closed-form solution for peak crushing force of the s-rails

one of the most important structural components of engine compartment assembly in a car body is the srail. s-rails has significant role in absorbing energy during crash events and therefore it is designed for efficient behavior in such conditions. driving the peak crushing force of the s-rails is one of the important objectives in the design process of such structures. peak crushing force is exactly the force applied to the downstream components and then will be transferred to the cabin of vehicle. in this paper, closed form solution is performed to drive the peak crushing force of the s-rails. results of such analytical model finally are compared with the results of finite element simulation. good agreement between such results shows the accuracy of the proposed analytical model.