Surrogate models for dynamic load factor and ductility ratio in blast response determination

In this article, the blast response of structures by the Single Degree of Freedom (SDOF) method is revisited. The existing literature in which the Biggs’ chart is used to determine the ductility ratio is examined in detail. The numerical method determines the SDOF response by considering the elastic perfectly plastic behaviour of the structure. The numerical values of the ductility ratio in various plastic Dynamic Load Factors (DLF) in each td/T ratio are collected. Such verifiable data can represent the whole chart in the elastic and plastic regions. The only available implicit formula suitable for sharp pulses is tested. It is shown that substantial inaccuracy exists in the formula. Since the error in the existing formula is up to 100%, an alternative formula is suggested to reduce the error. The new nonlinear surrogate model describes the chart by introducing 3 regions. In each region, an approximate formula is developed. The model computes the ductility ratio with less than 2% error. The newly suggested functions are nonlinear quadratic types and have been developed by using high-order polynomial optimization. In the numerical example, the result of the new surrogate model is commented on in comparison with SDOF and FEM. It is shown that it can be used in the computational design of protective structures without using Biggs’ chart. It is concluded that similar surrogate models can be developed for unsymmetrical blast pulses.