"[T]he basic assumption in the linear theory of shells that the displacements of the shell are considered to be small in comparison to the thickness is abandoned in the present nonlinear analysis of shells. A shell is called thin if the maximum value of the ratio h/R, where h is the thickness of the shell and R is the principal radius of curvature of the middle surface... is less than or equal to 1/20 ...beyond this range... the shell is regarded as thick. ...in a large number of practical applications the ratio... lies in the range between 1/50 and 1/1000, making the theory of thin shells of great practical importance. In this chapter the nonlinear equations... in terms of orthoganal are derived assuming the material... is isotropic, homogeneous, and elastic. An important simplification based on the assumption that second invariant of the median surface strains in the expression for the extensional ... can be neglected, originally made by [Noah] Burger, is introduced to derive a simplified set of nonlinear... differential equations."