Computational bifurcation theory: path-tracing, pinpointing and path-switching

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Abstract The stability points in nonlinear elasticity may be classified into limit points and bifurcation points. For limit points, the path-tracing scheme to successively compute the regular equilibrium points on the equilibrium path and the pinpointing scheme to precisely locate the singular equilibrium points are sufficient for the computational stability analysis. For bifurcation points, however, a specific procedure for path-switching is also necessary to detect the branching paths to be traced in the postbuckling region. The present paper briefly describes these fundamental strategies, path-tracing, pin-pointing and path-switching, in computational bifurcation theory.

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