M.Sc Thesis
M.Sc Student Weiss Joshua Penetration by Projectiles of Solid Barriers with Uncertainties Department of Mechanical Engineering Professor Yakov Ben-Haim

Abstract

The mechanical dynamics of penetration into a solid medium is highly complex and not perfectly understood. In dealing with a system such as that of a penetrating projectile there are many uncertainties that need to be dealt with. This research uses Info-gap theory which is a decision theory that seeks to assist in decision-making under uncertainty. Using Info-gap one finds the robustness of a system which is the maximum uncertainties it can handle without failing. We will find the robustness of different systems that have different uncertainties. By comparing the robustness functions we can decide on the best system to design.

The first model which was analyzed with Info-gap was that of a gate being held closed by an angular spring, and projectile attempting to penetrate through. This system was looked at given uncertainties in the velocity and point of contact of the projectile, and the spring constant and linearity. The robustness as a function of the critical angle was found for each case and by comparing them the system can be designed to best avoid failures.

Next, the robustness of a bullet penetrating through a wall was found, where the uncertain parameter is the friction force the wall applies to the bullet. In this case failure was defined as the bullet penetrating completely through the wall and exiting the other side.

After that the system was analyzed where the uncertain parameter is the deceleration of the projectile and failure occurs if it manages to penetrate farther than a critical depth. From here the innovation dilemma is explored. Is a system that is nominally better but more uncertain better to design than a system that may be nominally not as good but is more certain. More specifically in our case, is it better to design a barrier from a stronger material or a more quality controlled one. Through finding the robustness functions this dilemma is solved.

The last case to be analyzed is a case where it is known that the deceleration of the projectile acts like a normal distribution, but the mean and the standard deviation are uncertain. The robustness functions are found and compared to reveal which system is preferred to design.

In conclusion, there will always be uncertainties in the world around us, but by being aware and planning ahead accordingly we can deal with them and strengthen the chance of success.