Abstract
The widely used classic collocation-based time integration procedures like Newmark, Generalized-alpha etc.
generally work well within a framework of linear problems, but typically may encounter problems, when used in connection with
essentially nonlinear structures. These problems are overcome in the new generation of energy conserving algorithms developed
over the last two decades. However, the conservative algorithms typically rely on the special structure of the problem to be solved
and require intermediate calculations using a mean state. This seems to have limited their use outside academia. In the present paper
a conservative time integration algorithm is developed in a format using only the internal forces and the associated tangent stiffness
at the specific time integration points. Thus, the procedure is computationally very similar to a collocation method, consisting of a
series of nonlinear equivalent static load steps, easily implemented in existing computer codes. The paper considers two aspects:
representation of nonlinear internal forces in a form that implies energy conservation, and the option of an algorithmic damping
with the purpose of extracting energy from undesirable high-frequency parts of the response. The energy conservation property
is developed in two steps. First a fourth-order representation of the internal energy increment is obtained in terms of the mean
value of the associated internal forces and an additional term containing the increment of the tangent stiffness matrix over the time
step. This explicit formula is exact for structures with internal energy in the form of a polynomial in the displacement components
of degree four. A fully general form follows by introducing an additional term based on a secant representation of the internal
energy. The option of a simple monotonic algorithmic damping is included by introducing a slight shift in the weighting of the
displacement and velocity components at the forward and the current time, and the magnitude of the corresponding algorithmic
damping is therefore controlled by a single parameter.
Original language | English |
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Title of host publication | Proceedings of 9th European Conference on Structural Dynamics, EURODYN 2014 |
Editors | A. Cunha, E. Caetano, P. Ribeiro, G. Müller |
Number of pages | 10 |
Publisher | European Association for Structural Dynamics |
Publication date | 2014 |
ISBN (Electronic) | 978-972-752-165-4 |
Publication status | Published - 2014 |
Event | 9th International Conference on Structural Dynamics - Porto, Portugal Duration: 30 Jun 2014 → 2 Jul 2014 Conference number: 9 http://paginas.fe.up.pt/~eurodyn2014/ |
Conference
Conference | 9th International Conference on Structural Dynamics |
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Number | 9 |
Country/Territory | Portugal |
City | Porto |
Period | 30/06/2014 → 02/07/2014 |
Internet address |
Keywords
- Time integration
- Nonlinear dynamics
- Energy conservation