engleski

Nonlinear finite element stability analysis of elastic thin-walled framed structures

In this work, a finite element formulation for incremental stability analysis of framed structures is presented. Using the updated Lagrangian formulation and applying the principle of virtual works, incremental equilibrium equations of a space beam element are developed. The linear approximation is adopted for displacement parameters of the axial deformation and the cubic interpolation for bending as well as torsion deformations. The element geometric stiffness is derived including the nonlinear displacement field of a thin-walled cross-section, which includes second-order terms of large space rotations. Due to this inclusion, the incremental geometric potential corresponding to the semitangential moment is derived ensuring the moment equilibrium at a joint of two or more non-collinear beam elements to be achieved. Material is assumed to be isotropic and linear elastic. The obtained finite element algorithm is implemented into a computer program and its accuracy and reliability is validated through several benchmark problems.

thin-walled space frame, nonlinear stability analysis, finite elements, large rotations, semitangential moment

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