Mortar techniques and model reduction for vibro elastic structures

• Applicant: Professorin Dr. Barbara Wohlmuth
• Subject Area: Applied Mechanics, Statics and Dynamics
• Term: from 2012 to 2018
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 221056413

As pointed out in the rst application, mortar techniques are used for modeling and numerical simulation of vibro-elastic structures. In addition, dimensional reduced approaches based on new coupling conditions as well as special reduced basis methods are developed for the model reduction. This project focusses on mortar finite elements of higher order based on Lagrange multipliers and on approaches for model reduction. Precise statements to eigenvalues and eigenmodes of a system are of key importance for the optimal design of timber constructions. Since the related eigenproblem is investigated within the framework of mortar methods, discrete eigenmodes depend on the Lagrange multiplicator space and the continuous eigenmodes depend on the dimensional reduced coupling model. Therefore, the systematic investigation of these inuences is the central question of this project. Standard mortar formulations are based on a rigidly bond and model the joint insuciently. Due to this reason parameter dependent soft bonds are integrated and investigated. This leads to a regularized transmission condition. Thin walled structures prove to be a particular challenge as well as the geometrical nonconformity of the representative connections. New coupling conditions, leading to dimensionally reduced models, are developed to provide a robust and ecient way to handle the anisotropy. Another challenge will be the simulation of large multi-storey buildings. To determine the inuence of the elastomer on eigenvalues and eigenmodes many calculation processes with dierent parameters (elastomere) and for dierent building geometries have to be done. To reduce the computational cost a fast dimensional reduced method shall be developed. For this purpose reduced basis methods shall be used as an additional model reduction. The mathematical modeling is done in close cooperation with (TP2) and the implementation of the new concepts is based on the p-FEM software already developed by TP2. The choice of the parameters is done in close cooperation with TP2 and TP4 by comparing the numerical simulation results with the measured data. All methodological developments are transferable to a variety of applications in the eld of elasto-acoustics.

• DFG Programme: Research Grants