Three-dimensional linearized elasticity on a thin shell: formal series solution in power of the thickness

The three-dimensional equations of elasticity are posed on a domain of R-3 defining a thin shelf of thickness 2 epsilon. Only the inner equations together with traction conditions on the upper and lower faces of the shell are considered After a scaling on the transverse variable, the coefficients of the elasticity operator admit power series expansions in epsilon with intrinsic coefficients with respect to the middle surface of the shelf. This leads to define a formal series problem in epsilon associated to the three-dimensional equations. The main result is the reduction of this problem to formal series equations posed on the middle surface of the shell, with intrinsic operators. (C) 2000 Academie des sciences/Editions scientifiques et medicales Elsevier SAS.