Elasticity on a Thin Shell: Formal Series Solution

The three-dimensional equations of elasticity are posed on a domain of R^3 defining a thin shell of thickness 2ε. The traction free conditions are imposed on the upper and lower faces together with the clamped boundary conditions on the lateral boundary. After a scaling in the transverse variable, the elasticity operator admits a power series expansion in with intrinsic coefficients with respect to the mean surface of the shell. This leads to define a formal series problem in associated with the three-dimensional equations. The main result is the reduction of this problem to a formal series boundary value problem posed on the mean surface of the shell