Elastic Behaviour of Linear Structures Using Modal Superposition and Lagrangian Differencing Dynamics
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Elastic deformation and dynamics response of the linear structures due to fluid loads are studied to understand the Fluid Structure Interaction (FSI). A modal coupling solver is developed by solving dynamic equation of motion with external loads, using the mode superposition method with the help of relevant mode shapes and natural frequencies of the structure. Natural frequencies and mode shapes are pre-calculated and provided as input for the simulation. Modal coupling is integrated into the Lagrangian Differencing Dynamics (LDD) method, that is based on finite differences in Lagrangian context, and strong and implicit formulation of Navier-Stokes equations to model the incompressible free-surface fluid. Elastic deformation of the structure due to fluid force obtained from the flow solver is calculated in the modal coupling algorithm using direct numerical integration. Then the elastic deformation is imposed in the flow solver to account for change of the geometry and obtain new flow pressure and velocity fields. The two-way coupling of fluid and structure is successfully validated by simulating dam-break through an elastic gate. Since the LDD method works directly on surface meshes, the simulation is quickly setup and direct coupling of structural deformation eliminated the usual step of mapping of fluid results on the structural mesh and vice-versa.
