In this paper, new schemes are presented for the dynamic relaxation
DR method so that the snap-through and the snap-back regions can be traced automatically. These procedures are based on the minimization of the residual force
MRF and minimization of the residual energy
MRE, and they are capable of updating the load factor in each DR iteration. The suggested techniques are perfectly automatic. Therefore, they do not require any additional parameters such as arc length, incremental displacement, etc. For numerical verification, some frame and truss structures, all possessing geometrical nonlinear behaviors, are analyzed. Tracing the statical path shows that both the MRF and MRE methods can be used successfully in structures with snap-through and snap-back regions. The numerical results indicate that the MRE scheme traces the statical path with a greater number of increments than the MRF. While the jumping probability of the MRE is less than that of the MRF, the analysis time may increase in the MRE. Also, a comparison between the proposed DR methods and arc-length approach shows that the MRF and MRE procedures can present the limit points with higher accuracy.

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