On the Tracing Calculation of the Equilibrium Path for Imperfect Systems

Abstract

In this report, discussions on the numerical calculation of the non-linear equilibrium equation are stated, Especially, the problems arising in the tracing calculation of the path that exists the conjugate path in the vicinity of the branch point and that changes the direction due to yielding of the material are made clear and a more generalized incremental method elaborated for their disposal is proposed.Consequently, by adopting a spherical search surface in which the arc-length of the path is used as restrictive parameter, the equilibrium points can be obtained automatically with good intervals for the system in which the path makes an abrupt change, and furthermore, it is made clear that the elimination method proposal by the authors is highly effective for the systems that have small initial imperfection.