6,980 research outputs found
Energy conserving time integration scheme for geometrically exact beam
An energy conserving finite-element formulation for the dynamic analysis of geometrically non-linear beam-like structures undergoing large overall motions has been developed. The formulation uses classical displacement-based planar beam finite elements described in an inertial frame. It takes into account finite axial, bending and shear strains. A theoretically consistent approach is used to derive a novel and simple energy conserving scheme, using the unconventional incremental strain update rather than the standard strong form. Numerical examples demonstrate perfect energy and momenta conservation, stability and robustness of the scheme, and good convergence properties in terms of both the Newton-Raphson method and time step size. (c) 2006 Elsevier B.V. All rights reserved
Long-range forces in controlled systems
This thesis investigates new phenomena due to long-range forces and their effects
on different multi-DOFs systems. In particular the systems considered are metamaterials,
i.e. materials with long-range connections. The long-range connections
characterizing metamaterials are part of the more general framework of non-local
elasticity.
In the theory of non-local elasticity, the connections between non-adjacent particles
can assume different configurations, namely one-to-all, all-to-all, all-to-all-limited,
random-sparse and all-to-all-twin. In this study three aspects of the long-range
interactions are investigated, and two models of non-local elasticity are considered:
all-to-all and random-sparse.
The first topic considers an all-to-all connections topology and formalizes the mathematical
models to study wave propagation in long-range 1D metamaterials. Closed
forms of the dispersion equation are disclosed, and a propagation map synthesizes
the properties of these materials which unveil wave-stopping, negative group velocity,
instability and non-local effects. This investigation defines how long-range
interactions in elastic metamaterials can produce a variety of new effects in wave
propagation.
The second one considers an all-to-all connections topology and aims to define an
optimal design of the long-range actions in terms of spatial and intensity distribution
to obtain a passive control of the propagation behavior which may produces
exotic effects. A phenomenon of frequency filtering in a confined region of a 1D
metamaterial is obtained and the optimization process guarantees this is the best
obtainable result for a specific set of control parameters.
The third one considers a random-sparse connections topology and provides a new
definition of long-range force, based on the concept of small-world network. The
small-world model, born in the field of social networks, is suitably applied to a
regular lattice by the introduction of additional, randomly selected, elastic connections
between different points. These connections modify the waves propagation
within the structure and the system exhibits a much higher propagation speed and
synchronization. This result is one of the remarkable characteristics of the defined
long-range connections topology that can be applied to metamaterials as well as
other multi-DOFs systems. Qualitative experimental results are presented, and a
preliminary set-up is illustrated.
To summarize, this thesis highlights non-local elastic structures which display unusual
propagation behaviors; moreover, it proposes a control approach that produces
a frequency filtering material and shows the fast propagation of energy within a
random-sparse connected material
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