Absolute nodal coordinate formulation for dynamic analysis of reinforced concrete structures

Abstract An efficient and accurate beam element for performing explicit dynamic analysis of reinforced concrete beam elements was built using the absolute nodal coordinate formulation (ANCF). Such a formulation is useful for performing dynamic analysis under large strains and displacement with sudden load changes, such as during impact loading or for progressive collapse analysis. Compared with traditional nodal position formulations, ANCF uses position vector gradients to describe the rotation of the body and strain state, thereby avoiding the need for interpolating non-vectoral rotation parameters. The fiber element method was applied to calculate element stiffness from section deformations by subdividing beam elements into uniaxial fibers. The combined fiber element beam-column model with ANCF was validated by traditional co-rotational analysis and the quadrature element method (QEM), and thus may be used in general nonlinear dynamic analysis.

[1]  Feng Fu,et al.  3-D nonlinear dynamic progressive collapse analysis of multi-storey steel composite frame buildings — Parametric study , 2010 .

[2]  E. Spacone,et al.  Nonlinear Pushover Analysis of RC Structures , 2000 .

[3]  Vitelmo V. Bertero,et al.  Modeling of R/C Joints under Cyclic Excitations , 1983 .

[4]  M. Menegotto.  Method of Analysis for Cyclically Loaded R. C. Plane Frames Including Changes in Geometry and Non-Elastic Behavior of Elements under Combined Normal Force and Bending , 1973 .

[5]  E. Brunesi,et al.  Extreme response of reinforced concrete buildings through fiber force-based finite element analysis , 2014 .

[6]  A. Shabana,et al.  DEVELOPMENT OF SIMPLE MODELS FOR THE ELASTIC FORCES IN THE ABSOLUTE NODAL CO-ORDINATE FORMULATION , 2000 .

[7]  Ahmed A. Shabana,et al.  Dynamics of Multibody Systems , 2020 .

[8]  Griengsak Kaewkulchai.  Dynamic progressive collapse of frame structures , 2003 .

[9]  Enrico Spacone,et al.  FIBRE BEAM–COLUMN MODEL FOR NON‐LINEAR ANALYSIS OF R/C FRAMES: PART I. FORMULATION , 1996 .

[10]  Brock D. Hedegaard,et al.  Flexural, Compressive Arch, and Catenary Mechanisms in Pseudostatic Progressive Collapse Analysis , 2018 .

[11]  Finite element analysis of large displacements in flexural systems , 1981 .

[12]  A. Shabana.  Finite Element Incremental Approach and Exact Rigid Body Inertia , 1995 .

[13]  Marco Petrangeli,et al.  Fiber Element for Cyclic Bending and Shear of RC Structures. I: Theory , 1999 .

[14]  A. Goetz.  Introduction to differential geometry , 1970 .

[15]  A. Mikkola,et al.  Review on the Absolute Nodal Coordinate Formulation for Large Deformation Analysis of Multibody Systems , 2013 .

[16]  Sarah Orton,et al.  Experimental Evaluation of Disproportionate Collapse Resistance in Reinforced Concrete Frames , 2013 .

[17]  A. Shabana.  Definition of the Slopes and the Finite Element Absolute Nodal Coordinate Formulation , 1997 .

[18]  Theodor Krauthammer,et al.  Analysis of impulsively loaded reinforced concrete structural elements. I: Theory , 1993 .

[19]  Leslaw Kwasniewski,et al.  Nonlinear dynamic simulations of progressive collapse for a multistory building , 2010 .

[20]  Yan Xiao,et al.  Experimental Study on Progressive Collapse-Resistant Behavior of Reinforced Concrete Frame Structures , 2008 .

[21]  Reza Abbasnia,et al.  A theoretical method for calculating the compressive arch capacity of RC beams against progressive collapse , 2016 .

[22]  Hongzhi Zhong,et al.  Large deflection elasto-plastic analysis of frames using the weak-form quadrature element method , 2012 .

[23]  H. R. Milner,et al.  Accurate finite element analysis of large displacements in skeletal frames , 1981 .

[24]  Nicola Augenti,et al.  Progressive collapse fragility of reinforced concrete framed structures through incremental dynamic analysis , 2015 .

[25]  Youpo Su,et al.  Progressive Collapse Resistance of Axially-Restrained Frame Beams , 2009 .

[26]  Peter C. Kohnke,et al.  Large deflection analysis of frame structures by fictitious forces , 1978 .

[27]  Alessandra Marini,et al.  Analysis of Reinforced Concrete Elements Including Shear Effects , 2006 .

[28]  Fahim Sadek,et al.  An Experimental and Computational Study of Reinforced Concrete Assemblies under a Column Removal Scenario , 2011 .

[29]  Johannes Gerstmayr,et al.  On the correct representation of bending and axial deformation in the absolute nodal coordinate formulation with an elastic line approach , 2008 .

[30]  Feng Fu,et al.  Progressive collapse analysis of high-rise building with 3-D finite element modeling method , 2009 .