Introduction

A first step in gaining some understanding of the effect of impact by a foreign object on a structure is to predict the structure's dynamic response to such an impact. Predictions are made using a mathematical model that appropriately accounts for the motion of the projectile, the overall motion of the target, and the local deformations in the area surrounding the impact point. In general, details of the local interaction between the projectile and the target are not needed to predict the contact force history. A particular beam, plate, or shell theory is selected, and the local deformation in the through-the-thickness direction, which is not accounted for in such theories, is included through the use of an appropriate contact law. Contact laws relate the contact force to the indentation, which is the difference between the displacement of the projectile and the displacement of the target at the point of impact. With most low-velocity impacts, small amounts of damage are introduced in a small zone surrounding the impact point, and the dynamic properties of the structures usually are not affected by the presence of damage. Therefore, impact dynamic analyses generally do not attempt to model damage as it develops during the impact event.

The choice of a particular structural theory must be based on careful consideration of the effect of complicating factors such as transverse shear deformation and rotary inertia. For example, for beams, one can select to use the Bernoulli-Euler beam theory, the Timoshenko beam theory, or one of several other available beam theories.