Nonlinear deflection and thermal post-buckling analysis of sector annular poroelastic composite nanodisks using mathematical simulation and machine learning algorithm

•Nonlinear deflection and thermal post-buckling analysis of composite sector annular poroelastic nanodisks for the first time.•For the first time, presenting nonlinear discrete-singular convolution solution procedure to solve nonlinear PDE equations.•Utilizing RQLT, and considering Von-Karman nonlinearity to accurately capture the large deflection responses of these advanced nanostructures under thermal loading.•Presenting a machine learning algorithm to test, train, and validate the results for future analysis of the mentioned problem with low computational cost.•The successful integration of poroelasticity and functional gradation in the analysis and design of nanodisks marks a significant step forward in the field of nanotechnology science. Poroelastic nanodisks offer mechanical engineers enhanced control over material properties, enabling precise tuning of mechanical responses for advanced applications in sensors, actuators, and nano-mechanical systems. This study presents a comprehensive analysis of thermally-affected multi-directional functionally graded sector annular nanodisks, focusing on their thermal-post buckling and nonlinear deflection behaviors. Utilizing a refined quasi-3D logarithmic theory (RQLT), the study incorporates the effects of Von-Karman nonlinearity to accurately capture the large deflection responses of these advanced nanostructures under thermal loading. The material properties of the nanodisks are graded in multiple directions, enhancing their ability to withstand thermal stresses and maintain structural integrity. To solve the complex governing equations derived from the RQLT, a nonlinear discrete-singular convolution (DSC) solution procedure is employed. This novel numerical technique allows for precise computation of the nonlinear deformation and stability characteristics of the nanodisks, providing insights into their behavior under various thermal conditions. The nonlinear DSC method's ability to handle singularities and discontinuities makes it particularly suitable for this type of advanced analysis. After obtaining the mathematics simulation data, a machine learning algorithm is used to test, train, and validate the results for future analysis of the mentioned problem with low computational cost. The results demonstrate the critical influence of thermal gradients and material gradation on the post-buckling and nonlinear deflection responses of sector annular nanodisks. The interplay between thermal effects and material