Two-step incremental procedure associated with the normal flow technique applied to trusses

Two-step incremental procedure associated with the normal flow technique applied to trusses




Linear Arc-Length, positional formulation, Geometric nonlinearity, Normal Flow technique


To achieve the nonlinear structural behavior, there is a need to trace of their equilibrium path in the space of load-displacement. Truss systems are commonly implemented in several structural systems, including high-span bridges and bracing of the supporting structure of tall buildings. Our study adapts a two-step method with cubic convergence into an incremental-iterative procedure to analyze the geometric nonlinear behavior of trusses. The solution method is combined with the Linear Arc-Length path-following technique. To find the approximate root of nonlinear equation system in the two-step method, two formulas are used. Structures are discretized using the Positional Finite Element Method and all truss bars are assumed to remain linear elastic. The correction of the nodal coordinates subincrement vector is performed using the Normal Flow technique. A computational algorithm was implemented using the free program Scilab. Our numerical results show that, when compared to the standard and modified Newton-Raphson algorithms, the new algorithm decreases the number of iterations and the computing time in the nonlinear analysis of trusses. Equilibrium paths with force and/or displacement limit points are obtained with good precision.


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Author Biographies

Luiz Antonio Farani de Souza, Universidade Tecnológica Federal do Paraná - UTFPR Universidade Estadual de Maringá - UEM

Prof. Dr., Civil Engineering Course, UTFPR, Apucarana, Paraná


Wilson Doná Junior, Universidade Estadual de Maringá - UEM

Master's Student, Graduate Program in Civil Engineering - PCV, UEM, Maringá, Paraná

Everton Luis Consoni da Silva, Universidade Estadual de Maringá - UEM

Master's Student, Graduate Program in Civil Engineering - PCV, UEM, Maringá, Paraná.


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How to Cite

Souza, L. A. F. de, Doná Junior, W., & Silva, E. L. C. da. (2022). Two-step incremental procedure associated with the normal flow technique applied to trusses. Semina: Ciências Exatas E Tecnológicas, 43(1Esp), 29–40.



Original Article