非一様エラスティカのスナッピング

抄録

We study the snapping responses of a hemispherical arch with the inhomogeneity distribution of bending rigidity contacting in a rigid plane. We first introduce the elastica model with the inhomogeneity distribution of bending stiffness depending on the arc-length. Since the elastica involves geometrical nonlinearity and a contact problem involves unknown moving contact boundary, the problem yields a nonlinear free boundary value problem. To solve the problem numerically, we transform the free boundary value problem to the fixed boundary value problem by making a change of variables and then we use a continuation scheme with a relaxation method. We examine how the inhomogeneity distributions of bending rigidity affect the load-displacement responses and the critical loads for the snapping as well as the dropping loads after the snapping. We demonstrate that the snapping response can be tuned by controlling the distribution of bending rigidity of the arch.