On the effect of constraint parameters on the generalized displacement control method

• Generalized displacement control algorithm (GDCM) may be inaccurate at limit points.
• The constraint parameters of the GDCM is modified (MGDCM) to improve results.
• The constraint equation of the MGDCM is equivalent to that of the linearized cylindrical arc-length method.
• Numerical examples demonstrate the effectiveness of the MGDCM over the GDCM.

In this work, we investigate the generalized displacement control method (GDCM) and provide a modification (MGDCM) that results in an equivalent constraint equation as that of the linearized cylindrical arc-length control method (LCALCM). Through numerical examples, we illustrate that the MGDCM is more robust than the standard GDCM in capturing equilibrium paths in regions of high curvature. Moreover, we also provide a geometric and physical interpretation of the method, which sheds light on the general class of path following methods in structural mechanics.