Elasticity on a thin shell: Formal series solution

Article type: Research Article

Authors: Faou, Erwan

Affiliations: INRIA Rennes, Campus de Beaulieu, 35042 Rennes, France E‐mail: [email protected]

Abstract: The three‐dimensional equations of elasticity are posed on a domain of $\mathbb{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 ε with intrinsic coefficients with respect to the mean surface of the shell. This leads to define a formal series problem in ε 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.

Journal: Asymptotic Analysis, vol. 31, no. 3-4, pp. 317-361, 2002