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

• Final Report Year: 2018

Final Report Abstract

Mortar techniques for higher order finite elements are used for modeling and numerical simulation of vibro-elastic structures. To enhance the performance, we develop a combination of tailored reduced basis methods and dimension reduction coupling conditions. Accurate approximations of eigenvalues and eigenmodes of complex structures are of key importance for the optimal design of timber constructions. A systematic study of the new coupling conditions as well as the reduced basis approach plays a central role. Classic mortar formulations emanate from a stiff bonding but model the effect of an elastomer insufficiently. However resolving the thin layer in a 3D structure, results in a large computational complexity. Thus, we introduce parameter dependent soft bonds in our new tearing and interconnecting concept and replace the volumetric layer by an interface. This leads to a regularized transmission condition. We test this new coupling strategy for thin walled structures and geometrically complex representative connections. Our new coupling conditions provide a robust and efficient way to reduce significantly the complexity and computational cost for highly anisotropic structures. Another challenge is the simulation of large multi-storey buildings. To determine the influence of the elastomer properties and the sensitivity of building geometry on the spectrum, many calculations for different setups are required. The complexity for such fine-grain simulation can be drastically reduced if classical reduced basis methods are combined with domain decomposition ideas. Port and bubble modes can be associated with the different connection and wall types. The mathematical modeling is done in close cooperation with sub-project 2 (TP2) and the implementation of the new concepts is based on the p-FEM software already developed in TP2. The choice of the parameters is done in close cooperation with sub-project 4 (TP4) by comparing the numerical simulation results with the measured data. All methodological developments are transferable to a variety of applications in the field of elasto-acoustics.

Publications

• A new mortar formulation for modeling elastomer bedded structures with modal-analysis in 3D. Advanced Modeling and Simulation in Engineering Sciences, 1:1–18, 2014
  T. Horger, S. Kollmannsberger, F. Frischmann, E. Rank, and B. Wohlmuth
  (See online at https://doi.org/10.1186/s40323-014-0018-0)
• Energy-corrected finite element methods for scalar elliptic problems. ENUMATH 2013 proceedings, 103:19–36, 2014
  T. Horger, M. Huber, U. Rüde, C. Waluga, and B. Wohlmuth
  (See online at https://doi.org/10.1007/978-3-319-10705-9_2)
• On optimal L2- and surface flux convergence in FEM. Computing and Visualization in Science, 16:231–246, 2015
  T. Horger, M. Melenk, and B. Wohlmuth
  (See online at https://doi.org/10.1007/s00791-015-0237-z)
• Complexity Reduction for Finite Element Methods with Applications to Eigenvalue Problems. PhD thesis, Technical University Munich, 2016
  T Horger
  
• (2017). Higher order energy-corrected finite element methods
  Horger, Thomas; Pustejovska, Petra; Wohlmuth, Barbara
  
• Reduced basis isogeometric mortar approximations for eigenvalue problems in vibroacoustics. In Model Reduction of Parametrized Systems, Springer, pages 91–106, 2017
  T. Horger, B. Wohlmuth, and L. Wunderlich
  (See online at https://doi.org/10.1007/978-3-319-58786-8_6)
• Simultaneous reduced basis approximation of parameterized elliptic eigenvalue problems. ESAIM: Mathematical Modelling and Numerical Analysis, 51:443 – 465, 2017
  T. Horger, B. Wohlmuth, and T. Dickopf
  (See online at https://doi.org/10.1051/m2an/2016025)
• A mortar formulation including viscoelastic layers for vibration analysis. Computational Mechanics
  A. Paolini, S. Kollmannsberger, E. Rank, T. Horger, and B. Wohlmuth
  (See online at https://doi.org/10.1007/s00466-018-1582-9)
• BIM gestützte strukturdynamische Analyse mit Volumenelementen höherer Ordnung. Bauingenieur, 93:160–166, 2018
  A. Paolini, F. Frischmann, S. Kollmannsberger, A. Rabold, T. Horger, B. Wohlmuth, E. Rank