TUHH Open Research (TORE)https://tore.tuhh.deTORE captures, stores, indexes, preserves, and distributes digital research material.Sat, 10 Jun 2023 10:48:18 GMT2023-06-10T10:48:18Z5041- A high order fast multipole boundary element methodhttp://hdl.handle.net/11420/7844Title: A high order fast multipole boundary element method
Authors: Keuchel, Sören; Vater, Kerstin; Estorff, Otto von
Abstract: The Boundary Element Method can be used to solve the Helmholtz equation in three dimensions. Just the surface has to be discretized, but a solution for the complete domain is obtained. Especially for exterior domains this is an enormous advantage. A drawback of the solution procedure, however is its quadratic complexity. The Fast Multipole Method results in a quasi linear complexity due to an approximation of a matrix vector product and is therefore applicable for solving large scale systems. The variables on the surface are approximated by ansatz functions of a certain order. Typically constant, linear or quadratic element orders are used. In this contribution formulations for arbitrary ansatz functions are presented. Since an application to exterior cases leads to the problem of fictitious frequencies, a Burton Miller formulation is embedded. The presented Collocation Method can treat the hypersingular kernels for arbitrary ansatz functions correctly. The theoretical background is introduced and numerical examples show the performance of the formulation.
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/11420/78442015-01-01T00:00:00Z
- hp Fast multipole boundary element method for 3D acousticshttp://hdl.handle.net/11420/3946Title: hp Fast multipole boundary element method for 3D acoustics
Authors: Keuchel, Sören; Vater, Kerstin; Estorff, Otto von
Abstract: A fast multipole boundary element method (FMBEM) extended by an adaptive mesh refinement algorithm for solving acoustic problems in three-dimensional space is presented in this paper. The Collocation method is used, and the Burton–Miller formulation is employed to overcome the fictitious eigenfrequencies arising for exterior domain problems. Because of the application of the combined integral equation, the developed FMBEM is feasible for all positive wave numbers even up to high frequencies. In order to evaluate the hypersingular integral resulting from the Burton–Miller formulation of the boundary integral equation, an integration technique for arbitrary element order is applied. The fast multipole method combined with an arbitrary order h-p mesh refinement strategy enables accurate computation of large-scale systems. Numerical examples substantiate the high accuracy attainable by the developed FMBEM, while requiring only moderate computational effort at the same time. Copyright © 2016 John Wiley & Sons, Ltd.
Thu, 01 Jun 2017 00:00:00 GMThttp://hdl.handle.net/11420/39462017-06-01T00:00:00Z
- Towards neural network‐based numerical friction modelshttp://hdl.handle.net/11420/15121Title: Towards neural network‐based numerical friction models
Authors: Vater, Kerstin; Stender, Merten; Hoffmann, Norbert
Abstract: Friction contacts can be found in almost all mechanical systems and are often of great technical importance. However, they are usually difficult to describe, and their behavior and influence on the whole system are hard to predict accurately. Modern product design and system operation strongly benefit from numerical simulation approaches today, but reliable friction models still represent a major challenge in this context.
To tackle this problem, we employ neural network regression to capture the characteristics of frictional contacts and make them accessible for numerical methods in a minimal intrusive fashion. In particular, we test our approach using a Finite Element model of a 2D cantilever beam subject to stick-slip vibrations induced by a moving conveyor belt at its free end. As a reference solution, we perform a transient analysis based on a simple analytical friction model, where the kinetic friction force only depends on the normal load and the relative sliding velocity. We take the same friction model, add some artificial noise to mimic uncertainties coming with experimental measurements, and pick a limited set of data points to train a regression neural network. The machine learning friction model is then deployed in the Finite Element code to predict the kinetic friction force acting on the beam tip during the slip phases.
The deflection curves obtained by the transient numerical analysis using the new neural network friction model agree well with the reference solution based on the underlying analytical model. The results indicate that data-driven approaches may also be capable of capturing more complex frictional contacts, including effects of temperature, humidity, and load history. The trained neural network friction models can then be employed in numerical simulations in a minimally intrusive manner. This approach opens up new possibilities to predict individual mechanical system behavior as accurately as possible.
Fri, 24 Mar 2023 00:00:00 GMThttp://hdl.handle.net/11420/151212023-03-24T00:00:00Z
- Towards neural network-based numerical friction modelshttp://hdl.handle.net/11420/13470Title: Towards neural network-based numerical friction models
Authors: Vater, Kerstin; Stender, Merten; Hoffmann, Norbert
Abstract: Friction contacts can be found in almost all mechanical systems and are often of great technical importance. However, they are usually difficult to describe, and their behavior and influence on the whole system are hard to predict accurately. Modern product design and system operation strongly benefit from numerical simulation approaches today, but reliable friction models still represent a major challenge in this context.
To tackle this problem, we employ neural network regression to capture the characteristics of frictional contacts and make them accessible for numerical methods in a minimal intrusive fashion. In particular, we test our approach using a Finite Element model of a 2D cantilever beam subject to stick-slip vibrations induced by a moving conveyor belt at its free end.
As a reference solution, we perform a transient analysis based on a simple analytical friction model, where the kinetic friction force only depends on the normal load and the relative sliding velocity. We take the same friction model, add some artificial noise to mimic uncertainties coming with experimental measurements, and pick a limited set of data points to train a regression neural network. The machine learning friction model is then deployed in the Finite Element code to predict the kinetic friction force acting on the beam tip during the slip phases.
The deflection curves obtained by the transient numerical analysis using the new neural network friction model agree well with the reference solution based on the underlying analytical model. The results indicate that data-driven approaches may also be capable of capturing more complex frictional contacts, including effects of temperature, humidity, and load history. The trained neural network friction models can then be employed in numerical simulations in a minimally intrusive manner. This approach opens up new possibilities to predict individual mechanical system behavior as accurately as possible.
Thu, 18 Aug 2022 00:00:00 GMThttp://hdl.handle.net/11420/134702022-08-18T00:00:00Z