# Comparison of nonlinear solution techniques named arc-length for the geometrically nonlinear analysis of structural systems

### Abstract

The nonlinearity issue is one of the promising fields in the engineering area. Particularly, the geometric nonlinearity bears a big importance for the structural systems showing a tendency of larger deflection. In order to obtain a correct load-deflection relation for the structural system subject to any external load, an advanced incremental-iterative based approach has to be utilized in the analysis of nonlinear responses. Arc length method has been proven to be the most perfect one among the nonlinear analysis approaches. Thus, it is extensively applied to the structural systems with pin-connected joints. This study attempts to compare two variations of arc length method named “spherical” and “linearized” for the nonlinear analysis of planar structural system with rigid-connected joints. Also, two different element formulations are utilized to discretize the planar structural systems. Two open-source coded programs named Opensees and FEAP are employed for six benchmark structural systems in order to compare the performance of employed arc-length techniques. Furthermore, in order to make a further observation in the nonlinear behavior of application examples, their simulations are not only sketched using graphs but also displayed through the movies for each of benchmark tests. Consequently, the linearized type arc length technique implemented in FEAP shows a more success with a better prediction of load-deflection relation nothing that Opensees has a big advantage of having an element which capable of simulating both geometric and material nonlinearity at the same time.

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