New analytic buckling solution for stepped thin plates

Abstract

This paper investigates the buckling problem of a four-sided simply supported stepped thin plate under bilateral loading using the sine superposition method and analytical solution methods. To date, the buckling problem of this structure has primarily been solved using numerical methods and finite element methods, and analytical solution methods for this structure have not yet been verified. However, in practical applications, analytical methods offer higher accuracy and efficiency compared to numerical methods. This method transforms the original problem into the superposition of four subproblems and derives their exact analytical solutions. By establishing the dual equations of the Hamiltonian system and combining them with continuity conditions and boundary conditions, the analytical expression for the critical buckling load is obtained. Case studies indicate that there is an interaction between the load ratio, length-to-width ratio, and thickness ratio. When the load ratio and length-to-width ratio remain constant, the buckling load coefficient increases with an increase in the thickness ratio; when the load ratio and thickness ratio remain constant, it decreases with an increase in the length-to-width ratio; when the thickness ratio and length-to-width ratio remain constant, it decreases with an increase in the load ratio. Convergence results indicate that convergence is achieved around the 40th series term, significantly faster than numerical methods and finite element methods, offering better real-time performance and cost-effectiveness in industrial design. This study provides an efficient theoretical tool for the buckling analysis and application of stepped thin plates.