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Justification of the two-dimensional equations of a linearly elastic shallow shell. (English) Zbl 0769.73050
Summary: We consider a problem in three-dimensional linearized elasticity, posed over a shell with a specific geometry, subjected to general loadings, and clamped on a portion of its lateral surface. We show that, as the thickness of the shell goes to zero, the solution of the three- dimensional problem converges to the solution of two-dimensional shallow shell equations. This approach, which provides in particular a mathematical definition of “shallowness”, clearly delineates conditions under which a three-dimensional problem may be deemed asymptotically equivalent to a two-dimensional shallow shell problem.

MSC:
74K15 Membranes
74B05 Classical linear elasticity
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