|
Volume 10, Number 1, January 2025 , pages 1-34 DOI: https://doi.org/10.12989/acd.2025.10.1.001 |
||
|
Critical buckling analysis of functionally graded porous beam using Karush-Kuhn-Tucker conditions |
||
Geetha Narayanan Kannaiyan, Vivekanandam Balasubramaniam,
Bridjesh Pappula and Seshibe Makgato
|
||
| Abstract | ||
| Functionally graded porous beams (FGPB) are structural components engineered to enhance mechanical performance by customized material gradation and porosity distribution. The present study examines the buckling analysis of FGPB modelled using Higher-order shear deformation theory. The governing equations are formulated via Hamilton's principle and solved utilizing Karush-Kuhn-Tucker conditions. The analysis utilizes gradient indices (P_x, P_z), porosity distributions (even and uneven) and porosity indices to assess their influence on the dimensionless critical buckling loads under various boundary conditions, including Simply Supported (SS), Clamped-Simply supported (CS), Clamped-Clamped (CC), and Clamped-Free (CF). In line with this, the results show that an increase in P_x led to a decrease in the buckling load from 51.342 when P_x=0 to 8.811 when P_x=5 under the SS boundary conditions. Likewise, with increase in P_z the buckling load was reduced from 51.342 to 13.351. Uneven porosity consistently exhibited higher dimensionless critical buckling as compared to even porosity. Under CC boundary conditions, the dimensionless critical buckling load was 151.970 and 196.587 for even and uneven porosity distribution at P_x=0 and P_z=0. Among the boundary conditions, CC demonstrated the highest stability, with a dimensionless critical buckling load of 151.970, succeeded by CS (101.656), SS (51.342), and CF (13.175). These results prove the ability of the outlined methodology with errors less than 5% compared to literature. This study emphasizes the significance of material gradation and porosity in structural stability and presents a comprehensive method for designing innovative lightweight structures. Future studies may consider Machine Learning based predictive modeling for complex geometries. | ||
| Key Words | ||
| aspect ratio; dimensionless critical buckling; functionally graded porous beam; gradient index; higher order shear deformation theory; Karush-Kuhn-Tucker conditions; porosity | ||
| Address | ||
| Geetha Narayanan Kannaiyan: Department of Mathematics, Dayananda Sagar College of Engineering, Bengaluru 560078, India Vivekanandam Balasubramaniam: Faculty of Computer Science and Multimedia, Lincoln University College, Malaysia Bridjesh Pappula and Seshibe Makgato: Department of Chemical & Materials Engineering, College of Science, Engineering and Technology, University of South Africa (UNISA), c/o Christiaan de Wet & Pioneer Avenue, Florida Campus 1710, Johannesburg, South Africa | ||
