Skip to main content
Top
Published in: Meccanica 10/2013

01-12-2013

Elastic stability of all edges clamped stepped and stiffened rectangular plate under uni-axial, bi-axial and shearing forces

Authors: A. John Wilson, S. Rajasekaran

Published in: Meccanica | Issue 10/2013

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

The stability of clamped stepped and stiffened rectangular plate subjected to in-plane forces is examined. The plate is divided into 900 rectangular meshes and the partial derivatives are approximated using central difference formula. Altogether 841 equations of equilibrium and 248 equations representing boundary conditions are formed, finally leading to the solution of eigenvalue problem. The buckling coefficients are calculated for various types of stepped plates and the results are presented in tables for ready use by designers. The results are compared with the published results and they are in close agreement.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Literature
1.
go back to reference Timoshenko SP, Gere JM (1961) Theory of elastic stability. McGraw-Hill, New York Timoshenko SP, Gere JM (1961) Theory of elastic stability. McGraw-Hill, New York
2.
go back to reference Allen HB, Bulson PS (1980) Background to buckling. McGraw-Hill, London Allen HB, Bulson PS (1980) Background to buckling. McGraw-Hill, London
3.
go back to reference Szilard R (2004) Theory and applications of plate analysis—classical and numerical and engineering methods. Wiley, New York Szilard R (2004) Theory and applications of plate analysis—classical and numerical and engineering methods. Wiley, New York
4.
go back to reference Azhari M (1993) Local and post-local buckling of plates and plate assemblies using finite strip method. Ph.D. thesis, The University of New South Wales Kensington Azhari M (1993) Local and post-local buckling of plates and plate assemblies using finite strip method. Ph.D. thesis, The University of New South Wales Kensington
5.
go back to reference Wittrick WH, Ellen CH (1962) Buckling of tapered rectangular plates in compression. Aeronaut Q 13:308–326 Wittrick WH, Ellen CH (1962) Buckling of tapered rectangular plates in compression. Aeronaut Q 13:308–326
6.
go back to reference Navaneethakrishnan PV (1968) Buckling of nonuniform plates: spline method. J Eng Mech 114(5):893–898 CrossRef Navaneethakrishnan PV (1968) Buckling of nonuniform plates: spline method. J Eng Mech 114(5):893–898 CrossRef
7.
go back to reference Chung MS, Cheung YK (1971) Natural vibration of thin flat walled structures with different boundary conditions. J Sound Vib 18(3):325–337 ADSCrossRef Chung MS, Cheung YK (1971) Natural vibration of thin flat walled structures with different boundary conditions. J Sound Vib 18(3):325–337 ADSCrossRef
9.
go back to reference Chehil DS, Dua SS (1973) Buckling of rectangular plates with general variation in thickness. J Appl Mech, Trans ASME 40:745–751 CrossRef Chehil DS, Dua SS (1973) Buckling of rectangular plates with general variation in thickness. J Appl Mech, Trans ASME 40:745–751 CrossRef
10.
go back to reference Hwang SS (1973) Stability of plats with piecewise varying thickness. J Appl Mech, Trans ASME 40(4):1127–1128 CrossRef Hwang SS (1973) Stability of plats with piecewise varying thickness. J Appl Mech, Trans ASME 40(4):1127–1128 CrossRef
11.
go back to reference Hancock GJ (1978) Local distortional and lateral buckling of I beams. J Struct Div 104(ST11):1787–1798 Hancock GJ (1978) Local distortional and lateral buckling of I beams. J Struct Div 104(ST11):1787–1798
12.
go back to reference Chen WF, Lui EM (1987) Structural stability theory and implementation. Elsevier, New York Chen WF, Lui EM (1987) Structural stability theory and implementation. Elsevier, New York
13.
go back to reference Singh JP, Dey SS (1990) Variational finite difference approach to buckling of plates of variable thickness. Comput Struct 36:39–45 CrossRefMATH Singh JP, Dey SS (1990) Variational finite difference approach to buckling of plates of variable thickness. Comput Struct 36:39–45 CrossRefMATH
14.
go back to reference Harik IE, Liu X, Ekambaram R (1991) Elastic stability of plats with varying rigidities. Comput Struct 38:161–168 CrossRefMATH Harik IE, Liu X, Ekambaram R (1991) Elastic stability of plats with varying rigidities. Comput Struct 38:161–168 CrossRefMATH
15.
go back to reference Subramanian K, Elangovan A, Rajkumar R (1993) Elastic stability of varying thickness plates using the finite element method. Comput Struct 48(4):733–738 CrossRefMATH Subramanian K, Elangovan A, Rajkumar R (1993) Elastic stability of varying thickness plates using the finite element method. Comput Struct 48(4):733–738 CrossRefMATH
16.
go back to reference Bradford MA, Azhari M (1995) Buckling of plates with different end conditions using the finite strip method. Comput Struct 56(1):75–83 CrossRefMATH Bradford MA, Azhari M (1995) Buckling of plates with different end conditions using the finite strip method. Comput Struct 56(1):75–83 CrossRefMATH
17.
go back to reference Nerantzaki MS, Katsikadalils JT (1996) Buckling of plates with variable thickness and analog equation solution. Eng Anal Bound Elem 18:149–154 CrossRef Nerantzaki MS, Katsikadalils JT (1996) Buckling of plates with variable thickness and analog equation solution. Eng Anal Bound Elem 18:149–154 CrossRef
18.
go back to reference Bradford MA, Azhari M (1997) The use of bubble functions for the stability of plates with different end conditions. Eng Struct 19(2):151–161 CrossRef Bradford MA, Azhari M (1997) The use of bubble functions for the stability of plates with different end conditions. Eng Struct 19(2):151–161 CrossRef
19.
go back to reference Yuan S, Yin Y (1998) Computation of elastic buckling loads of rectangular thin plates using the extended Kantorovich method. Comput Struct 66(6):861–867 CrossRefMATH Yuan S, Yin Y (1998) Computation of elastic buckling loads of rectangular thin plates using the extended Kantorovich method. Comput Struct 66(6):861–867 CrossRefMATH
20.
go back to reference Xiang Y, Wang CM (2002) Exact buckling and vibration solutions for stepped rectangular plates. J Sound Vib 250(3):503–517 ADSCrossRef Xiang Y, Wang CM (2002) Exact buckling and vibration solutions for stepped rectangular plates. J Sound Vib 250(3):503–517 ADSCrossRef
21.
go back to reference Eisenberger M, Alexandrov A (2003) Buckling loads of variable thickness thin isotropic plates. Thin-Walled Struct 41:871–889 CrossRef Eisenberger M, Alexandrov A (2003) Buckling loads of variable thickness thin isotropic plates. Thin-Walled Struct 41:871–889 CrossRef
22.
go back to reference Xiang Y, Wei GW (2004) Exact solutions for buckling and vibration of stepped rectangular Mindlin plates. Int J Solids Struct 41:279–294 CrossRefMATH Xiang Y, Wei GW (2004) Exact solutions for buckling and vibration of stepped rectangular Mindlin plates. Int J Solids Struct 41:279–294 CrossRefMATH
23.
go back to reference John Wilson A, Rajasekaran S (2012) Elastic stability of all edges simply supported, stepped and stiffened rectangular plate under uni-axial loading. Appl Math Model 36:5758–5772 MathSciNetCrossRef John Wilson A, Rajasekaran S (2012) Elastic stability of all edges simply supported, stepped and stiffened rectangular plate under uni-axial loading. Appl Math Model 36:5758–5772 MathSciNetCrossRef
25.
go back to reference Malekzadeh P, Golbahaar Haghigh MR, Atashi MM (2011) Free vibration of elastically supported functionally graded annular plates subjected to thermal environment. Meccanica 46:893–913 MathSciNetCrossRefMATH Malekzadeh P, Golbahaar Haghigh MR, Atashi MM (2011) Free vibration of elastically supported functionally graded annular plates subjected to thermal environment. Meccanica 46:893–913 MathSciNetCrossRefMATH
26.
go back to reference Eftekhari SA, Jafari AA (2012) A simple and accurate method FE-DQ formulation for free vibration of rectangular and skew Mindlin plates with general boundary conditions. Meccanica. doi:10.1007/s111012-012-9657-8 Eftekhari SA, Jafari AA (2012) A simple and accurate method FE-DQ formulation for free vibration of rectangular and skew Mindlin plates with general boundary conditions. Meccanica. doi:10.​1007/​s111012-012-9657-8
27.
go back to reference Malekzadeh P, Golbahaar Haghigh MR, Alibeygi Beni A (2012) Buckling analysis of functionally graded arbitrary straight sided quadrilateral plates on elastic foundation. Meccanica 47:321–333 MathSciNetCrossRef Malekzadeh P, Golbahaar Haghigh MR, Alibeygi Beni A (2012) Buckling analysis of functionally graded arbitrary straight sided quadrilateral plates on elastic foundation. Meccanica 47:321–333 MathSciNetCrossRef
29.
go back to reference Gambir ML (2004) Stability analysis and design of structures. Springer, Berlin CrossRef Gambir ML (2004) Stability analysis and design of structures. Springer, Berlin CrossRef
Metadata
Title
Elastic stability of all edges clamped stepped and stiffened rectangular plate under uni-axial, bi-axial and shearing forces
Authors
A. John Wilson
S. Rajasekaran
Publication date
01-12-2013
Publisher
Springer Netherlands
Published in
Meccanica / Issue 10/2013
Print ISSN: 0025-6455
Electronic ISSN: 1572-9648
DOI
https://doi.org/10.1007/s11012-013-9751-6

Other articles of this Issue 10/2013

Meccanica 10/2013 Go to the issue

Meccanica Information & Calendar

Calendar

Premium Partners