Application of Absolute Nodal Coordinate Formulation for Dynamic Progressive Collapse Analysis

Progressive collapse, a chain reaction or disproportionate propagation of failures following damage to a relatively small portion of a structure, has drawn attention from researchers and the public because it may lead to severe loss of life and property. Progressive collapse data are difficult to observe in situ and expensive to produce at large scales in laboratory testing. Because of the large deformations involved in structural collapse, lateral constraints at the beam ends exert variable axial forces on beams, which then provide extra collapse resistance known as compressive arch action and catenary action. In this paper, the absolute nodal coordinate formulation (ANCF) is combined with the fiber element method to build a finite element beam formulation for nonlinear dynamic progressive collapse simulation of reinforced concrete Euler-Bernoulli beam-column elements. ANCF is a non-incremental nonlinear finite element formulation proposed to describe the large deformation of moving bodies in multibody systems. Compared with traditional formulations, ANCF uses position vector gradients to describe the rotation of the body and strain state, thereby keeping the mass matrix constant and avoiding the need for interpolating non-vectoral rotation parameters. The explicit central difference method is applied to calculate the dynamic response of collapsing structural systems, and an example is presented in this paper.