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The influence of lateral boundary conditions on the asymptotics in thin elastic plates. (English) Zbl 0958.74034
Based mainly on their former studies, the authors investigate the limits of three-dimensional plate theory as the thickness tends to zero for eight types of lateral boundary conditions (Dirichlet, Neumann, and mixed ones). An infinite asymptotic expansion of the displacements with optimal error estimates in different norms is established, combining outer and inner expansions, the first ones containing the Kirchhoff-Love plate theory (including the membrane equations), and the last ones describing the effect of boundary layers. The mechanical model is constructed by means of a variational formulation. The paper also contains a careful and extensive discussion of the relevant literature.

MSC:
74K20 Plates
74G10 Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.) of equilibrium problems in solid mechanics
35Q72 Other PDE from mechanics (MSC2000)
74K15 Membranes
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