Path-following methods

Completed Research project

Algorithms for the computation of static equilibrium paths and critical points for slender structures with nonlinear structural behaviour.


  • Adaptive path-following methods
  • Direct computation of critical points for Systems sensitive to imperfections

Project description

Adaptive path-following methods

Computation of static equilibrium paths for slender structures with nonlinear structural behaviour is still a challenge. New adaptive control algorithms are developed at the Institute for Structural Mechanics with the aim to increase reliability of the control methods. One idea consists in adaptive displacement control, thereby considering a well-chosen subset of the displacement increments. This leads to a considerable improvement in convergence behaviour compared to classical arc-length methods. Further further information can be found at Pohl (2014).

static equilibrium path of the buckling of a cylindrical shell
buckling simulation of a cylindrical shell

Direct computation of critical points for systems sensitive to imperfections

Via adaptive path-following techniques, the primary path of a system with highly nonlinear structural behaviour can be determined efficiently. If the secondary paths should also be investigated, the bifurcation points must be pinpointed. Therefore, one goal of the research project is the development of stable and powerful algorithms for the direct determination of bifurcation points and snap-through points, based on so-called extended systems. To increase the efficiency, new methods of numerical differentiation (complex step derivative approximation) and new hierarchic shell formulations, developed at the Institute for Structural Mechanics, are used.


  1. Pohl, T. (2014). Adaptive Methoden zur Pfadverfolgung bei Entfestigung. Doktorarbeit, Bericht Nr. 62, Institut für Baustatik und Baudynamik, Universität Stuttgart.
  2. Ramm, E. (1981). Strategies for Tracing the Nonlinear Response Near Limit Points. 2nd US-Europe Workshop “Nonlinear Finite Element Analysis in Structural Mechanics” (eds. W. Wunderlich, E. Stein, K.-J. Bathe), Bochum, Germany, 1980, Springer., 63–89.

Project data

Steffen Roth


This image shows Malte von Scheven

Malte von Scheven


Deputy Head of Institute

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