Object-oriented modelling and simulation of flexible multibody thin beams in Modelica with the finite element method

In this paper the development, simulation and validation of Modelica models for flexible thin beams is presented. The models are based on the application of the finite element method. Exploiting the object-oriented features of the language, mixed-mode models (finite element-finite volume) are developed as well. All the models use the standard connectors defined within the Modelica multibody library, guaranteeing thus full compatibility with the library components. The details of the mathematical modelling are fully analyzed, showing the development of the equations of motion. The models feature also a graphical interface, with visualization of the simulation outcomes within the same 3D environment used in the multibody library, allowing the user to have an immediate visual feedback. Finally, the models are analyzed and validated by mean of selected simulation experiments, with reference both to theoretical predictions and to results commonly accepted within the scientific literature.