Solving problems in structural dynamics using beam elements:
From collapse behaviors of buildings to torque cancelling of robots
Daigoro Isobe¹
1

Division of Engineering Mechanics and Energy, University of Tsukuba, Japan.

Abstract
In this lecture, several finite element approaches to solve various problems in structuraldynamics, all using beam elements for numerical modelling, are presented.
First, a brief outline of the Adaptively Shifted Integration (ASI)-Gauss code [1] incorporated
with linear Timoshenko beam elements is introduced. This code provides higher computational
efficiency than the conventional code in those problems with strong nonlinearities including
phenomena such as member fracture and elemental contact. Several results obtained by using
the numerical code are shown in this lecture. One of them are an aircraft impact analysis of ahigh-rise tower, conducted to identify the specific structural cause of the high-speed totalcollapse of the World Trade Center (WTC) towers, which occurred during the 9.11 terrorist
attacks. It is followed by a seismic pounding analysis of the Nuevo Leon buildings, a 14-story
apartment consisted of three similar buildings connected with narrow expansion joints, in which
two out of the three collapsed completely during the 1985 Mexican earthquake. Furthermore,
outcomes of a one-way coupling analysis of a steel frame building subjected under tsunami
wave and debris collision [2] is described. Finally, some numerical results obtained frommotion behavior analyses of indoor non-structural components such as ceilings and furnitureare compared with experimental results [3].
Next, a torque cancelling system (TCS) [4] that stabilizes mechanical sway in quick-motion
robots is described. The TCS computes reaction moments generated by motors in robots byconsidering the precise dynamics of the whole system. The reaction moments can be computed
using the parallel solution scheme of inverse dynamics [5], which handles the dynamics ofcomplex robotic architectures by modelling them with Bernoulli-Euler beam elements. In
contrast to the conventional schemes based upon dynamic equations, the developed scheme canhandle different types of configurations and can also consider the elasticity of constituted links
or passive joints by only changing the input numerical model. Once the reaction moment isknown, it can be cancelled by applying an anti-torque to a torque generating device. Someexperimental results of torque cancelling are presented in this lecture.
Keywords: Structural dynamics, FEM, Beam element, Collapse behaviors, Torque cancellingsystem, Inverse dynamics, Robot
References[1] D. Isobe: Progressive Collapse Analysis of Structures: Numerical Codes and Applications, Elsevier, eBook
ISBN: 9780128130421, Paperback ISBN: 978-0-12-812975-3, 2017.
[2] D. Isobe and S. Tanaka: Damage Estimation of a Steel-Framed Building under Tsunami Flow Occurring after
Earthquake, Earthquakes - Forecast, Prognosis and Earthquake Resistant Construction (Editor: ValentinaSvalova), InTech, ISBN:978-1-78923-950-8, pp.229-248, 2018.
[3] D. Isobe: Simulating Collapse Behaviors of Buildings and Motion Behaviors of Indoor Components During
Earthquakes, Earthquakes - Tectonics, Hazard and Risk Mitigation (Editor: Taher Zouaghi), InTech,
ISBN:978-953-51-2885-4, pp.341-363, 2017.
[4] D. Isobe: A Torque Cancelling System for Quick-Motion Robots, Intelligent Mechatronics (Editor: GaneshNaik), InTech, ISBN:978-953-307-300-2, pp.21-40, 2011.
[5] D. Isobe: Unified Solution Scheme for Inverse Dynamics of Robotic Systems, Progress in Autonomous Robot
Research (Editor: F.N. Mortensen), Nova Science Publishers, ISBN:978-1-60456-281-1, pp.125-173, 2008.