration, 130(1): 27–39, 1989.
[14] M. Mukhopadhyay, A. Mukherjee. Finite element buckling analysis of stiffened plates. Computers & Structures, 34(6): 795–803, 1990.
[15] S. Panda, M. Barik. Finite element buckling analysis of thin plates with complicated geometry. International Congress and Exhibition “Sustainable Civil Infrastructures: Innovative Infrastructure Geotechnology”, 867–871, 2016.
[16] S.N. Patel, A.H. Sheikh. Buckling response of laminated composite stiffened plates subjected to partial inplane edge loading. International Journal for Computational Methods in Engineering Science and Mechanics, 17(5–6): 322–338, 2016.
[17] L.X. Peng, S. Kitipornchai, K.M. Liew. Analysis of rectangular stiffened plates under uniform lateral load based on FSDT and element-free Galerkin method. International Journal of Mechanical Sciences, 47(2): 251–276, 2005.
[18] L.X. Peng, K.M. Liew, S. Kitipornchai. Buckling and free vibration analyses of stiffened plates using the FSDT mesh-free method. Journal of Sound and Vibration, 289(3): 421–449, 2006.
[19] S. Peng-Cheng, H. Dade, W. Zongmu. Static, vibration and stability analysis of stiffened plates using B-spline functions. Computers & Structures, 27(1): 73–78, 1987.
[20] K. Ramkumar, H. Kang. Finite element based investigation of buckling and vibration behaviour of thin walled box beams. Applied and Computational Mechanics, 7: 155–182, 2013.
[21] R. Rikards, A. Chate, O. Ozolinsh. Analysis for buckling and vibrations of composite stiffened shells and plates. Composite Structures, 51(4): 361–370, 2001.
[22] P. Shi, R.K. Kapania, C.Y. Dong. Vibration and buckling analysis of curvilinearly stiffened plates using finite element method. AIAA Journal, 53(5): 1319–1335, 2015.
[23] S.K. Singh, A. Chakrabarti. Buckling analysis of laminated composite plates using an efficient C0 FE model. Latin American Journal of Solids and Structures, 9(3): 1–13, 2012.
[24] A.K.L. Srivastava, P.K. Datta, A.H. Sheikh. Buckling and vibration of stiffened plates subjected to partial edge loading. International Journal of Mechanical Sciences, 45(1): 73–93, 2003.
[25] A.K.L. Srivastava, P.K. Datta, A.H. Sheikh. Dynamic instability of stiffened plates subjected to non-uniform harmonic in-plane edge loading. Journal of Sound and Vibration, 262(5): 1171–1189, 2003.
[26] A.Y. Tamijani, R.K. Kapania. Buckling and static analysis of curvilinearly stiffened plates using mesh-free method. AIAA Journal, 48(12): 2739–2751, 2010.
[27] S.M. Timoshenko, J.M. Gere. Theory of Elastic Stability, 2nd Edition, McGrawHill International, New York, 1961.
[28] O.C. Zienkiewicz, R.L. Taylor. The Finite Element Method, 4th Edition, McGraw-Hill, 1989.
Published
Mar 25, 2018
How to Cite
PANDA, Saleema; BARIK, Manoranjan. Flexural stability analysis of stiffened plates using the finite element method. Computer Assisted Methods in Engineering and Science, [S.l.], v. 24, n. 3, p. 181–198, mar. 2018. ISSN 2299-3649. Available at: <https://cames.ippt.pan.pl/index.php/cames/article/view/218>. Date accessed: 26 jan. 2022. doi: http://dx.doi.org/10.24423/cames.218.
Section
Articles