Design of porous and graded NiTi smart energy absorbers considering synthetic uncertainty in parameters

The synthetic uncertainty (SU) method is introduced and applied to the optimal design of energy absorbing NiTi shape memory alloy (SMA) bars. A sensitivity analysis for a large number of stochastic parameters identifies geometrical grading, porosity, and imposed maximum nominal stress as critical design parameters for the energy dissipation capacity of the bars. Parametric uncertainty on the optimal design of the energy absorber is incorporated and estimated through the SU formalism. The SU method provides a unified approach to discover the critical design parameters, quantify uncertainty, and optimally design a system around its extreme response (maximum or minimum). Therefore, the SU method is placed next to the robust design optimization (RDO) process, yet with a discovery component. It is found that variations in porosity and shape factor can significantly alter the stress-strain response and energy dissipation capacity. For a given value of maximum nominal stress, it is found that there exists an optimal combination of shape factor and porosity which maximizes the energy dissipation capacity of a tapered and porous NiTi bar.