Conference Papers
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Item Bifurcation buckling of isotropic annular disc using conforming and non-conforming finite element(Elsevier Ltd, 2022) Kumar, A.; Kadoli, R.; Joladarashi, S.Non-conforming and conforming polynomial is used to develop sector finite element for analysing the isothermal bifurcation buckling of isotropic annular disc. The sector finite element has three degrees of freedom for non-conforming and four degrees of freedom for conforming element respectively. To obtain the shape function for the sector finite element, the displacement polynomial is chosen from the Pascal's triangle, the displacement polynomial is used to obtain the polynomial corresponding to the nodal degree of freedom for the element and evaluated at each node of the sector finite element using the nodal coordinates. The kinematics, strain displacement relations and the stress strain relations is based on the Kirchhoff's plate theory. The stiffness matrix and geometric stiffness matrix are evaluated in MATHEMATICA and then imported in the FORTRAN complier. A FORTRAN CODE is developed to solve the eigenvalue problem for bifurcation buckling of clamped-clamped isotropic annular disc with uniform temperature rise. ORIGIN software is used to plot the buckled mode shape for non-conforming and conforming sector finite element for isotropic annular disc. The number of circumferential waves at the onset of bifurcation buckling increase as the radius ratio increases. The critical buckling temperature increases with increase in thickness of the annular disc, so is the case when the inner radius increases for a given outer radius and thickness of the annular disc. © 2022Item The Sector Finite Element for Thermal Buckling Analysis of Isotropic Annular Disc(Springer Science and Business Media Deutschland GmbH, 2024) Kumar, A.; Kadoli, R.; Joladarashi, S.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.