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Steel and Composite Structures
  Volume 27, Number 1, April10 2018 , pages 13-25

A dual approach to perform geometrically nonlinear analysis of plane truss structures
AliReza Habibi and Shaahin Bidmeshki

    The main objective of this study is to develop a dual approach for geometrically nonlinear finite element analysis of plane truss structures. The geometric nonlinearity is considered using the Total Lagrangian formulation. The nonlinear solution is obtained by introducing and minimizing an objective function subjected to displacement-type constraints. The proposed method can fully trace the whole equilibrium path of geometrically nonlinear plane truss structures not only before the limit point but also after it. No stiffness matrix is used in the main approach and the solution is acquired only based on the direct classical stress-strain formulations. As a result, produced errors caused by linearization and approximation of the main equilibrium equation will be eliminated. The suggested algorithm can predict both pre- and post-buckling behavior of the steel plane truss structures as well as any arbitrary point of equilibrium path. In addition, an equilibrium path with multiple limit points and snap-back phenomenon can be followed in this approach. To demonstrate the accuracy, efficiency and robustness of the proposed procedure, numerical results of the suggested approach are compared with theoretical solution, modified arc-length method, and those of reported in the literature.
Key Words
    plane truss; geometric; nonlinear finite element; total Lagrangian; dual approach; snap-through
(1) AliReza Habibi:
Department of Civil Engineering, Shahed University, Tehran, Iran;
(2) Shaahin Bidmeshki:
Department of Civil Engineering, University of Kurdistan, Sanandaj, Iran.

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