Arch length method can be used to trace the snap through or snap back behaviors(type of temporal instability ) which may occur in some structures as gable frames, arches and some types of shells etc.

Good discussion Chitaranjan Pany

Thanks Dr. Qasim M.Shakir.

I recommended your answer

Good discussion dr.Pany

In Mechanical engineering, where there is an instability problem (buckling of beams and shells), it is a good choice over Newton Raphson's classical methods, it allows us to draw the equilibrium path flowing of mechanical response.

Thanks dear Dr abdlarhmane