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

Abstract

The dynamic plastic response with large deformation of thin plates under simple pulse loading has been studied systematically over past decades by using modal analysis and transient analysis. However, it is difficult to carry out the corresponding theoretical analysis directly for the more complex-shaped loading pulse. Hence, it is highly desired to find a pulse-equivalent technique to replace the real complex-shaped pulse by a simple pulse (e.g., a rectangular pulse), which produces the same deflection as the complex-shaped loading pulse while is relatively easier to analyze. In this paper, taking the fully clamped square plate under exponentially decaying (ED) pulse as a major example, for which the complete solution is given in [37], as obtained by the combination of Membrane Factor Method (MFM) and Saturation Analysis (SA). With the formulae on the saturated deflection and saturated impulse resulted from this solution, we are able to not only compare the Saturation Equivalent Method (S-EM) with the classical Youngdahl Equivalent Method (Y-EM), but also propose a new equivalent method, named as Progressive Equivalent Method (P-EM). By adopting a multi-step equivalency to gradually approach the saturated deflection, P-EM is capable of handling various complex-shaped loading pulses while Youngdahl empirical formula is no longer in need. The procedure of applying P-EM is also demonstrated by an example of handling complex-shaped pulses produced by constrained explosion loading, which contain multiple peaks. An extensive comparison concludes that in case of complex-shaped pulse loading, the innovative P-EM shows clear advantages over Y-EM and S-EM, and provides great convenience for engineering assessment and design.