Asymptotic 2D-modelling for dynamics of linear elastic thick shells

A two dimensional model for a time dependent evolution problem of a linear elastic thick shell is deduced from the three dimensional elastodynamic problem without any ad hoc assumption whether of a geometrical or mechanical nature. By a thick shell we mean a shell whose midsurface characteristic parameter X = h/R is less than 1, where h is half the thickness and R the minimum absolute value of its radius of curvature (here considered to be strictly positive). In practice this parameter is bounded far smaller than 1 for thin shells. The two dimensional equations are deduced by applying asymptotic analysis on a family of variational equations obtained on an abstract scaled shell through multiple scaling of the initial three dimensional equations. The real model is obtained by inverse transformation.