Flexible Multibody Dynamics Finite Element Formulation Applied to Structural Progressive Collapse Analysis

Abstract

This paper presents a two-dimensional frame finite element methodology to deal with flexible multi-body dynamic systems and applies it to building progressive collapse analysis. The proposed methodology employs a frame element with Timoshenko kinematics and the dynamic governing equation is solved based on the stationary potential energy theorem written regarding nodal positions and generalized vectors components instead of displacements and rotations. The bodies are discretized by lose finite elements, which are assembled by Lagrange multipliers in order to make possible dynamical detachment. Due to the absence of rotation, the time integration is carried by classical Newmark algorithm, which reveals to be stable to the position based formulation. The accuracy of the proposed formulation is verified by simple examples and its capabilities regarding progressive collapse analysis is demonstrated in a more complete building analysis.

Analysis of dynamic coefficients for damage to the middle support of two-span and three-span continuous beams

“…Numerical studies are performed using finite element models of a damaged design in a static and dynamic setting [22][23][24][25]. With dynamic calculations, the damaged element is removed, and the internal forces arising in the removed element are applied to the structure, which decrease to zero during the element's damage time [22][23][24].…”

Análise mecânica e probabilística de estruturas treliçadas sujeitas ao colapso progressivo

“…Para o desenvolvimento que se segue, usa-se a matriz de amortecimento proporcional à massa [212,224], i.e., ς 1 = 0. Consequentemente, a Equação 3.63 resulta [203]:…”