Nonlinear analysis of an imperfect radially graded annular plate with a heated edge

The present work deals with a geometrically nonlinear finite element analysis of an imperfect radially graded annular plate with a heated edge. The geometrical imperfection of the graded annular plate is assumed in aspect of its little intrinsic transverse deflection. The analysis is mainly for investigating the effects of intrinsic geometrical imperfection and temperature in the graded annular plate on its nonlinear flexural behaviour under a transverse mechanical load. The temperature is uniformly distributed across the thickness of the plate and it varies along the radial direction only. The temperature-dependent material properties are radially graded according to a simple power-law that is formed by power-law exponent and material properties of constituent materials (ceramic and metal). Based on the Von Karman nonlinear strain-displacement relations for imperfect annular plates, the nonlinear finite element equations of equilibrium are derived employing the principle of minimum potential energy. A single nodal displacement-control solution strategy is described for numerical solutions of nonlinear finite element equations of equilibrium. The numerical illustrations show a significant role of geometrical imperfection of the annular plate for its unstable equilibrium and alteration of structural behaviour under thermo-mechanical load. The analysis reveals the usefulness of radially graded annular plate in order to mitigate the unstable equilibrium of imperfect monolithic annular plate under thermo-mechanical load. It is found that the radial location for maximum value of a stress component insignificantly depends on the magnitudes of power-law exponent and applied temperature. The effects of material properties and applied temperature on the critical mechanical load corresponding to the unstable equilibrium of the imperfect radially graded annular plate are also presented.