A new equivalent method for complex-shaped pulse loading based on saturation analysis and membrane factor method

•Applying the Membrane Factor Method (MFM) in the Saturation Analysis (SA) provides a pathway to the pulse-equivalent technique for large dynamic deflection of pulse-loaded plates.•A new pulse-equivalent technique named Progressive Equivalent Method (P-EM) is proposed, which can handle more complex-shaped loading pulses while Youngdahl's empirical formula is no longer in need.•The saturated deflections of the square plate under Exponentially Decaying (ED) pulse and complex-shaped pulse with no analytical expression are predicted by P-EM.•By comparing Youngdahl Equivalent Method (Y-EM), Saturation Equivalent Method (S-EM) and Progressive Equivalent Method (P-EM), the applicability of three pulse-equivalent methods is discussed.