Abstract
The major novelty of the paper in the study, post-buckling of simply supported FGM beams using various theory, classical beam theory (CBT), first-order shear deformation beam theory (FSDBT), parabolic shear deformation beam theory (PSDBT) and exponential shear deformation beam theory (ESDBT). Governing equations of FGM beam for post-buckling problem were found by applying Hamilton principle and Navier type solution method was used to solve post-buckling problem. It is assumed that elasticity modulus is changing in the thickness direction and all other material properties are taken to be constant. Variation of elasticity modulus in the thickness direction, are described by a simple power law distribution in terms of the volume fractions of constituents. The shear effect is shown to have a significant contribution to both the buckling and post-buckling behaviors. Results of this analysis show that classical and first-order theories underestimate the amplitude of buckling while all higher order theories, considered in this study, yield very close results for the static post-buckling response.
Highlights
Graded materials (FGMs) are novel, microscopically inhomogenous in which the mechanical properties vary smoothly and continuously from one surface to another
Theory Ceramic k = 0.3 k = 1 k = 3 k = 5 classical beam theory (CBT) 4.906 3.812 2.905 2.305 2.047 first-order shear deformation beam theory (FSDBT) 4.905 3.811 2.904 2.304 2.047 parabolic shear deformation beam theory (PSDBT) 4.905 3.811 2.904 2.304 2.047 exponential shear deformation beam theory (ESDBT) 4.905 3.812 2.904 2.304 2.046 k = 10 Metal 1.688 0.904 1.687 0.904 1.687 0.904 1.6867 0.904. It is worth investigating the significance of shear deformation on the critical buckling load and on the resulting postbuckling response, which is considered to be the contribution of this study
Numerical results show the significant effect of the shear deformation on the buckling and postbuckling responses of moderately thick beams or beams made of functionally graded materials
Summary
Graded materials (FGMs) are novel, microscopically inhomogenous in which the mechanical properties vary smoothly and continuously from one surface to another. In thermal buckling of functionally graded material plates Bouazza et al [14, 15] discussed the thermal buckling of plates based on the classical and first order displacement plate theories They studied three types of thermal loadings for critical bucking temperature of plates and found that the classical plate theory over-predicts the buckling behaviour of thick plates. The effects of slenderness ratio, material variations, the different formulations and the beam theories on the first critical buckling load are examined. Where Ec and Em denote values of the elasticity modulus at the top and bottom of the beam, respectively, and Vc denotes the volume fraction of the ceramic and is assumed as a power function as follows: Vc. Where k is a variable parameter. Using Hook’s law, the stress resultants are expressed in terms of the strains as follows: N
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
