積分方程式法による不伸長弾性リングの分岐解析  [in Japanese] BIFURCATION ANALYSIS OF AN INEXTENSIBLE ELASTIC RING BY INTEGRAL EQUATION METHOD  [in Japanese]

The problem of determining possible equilibrium states of buckled elastic rings subjected to a uniform pressure is discussed in this paper. This problem is known as the nonlinear bifurcation problem in which there exist many bifurcation solutions and limit points. The nonlinear governing equations based on the Bernoulli-Euler theory of elastica are transformed into the nonlinear integral equations. The integral equations are discretized by means of the numerical integral procedure. In order to find the bifurcation solution at a bifurcation point, the bifurcation technique in conjunction with the arc-length method is applied effectively. In numerical results for the pressure P (0≥P≥100) it is shown that there exist nine bifurcation solutions.