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Nonlinear dynamic analysis of reticulated structures through the co-rotational finite element considering the shear and different mass matrixes
DOI:
https://doi.org/10.5216/reec.v19i2.75787Keywords:
Nonlinear dynamic analysis, Co-rotational formulation, Timoshenko mass matrix, Timoshenko beam, Finite ElementAbstract
ABSTRACT: Second-order effects on structures with a high slenderness index may play an important role regarding the mechanical behavior of such structures, since they imply an increase in the risk of instability. Additionally, linear static analysis may not describe the real behavior of a structure subjected to various external loads, especially in the case of atypical situations, such as earthquakes and strong wind gusts. In this context, a co-rotational formulation of the Finite Element Method is computationally implemented with the free program Scilab for dynamic nonlinear analysis of beams and frames. The Euler-Bernoulli and Timoshenko beam models are used to evaluate the stiffness matrix and the internal force vector of the structural system. The pseudocode of the incremental and iterative procedure based on the Newton-Raphson and Newmark methods is presented, which is used to obtain the approximate solution of the differential equation of motion. To verify the effectiveness of the implemented formulation, transient dynamic analyzes of structures with geometric nonlinearity found in the literature are performed. Furthermore, the first three natural frequencies of the structures are presented. Numerical results show the importance of choosing the appropriate mass matrix and considering the shear effect on the stiffness of the structural system, contributing to the development of computational models for the analysis and design of structures.
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