Boundary Layer Analysis for Some Problems of Singular Domain Perturbation
This article is concerned with analyzing the effect of small circular holes in a plane domain on the solution of certain nonlinear boundary value problems. Apart from its intrinsic mathematical interest, this problem has various applications. Examples include the stress concentration in thin elastic membranes and shells at the edge of a small hole, and the buckling of plates and shells, which may be of the bifurcation or snapping type. It is usually much simpler to calculate stresses and critical loads for a shell without hole. Therefore, it is of interest to assess asymptotically the effect of the singular domain perturbation on the stresses and on the critical loads. Another application relates to tubular chemical reactors, where internal cooling pipes of small diameter are inserted into the reactor vessel.
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