コンポジットアーチと剛体平板の接触に伴う座屈後挙動

抄録

We study the buckling behavior of a hemispherical composite arch with step type distribution of bending stiffness contacting in a rigid plane. The arch is divided into two regions with the different bending stiffness and is characterized by two parameters: the stiffness ratio and the arc-length at the boundary point between two parts. Also, to elucidate the influence of the initial curvature on the mechanical responses, we consider two initial states of the arch. One is the arch by bending a straight line without initial curvature, and the other is a naturally curved arch with the initial curvature. Using an elastica model, we model the arch and formulate the contact problem as a two-point boundary value problem which involves an unknown moving contact boundary, so that the problem yields a nonlinear free boundary value problem.

To solve the problem numerically, we transform it into the fixed boundary value problem by making a change of variables. We examine how the distribution of bending stiffness and the initial curvature affects the load-displacement responses and snapping behaviors. As a result, we found that the snapping responses can be tuned by controlling the distribution of bending stiffness and the initial curvature of the arch. We also find the structure such that the overall stiffness of the arch is low in the low load range while high in the high load range.