Introduction

Beams and bars alone do not a vehicular structure make. Vehicular structures are typically beam frames and grids enveloped in a thin skin. See, for example, the illustrations in the front of this textbook, or the illustration in Endnote (2) of this chapter, which discusses the function of the thin skin, the stringers, and the frames. Characteristically, the skin thickness is much smaller than the distances between the beams that support the skin. In order to extend the finite element method to analytical models of vehicular structures, it is now necessary to begin to consider the analysis of thin skins in combination with the beam grids and frames that provide support for the skin. For the sake of simplicity, the discussion of thin skins in this introductory chapter is restricted to those that have a midsurface that parallels a single plane.

There are two distinct load cases for a planar, thin skin. In the first load case the edge traction vectors and the internal stress vectors parallel the plane of the skin, and are constant across the small thickness dimension of the skin. Furthermore, in this plane stress case, the skin is thick enough, or the lateral beam supports are sufficiently close to each other, that the skin does not buckle. Thus the deflection vectors also parallel the unloaded skin midsurface. The purpose of this chapter is to introduce a finite element-based deflection formulation to this plane stress problem.