Perturbation of Domains for Some Non‐Classical BVP in Elasticity
Johannes Maul · ZAMM ‐ Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik · 1987
Abstract The paper deals with two non‐classical boundary value problems of plane elastostatics, which have mechanical significance. The first problem A is studied for epitrochoids, but the second one for domains, upon which the unit circle can be mapped conformally by a rational function. The behaviour of the defect (dimension of the kernel) of these problems is investigated for small perturbations of the domain. In the case of problem B the following result is obtained: For a given simply connected bounded domain D of the class Cm, m ≧ 2, there exists a sequence of domains {Dp} such that lim p→∞ n = ∞ (n – defect of problem B in Dp). Simultaneously, the defect nD is finite, and the boundaries δDp converge to δD in the sense of Cm.