An analytical method for nonlinear thermo-mechanical buckling evaluation of functionally graded circular microplates

This paper analytically investigates the nonlinear static buckling behavior of functionally graded (FG) circular microplates by integrating Kirchhoff plate theory, von Kármán geometric nonlinearity, and the modified couple stress theory to account for size-dependent effects. The microplate is concurrently exposed to a uniform pressure and a uniformly increasing through-thickness thermal load. A method based on displacement is used, where the expected movement and bending of the plate are described using polynomial functions that fit the fixed edges of the plate. This choice reduces computational cost while maintaining sufficient accuracy in predicting the nonlinear structural response. By using the Ritz energy method, we can derive straightforward formulas for the critical thermal buckling load and how the load relates to deflection after buckling for the FG circular microplate. The numerical results show that changes in the volume fraction index, material length-scale parameter, and shape features are very important in determining how strong the FGM structure is against buckling and how it behaves after buckling. The results give important insights and serve as a helpful guide for designing microscale functionally graded structures that experience both heat and mechanical stress.