Justification of the two‐dimensional equations of a linearly elastic shallow shell
Philippe G. Ciarlet, Bernadette Miara · Communications on Pure and Applied Mathematics · 1992
Abstract 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.