Perturbation of Domains for Some Non‐Classical BVP in Elasticity

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 C m , m ≧ 2, there exists a sequence of domains { D p }   p=1 ∞such that lim p→∞ n   D   p= ∞ ( n   D   p– defect of problem B in D p ). Simultaneously, the defect n D is finite, and the boundaries δD p converge to δD in the sense of C m .