Abstract:

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.

Reference:

• Kimmerle, S.-J.: Modelling, Simulation and Optimization of an Elastic Structure under Moving Loads, Proc. Appl. Math. Mech. 16(1) (2016), 697-698, DOI: 10.1002/pamm.201610337.