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Modelling, simulation and optimization of an elastic structure under moving loads
Author(s) -
Kimmerle SvenJoachim
Publication year - 2016
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201610337
Subject(s) - ode , ordinary differential equation , partial differential equation , bridge (graph theory) , moving load , differential (mechanical device) , class (philosophy) , mathematics , mathematical optimization , optimal control , computer science , differential equation , mathematical analysis , structural engineering , finite element method , engineering , medicine , aerospace engineering , artificial intelligence
We consider an elastic structure that is subject to moving loads representing e.g. heavy trucks on a bridge or a trolley on a crane beam. A model for the quasi‐static mechanical behaviour of the structure is derived, yielding a coupled problem involving partial differential equations (PDE) and ordinary differential equations (ODE). The problem is simulated numerically and validated by comparison with a standard formula used in engineering. We derive an optimal policy for passing over potentially fragile bridges. In general, our problem class leads to optimal control problems subject to coupled ODE and PDE. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)