ABSTRACT
In the undeformed configuration the shell reference surfaceM is given by the position vector r = r(θα) relative to a point O ∈E.The geometry ofM is described by the covariant base vectors aα = r,α, the covariant components aαβ = aα · aβ of the surface metric tensor awith a = det (aαβ) > 0, the contravariant components εαβ of the surface permutation tensor ε, the unit normal vector n= 12εαβaα×aβ orientingM, and the covariant components bαβ =−a,α ·n,β =n · aα,β of the surface curvature tensor b. The boundary contour ∂M of M consists of a finite number of piecewise smooth curves given by r(s) = r[θ(s)], where s is the arc-length along ∂M. With each regular point M ∈ ∂M we associate the unit tangent vector τ ≡ r,s = dr/ds= ταaα, and the outward unit normal vector ν= τ × n= ναaα. For other geometric definitions and relations we refer to Pietraszkiewicz (1977).
