We first show how the classical Marguerre–von Kármán equations modeling the deformation of a nonlinearly elastic shallow shell can be recast as equations whose sole unknowns are the bending moments and stress resultants inside the middle surface of the shell. Thus, these equations allow to compute the stresses inside the shell without having to compute first the displacement field. We then show that the boundary value problem formed by these new equations is well posed by establishing an existence theorem.
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