Novel Kuhn–Tucker conditions with R-program to analyze the buckling of a functionally graded porous beam

A functionally graded porous beam is engineered to have various material properties and porous characteristics in a controlled and deliberate manner. The tailored material properties can help optimize structural performance, improve energy absorption, and enhance the overall efficiency and safety of engineered systems. Adapting the higher-order shear deformation theory, this paper investigates the buckling behavior of two-directional functionally graded porous beams (FGPB). The development of a mathematical model that incorporates material properties with a power law distribution and polynomial functions for axial and transverse deflections. The critical buckling analysis is undertaken using the Kuhn–Tucker analytical solution approach with the R-program. On the behavior of buckling, the influences of aspect ratio, gradient index, porosity index, and even/uneven porosity distributions are investigated. Comparisons with established numerical methods are used to validate the accuracy of the suggested analytical methodology. The effect of various parameters on the critical buckling response is investigated by means of a parametric investigation. The results contribute to the comprehension of the buckling behavior of FGPB and shed light on the optimization of their design. The proposed methodology provides a valuable instrument for analyzing these structures under various boundary conditions.