A unified analytic solution framework for buckling analysis of single-edge-cracked rectangular plates

Investigating the buckling behaviors of cracked plates carries substantial significance, since crack existence induces remarkable modifications to plate mechanical properties, potentially leading to significant degradation of structural load-carrying capability. This study develops a novel analytic solution framework that integrates the finite integral transform (FIT) method with an elementary domain decomposition strategy for solving buckling problems of single-edge-cracked rectangular thin plates. The through-thickness edge crack is modeled as an internal free boundary. The proposed framework exhibits universal applicability to plates with arbitrary combinations of simply supported, clamped, and free edges, and requires no assumptions regarding the form of the solutions throughout the derivation. The framework briefly comprises four key steps: decomposition of a single-edge-cracked plate into four elementary domains, followed by the application of a double cosine FIT to the governing equation of each domain; enforcement of all boundary and continuity conditions pertaining to Kirchhoff shear forces and rotations to eliminate a subset of the unknowns; substitution of inverse transforms into unapplied bending moment and deflection conditions to formulate the complete system of linear algebraic equations; determination of analytic solutions by solving the equations. Comprehensive buckling load/mode solutions of representative single-edge-cracked plates are presented as new benchmarks. A comparison of the solutions with other methods is conducted to validate the effectiveness of the FIT-based new solution framework. Utilizing the derived analytic solutions, a parametric study is conducted to quantitatively investigate the influences of boundary conditions, crack length ratio, crack location, and aspect ratio on the buckling behaviors.