Abstract: A tensor-based updated Lagrangian (UL) formulation for the geometrically nonlinear analysis of 2D beam-column structures is developed by using curvilinear coordinates, which has considered the effects of the deformed curvature. Between the known configuration C₁ and the desired configuration C₂, a configuration C₂^* derived by rigid-body motion of C₁ is introduced to eliminate the element-end transverse displacements between C₂^* and C₂. A stiffness matrix is obtained in C₂^*; and then by a transformation defined by the element-end displacements, the stiffness matrix in C₂^* is transformed into that in C₁. Comparing the stiffness matrix with that in the conventional UL formulation for a 2D beam element, the initial displacement stiffness matrix emerges, which results from the deformed curvature within the element. Numerical examples have verified the accuracy and efficiency of the present formulation, and the results show that the deformed curvatures have significant effects when deformations are large.

Key words: Deformed curvature, Beam element, Updated Lagrangian (UL) formulation, Geometrical no-linearity, Finite element

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