Ultimate compressive strength inversion in initially imperfect plates under different boundary conditions: A conservative assessment method

Abstract

This study presents a predictive framework for the ultimate compressive strength (UCS) of initially deflected plates subjected to longitudinal axial compression under simply supported (SS) and clamped (CL) boundary conditions. A comprehensive database comprising 2800 non-linear finite element analyses (NLFEA) is established, covering plate slenderness ratios ( β ) from 0.67 to 4.06, four material yield stresses ( σ Y ), and seven initial deflection coefficients, with boundary-condition-specific fundamental eigen-buckling modes adopted as the initial deflection profiles. Systematic regression of the database produces a unified empirical formulation for predicting the UCS under both SS and CL boundary conditions. Statistical analysis confirms good predictive accuracy ( R 2 = 0.99; mean = 1.000) and a low coefficient of variation (COV = 0.003). Beyond conventional strength prediction, a key finding is the non-intuitive strength-inversion phenomenon, in which the ultimate compressive strength of SS plates exceeds that of CL plates beyond an initial-deflection-dependent slenderness threshold. This behaviour is physically interpreted through the combined variation in the normalised strain at the ultimate limit state (ULS) and the central-deflection response. A predictive expression for the transition point (T.P.), defined by equal ultimate compressive strength values under the SS and CL conditions, is proposed to identify the inversion boundary and support conservative assessment. The proposed framework provides both a physically interpretable basis and practical applicability, offering a computationally efficient tool for preliminary design and a foundation for future extensions toward digital structural assessment and condition-aware design methodologies.