A mixed boundary value problem for the Lamé equation in a thin layer ? h = C × [?h, h] around a surface C with the Lipshitz boundary is investigated.The main goal is to find out what happens when the thickness of the layer tends to zero, h → 0.To this end, we reformulate BVP into an equivalent variational problem and prove that the energy functional has the Γ-limit of the energy functional on the mid-surface C.The corresponding BVP on C, considered as the Γ-limit of the initial BVP, is written in terms of Günter’s tangential derivatives on C and represents a new form of the shell equation.It is shown that the Neumann boundary condition from the initial BVP on the upper and lower surfaces transforms into the right-hand side of the basic equation of the limit BVP.The finite element method is established for the obtained BVP.
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