中国物理B ›› 2017, Vol. 26 ›› Issue (7): 74602-074602.doi: 10.1088/1674-1056/26/7/074602

• ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID DYNAMICS • 上一篇    下一篇

Buckling analysis of nanobeams with exponentially varying stiffness by differential quadrature method

S Chakraverty, Laxmi Behera   

  1. Department of Mathematics, National Institute of Technology Rourkela, Odisha, India
  • 收稿日期:2016-11-12 修回日期:2017-03-03 出版日期:2017-07-05 发布日期:2017-07-05
  • 通讯作者: S Chakraverty E-mail:sne_chak@yahoo.com

Buckling analysis of nanobeams with exponentially varying stiffness by differential quadrature method

S Chakraverty, Laxmi Behera   

  1. Department of Mathematics, National Institute of Technology Rourkela, Odisha, India
  • Received:2016-11-12 Revised:2017-03-03 Online:2017-07-05 Published:2017-07-05
  • Contact: S Chakraverty E-mail:sne_chak@yahoo.com

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摘要： We present the application of differential quadrature (DQ) method for the buckling analysis of nanobeams with exponentially varying stiffness based on four different beam theories of Euler–Bernoulli, Timoshenko, Reddy, and Levison. The formulation is based on the nonlocal elasticity theory of Eringen. New results are presented for the guided and simply supported guided boundary conditions. Numerical results are obtained to investigate the effects of the nonlocal parameter, length-to-height ratio, boundary condition, and nonuniform parameter on the critical buckling load parameter. It is observed that the critical buckling load decreases with increase in the nonlocal parameter while the critical buckling load parameter increases with increase in the length-to-height ratio.

关键词: differential quadrature method, exponentially varying stiffness, different beam theories

Abstract: We present the application of differential quadrature (DQ) method for the buckling analysis of nanobeams with exponentially varying stiffness based on four different beam theories of Euler–Bernoulli, Timoshenko, Reddy, and Levison. The formulation is based on the nonlocal elasticity theory of Eringen. New results are presented for the guided and simply supported guided boundary conditions. Numerical results are obtained to investigate the effects of the nonlocal parameter, length-to-height ratio, boundary condition, and nonuniform parameter on the critical buckling load parameter. It is observed that the critical buckling load decreases with increase in the nonlocal parameter while the critical buckling load parameter increases with increase in the length-to-height ratio.

Key words: differential quadrature method, exponentially varying stiffness, different beam theories

中图分类号:  (Other structures)

  • 46.70.Lk
46.70.De (Beams, plates, and shells) 46.15.Cc (Variational and optimizational methods) 45.10.Db (Variational and optimization methods)