The Effect of Vehicle Planar Geometry Model Non-Orthogonality for the Constant Stiffness Force-Crush Model: Part 1

The subject study is the first in a multi-part study that assesses the effects of vehicle planar geometry model non-orthogonality within the context of the constant stiffness force-crush model. The concept of the crush space is first developed. It is shown that under the constraints of the constant stiffness force-crush model that regardless of the complexity of the undeformed vehicle geometry that the crush space is orthogonal and the mapping of vehicle crush into this space retains this orthogonality. Closed form analytical solutions are developed for the mapping of vehicle crush for simple multilinear approximations, the general multilinear approximation and simple circular segment model. Included in this development is the use of measurements taken with respect to a reference plane or line that is parallel to one of the undeformed vehicle principal axes. The solutions are also developed for those cases in which the undeformed vehicle projected geometry is modeled using basis spline functions and using polynomial regression. The analytical solutions are also developed for determining the geometric centroid of the crushed area for each of these geometry modeling methods. A complete example is provided showing the implementation of the analytical solutions.