Improved First Order Formulation for Buckling Analysis of Functionally Graded Beams

In this research, an improved first order formulation is presented to study the critical buckling load in functionally graded beams. The formulation has five independent variables in comparison with the Timoshenko theory that has three. The Trefftz criterion is utilized with incremental and fundamental states to define the stability analysis. Virtual work statements are derived for the finite element model where the field variables are interpolated by Lagrange polynomials. The numerical results are compared and verified with other formulations found in literature. Parametric studies are also carried out for buckling behavior due to different slenderness ratios, power-law indices and boundary conditions. Applications of the model to functionally graded materials show the validity of the present approach.

[1]  R. Arciniega,et al.  Bending Analysis of Nonlocal Functionally Graded Beams , 2020, IOP Conference Series: Materials Science and Engineering.

[2]  R. Arciniega,et al.  Postbuckling Analysis of Functionally Graded Beams , 2019, IOP Conference Series: Materials Science and Engineering.

[3]  V. Kahya,et al.  Finite element model for vibration and buckling of functionally graded beams based on the first-order shear deformation theory , 2017 .

[4]  Huu-Tai Thai,et al.  Vibration and buckling analysis of functionally graded sandwich beams by a new higher-order shear deformation theory , 2015 .

[5]  Alireza Maheri,et al.  Finite element model for vibration and buckling of functionally graded sandwich beams based on a refined shear deformation theory , 2014 .

[6]  Huu-Tai Thai,et al.  Static and free vibration of axially loaded functionally graded beams based on the first-order shear deformation theory , 2013 .

[7]  R. Batra,et al.  Relations between buckling loads of functionally graded Timoshenko and homogeneous Euler-Bernoulli beams , 2013 .

[8]  Xian‐Fang Li,et al.  BUCKLING OF FUNCTIONALLY GRADED CIRCULAR COLUMNS INCLUDING SHEAR DEFORMATION , 2010 .

[9]  J. Reddy,et al.  BUCKLING AND POSTBUCKLING ANALYSIS OF LAMINATED CYLINDRICAL SHELLS USING THE THIRD-ORDER SHEAR DEFORMATION THEORY , 2004 .

[10]  S. Suresh,et al.  Graded Materials for Resistance to Contact Deformation and Damage , 2001, Science.

[11]  M. Koizumi.  FGM activities in Japan , 1997 .

[12]  Subra Suresh,et al.  Small and large deformation of thick and thin-film multi-layers: Effects of layer geometry, plasticity and compositional gradients , 1996 .