Influence evaluation of high-order terms in the strain tensor for a complete geometric nonlinear analysis with Timoshenko element
Palavras-chave:
beam-column elements, Timoshenko theory, geometric stiffness matrix, post-critical behaviorResumo
This work evaluates the influence of high-order terms in the strain tensor associated to Timoshenko
beam theory for a geometric nonlinear analysis. The tangent stiffness matrix of the studied element considers an
updated Lagrangian formulation, shear deformation and the high-order terms in the strain tensor. A complete
geometric nonlinear analysis with robust nonlinear solution schemes are performed for structures with a
moderate slenderness ratio. The response is compared with a conventional updated Lagrangian formulation
disregarding the high-order terms in the strain tensor, and with a corotational formulation. Examples evidence
the importance of the high-order terms in strain tensor to perform geometric nonlinear analyses when
considering an updated Lagrangian formulation. Moreover, the analysis with reduced element discretization,
using the proposed formulation, provides equilibrium paths that are closer to highly discretized models
compared to the others formulations.
