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

Abstract

In this lecture, several finite element approaches to
solve various problems in structural dynamics, all using beam elements for
numerical modelling, are presented.

First, a brief outline of the Adaptively Shifted Integration (ASI)-Gauss
code 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 a high-rise tower, conducted to identify the specific
structural cause of the high-speed total collapse 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
is described. Finally, some numerical results obtained from motion behavior
analyses of indoor non-structural components such as ceilings and furniture
are compared with experimental results.

Next, a torque cancelling system (TCS) that stabilizes mechanical sway
in quick-motion robots is described. The TCS computes reaction moments
generated by motors in robots by considering the precise dynamics of the
whole system. The reaction moments can be computed using the parallel solution
scheme of inverse dynamics, which handles the dynamics of complex robotic
architectures by modelling them with Bernoulli-Euler beam elements. In
contrast to the conventional schemes based upon dynamic equations, the
developed scheme can handle 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 is known,
it can be cancelled by applying an anti-torque to a torque generating device.
Some experimental results of torque cancelling are presented in this lecture.

PDF file