Analysis of Buckling Problems of Trigonometric Shear Deformable Plates: Variational Formulation and Solutions for Simply Supported Plate Buckling Problems using Galerkin Method

Ike, Charles Chinwuba

doi:10.22059/ceij.2025.391455.2263

Analysis of Buckling Problems of Trigonometric Shear Deformable Plates: Variational Formulation and Solutions for Simply Supported Plate Buckling Problems using Galerkin Method

Articles in Press

Document Type : Technical Notes

Author

Charles Chinwuba Ike

Enugu State University of Science and Technology, ESUT, Agbani, Enugu State, Nigeria. Member, Nigerian Society of Engineers. COREN REGISTERED ENGINEER.

10.22059/ceij.2025.391455.2263

Abstract

This work considered transverse shear deformations in the derivation of thick plate buckling problem. Trigonometric shear form functions were derived using first principles to ensure that the plate surfaces are free of transverse shear strains. Hence shear correction factors were not needed. The first variation of the total energy functional was made to vanish to establish the differential equations of stability (DES). Exact displacement shape functions were used in the Galerkin variational method (GVM) to determine analytical and numerical solutions. The GVM simplified the DES to a homogeneous algebraic eigenvalue problem. The condition for nontrivial solutions was used to determine the characteristic buckling equation, with the least eigenvalue yielding the critical buckling load, which were determined for uniaxial and biaxial compressive loads studied. The work was validated by favourable comparisons with previous shear deformation plate results. It was also found that the critical buckling loads were significantly lower than those predicted by classical Kirchhoff thin plate theory (CPT) confirming that CPT overestimates the critical buckling loads of thick plates for all aspect ratios. The GVM is mathematically rigorous as the boundary conditions are satisfied as well as the DES, making the method exact within the theoretical framework considered.

Keywords

Trigonometric Shear Deformable Plate

Galerkin Variational Method

Critical Buckling Load

Subjects