Saint-Venant end effects in composite structures

Abstract

Thin-walled structures, such as rifle barrels, rocket casings, helicopter blades and containment vessels, are often constructed of layers of anisotropic, filament or fiber-reinforced materials which must be designed to remain elastic. A proper assessment of end or edge effects in such structures is of fundamental technological importance. The extent to which local stresses, such as those produced by fasteners and at joints, can penetrate girders, beams, plates and shells must be understood by the designer. Thus a distinction must be made between global structural elements (where Strength of Materials or other approximate theories may be used) and local elements which require more detailed (and more costly) analyses based on exact elasticity. Moreover, it must be recognized that it is impossible, in general, to refine global approximate theories (such as various so-called higher-order plate and shell theories) without a simultaneous consideration of local effects. The neglect of end effects is usually justified by appeals to some form of Saint-Venant's principle, and years of experience with homogeneous isotropic elastic structures have served to establish this standard procedure. Saint-Venant's principle also is the fundamental basis for static mechanical tests of material properties. Thus property measurements are made in a suitable gage section where uniform stress and strain states are induced and local effects due to clamping of the specimen are neglected by an appeal to Saint-Venant's principle. Such traditional applications of Saint-Venant's principle require major modifications when strongly anisotropic and composite materials are of concern. For such materials, local stress effects persist over distances far greater than are typical for isotropic materials. In this paper, we describe some problems of static and dynamic elasticity where anisotropy induces such extended Saint-Venant end zones. The paper is a review and a comprehensive list of references is given to original work where details of the analysis may be found. The consideration of such extended end zones due to anisotropy is essential in the proper analysis and design of structures using advanced composite materials.