Bifurcation buckling of isotropic annular disc using conforming and non-conforming finite element

Abstract

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. © 2022