The Sector Finite Element for Thermal Buckling Analysis of Isotropic Annular Disc

Abstract

Annular disc-type structural elements may be subjected to thermal loads other than mechanical loads. Buckling of annular disc due to thermal load could lead to non-operationality of the machineries. The present study illustrates a step-by-step procedure for setting up the finite element equations for solving the thermal buckling problem of the annular disc. Sector finite elements with four nodes and five degrees of freedom at each node are used to discretize the computational domain of an annular disc. Using the nodal coordinates, the nodal degree of freedom based on the thin plate theory of elasticity is assessed at each node of the sector finite element. The two-dimensional plane stress–strain relationship is invoked, as well as temperature effects. The work done by the external load owing to temperature effects is expressed using nonlinear strains. The first potential energy minimization produces the equation for pre-buckling analysis, whereas the second time minimization yields the eigenvalue problem for obtaining post-buckling findings. To solve for buckling factors, a FORTRAN code is constructed, and the results for an isotropic circular thin plate with varying isothermal conditions are compared to an analytical solution published in the literature. © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2024.