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| EPSRC Reference: |
GR/N05673/01 |
| Title: |
TIME INTEGRATION ALGORITHMS FOR THE STEADY STATES OF DISSIPATIVE NON-LINEAR DYNAMIC SYSTEMS |
| Principal Investigator: |
Dr U Galvanetto |
| Other Investigators: |
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| Researcher Co-investigator: |
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| Project Partner: |
| Finite Element Analysis Ltd |
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| Department: |
Aeronautics |
| Organisation: |
Imperial College London |
| Scheme: |
Standard Research |
| Starts: |
30 June 2000 |
Ends: |
29 June 2003 |
Value (£): |
53,371
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| EPSRC Research Topic Classifications: |
| Engineering of Matrs/Props/Test: Mechanical |
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| EPSRC Industrial Sector Classifications: |
| Aerospace, Defence and Marine |
Construction |
| Information Technologies |
Transport Systems and Vehicles |
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| Related Grants: |
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| Panel History: |
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Summary |
The solution of the steady-state dynamics of dissipative non-linear mechanical systems involves the numerical integration of the governing equations of motion over a large time duration. This time duration should be adequately large to ensure that the transients die down and the solution captures the steady-state dynamics. This demands that the integration scheme be stable and accurate. The scheme, which was found wide acceptance for non-linear dynamic problems, is the fourth-order Runge-Kutta method that is not a preferred integration scheme for engineering solutions, because it calls for four equations solutions per time-step and requires a small time step to get accurate results from stiff equations. These drawbacks have restricted the study of non-linear dynamics and chaos to a limited number of degrees of freedom. This fast stream proposal aims to simulate the non-linear dynamics of dissipative structures with the finite element method and to check the validity of the results by using non-linear dynamic systems theory. This proposal will examine the capability of different integration schemes to describe the attractors, their shape, their size and their transitions as a driving parameter is changed. It will also try to develop new variable-step integrations schemes and realistic simulations of structural damping.
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| Final Report Summary |
This is not a different abstract, it is only written for a non-specialist audience.
Modern structures are making an increasing use of light flexible components; clear examples of such a tendency are given by light bridges, helicopter and windmill blades, telecom towers, satellite components, vibrating mechanical tools, pipes suspended on the sea bed ... In general non-linear effects cannot be neglected when studying the dynamics of such structures and they can constitute an insidious risk for the structural engineer, as the problems with the Millennium bridge in London have recently shown. The complexity of a large variety of modern structures reduces considerably the possibility of using analytical methods in the study of the structural dynamics. Therefore computational techniques seem to be the most appropriate tool to predict the long-term dynamic behaviour of complex structures. The main objective of the project was to develop time integration schemes that could be effectively used in structural dynamics applications by applying ideas coming from the theory of non-linear dynamical systems and chaos. The results obtained in the project should probably allow faster and cheaper structural computations for complex flexible structures.
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| Further Information: |
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| Organisation Website: |
http://www.ic.ac.uk |
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