Jörg Fehr

Model Order Reduction in Elastic Multibody Systems using the Floating Frame of Reference Formulation

Abstract System analysis and optimization of technical products are increasingly supported by virtual prototypes. For the modeling of the dynamical behavior of mechanical subsystems, elastic multibody systems are frequently used. In this contribution, an overview of the basic approaches to model elastic multibody systems with the help of the floating frame of reference formulation is given. It is one of the most common approaches in the field of modeling flexible multibody systems. Here, the discretization of the elastic bodies, e.g. with the help of the Finite Element Method, introduces a large number of elastic degrees of freedom and an efficient simulation of the system becomes difficult. A focus in this work is the linear model order reduction of the elastic degrees of freedom, which is a key step for using flexible bodies in elastic multibody systems. Thereby, the simulation of the elastic multibody system becomes possible or more efficient from a computational point of view. Recently a variety of modern reduction techniques, based on Krylov subspaces or based on a singular value decomposition have been developed and applied successfully in engineering applications. The topic of this work is the application of this techniques in elastic multibody systems with its special requirements, such as, e.g., structure preservation. The differences of these reduction methods are introduced and compared.

Best practices for replicability, reproducibility and reusability of computer-based experiments exemplified by model reduction software

Over the recent years the importance of numerical experiments has gradually been more recognized. Nonetheless, sufficient documentation of how computational results have been obtained is often not available. Especially in the scientific computing and applied mathematics domain this is crucial, since numerical experiments are usually employed to verify the proposed hypothesis in a publication. This work aims to propose standards and best practices for the setup and publication of numerical experiments. Naturally, this amounts to a guideline for development, maintenance, and publication of numerical research software. Such a primer will enable the replicability and reproducibility of computer-based experiments and published results and also promote the reusability of the associated software.

Einfluss von Schnittstellenmodellierungen bei der Reduktion elastischer Mehrkörpersysteme

Zusammenfassung Für die effiziente Simulation elastischer Mehrkörpersysteme sind wenige wohldefinierte Rand- und Koppelbedingungen bzw. Ein- und Ausgänge notwendig. Bisher müssen in der Modellierungsphase Schnittstellenknoten zur Verringerung der Ein- und Ausgangsanzahl gebildet werden. Ein neuer mathematischer Ansatz basiert auf der Zerlegung der Ein- und Ausgangsmatrix und verzichtet auf zusätzliche Schritte in der Modellerstellung. Eine Gegenüberstellung beider Ansätze erfolgt in diesem Beitrag. Abstract A small number of well-defined boundary and coupling conditions respectively inputs and outputs is essential for the efficient simulation of Elastic Multibody Systems. Up to now interface nodes have to be build to reduce the number of inputs and outputs in the modeling step. A new mathematical approach without an additional modeling step is based on the decomposition of the inputs and output matrix. A comparison of both methods is presented in this paper.

Flexible multibody simulation of automotive systems with non-modal model reduction techniques

The stiffness of the body structure of an automobile has a strong relationship with its noise, vibration, and harshness (NVH) characteristics. In this paper, the effect of the stiffness of the body structure upon ride quality is discussed with flexible multibody dynamics. In flexible multibody simulation, the local elastic deformation of the vehicle has been described traditionally with modal shape functions. Recently, linear model reduction techniques from system dynamics and mathematics came into the focus to find more sophisticated elastic shape functions. In this work, the NVH-relevant states of a racing kart are simulated, whereas the elastic shape functions are calculated with modern model reduction techniques like moment matching by projection on Krylov-subspaces, singular value decomposition-based reduction techniques, and combinations of those. The whole elastic multibody vehicle model consisting of tyres, steering, axle, etc. is considered, and an excitation with a vibration characteristics in a wide frequency range is evaluated in this paper. The accuracy and the calculation performance of those modern model reduction techniques is investigated including a comparison of the modal reduction approach.

Interface and model reduction for efficient explicit simulations - a case study with nonlinear vehicle crash models

ABSTRACT This work presents an approach to save simulation time in explicit crash simulations of vehicles by applying model order reduction (MOR). The model of a kart frame is split into linear and nonlinear parts. The linear part is reduced with linear MOR techniques in MatMorembs. Optimal substructuring methods are used to calculate suitable reduced models which are exported to LS-DYNA. Afterwards, the model consisting of a linear reduced part and a nonlinear part is simulated in the online step. The plastic deformation of the kart frame as well as the accelerations of the driver calculated with various reduction and parameter settings are compared with the accelerations measured when the original, unreduced nonlinear model is simulated. For optimal simulation results, the large interface between the models needs to be approximated by suitable interface-reduction approaches. The novel contribution is the application of advanced interface-reduction techniques in nonlinear explicit crash simulations. Craig–Bampton and Gramian matrix-based-like techniques with global, local and no interface reduction are compared to find optimally reduced substructures in terms of approximation quality of the assembled system and computational effort. For the kart frame, the applicability of the method is proven by gaining a small simulation speed up which cannot be achieved with the standard reduction methods provided by LS-DYNA.

Morembs—A Model Order Reduction Package for Elastic Multibody Systems and Beyond

Many new promising model order reduction (MOR) methods and algorithms were developed during the last decade. Industry and academic research institutions intend to test, validate, compare, and use these new promising MOR techniques with their own models. Therefore, an MOR toolbox bridging the gap between theoretical, algorithmic, and numerical developments to an end-user-oriented program, usable by non-experts, was developed called ‘Model Order Reduction of Elastic Multibody Systems’ (Morembs). A C++ implementation as well as a Matlab implementation including an intuitive graphical user interface is available. Import from various FE programs is possible, and the reduced elastic bodies can be exported to a variety of programs to simulate the compact models. In the course of the various projects, many improvements on the algorithmic side were added. As we learned over the years, there is not one ‘optimal’ MOR method. ‘Optimal’ MOR depends on circumstances, like boundary conditions, excitation spectra, further model usage. The toolbox is now used, e.g., in solid mechanics, biomechanics, vehicle dynamics, control of flexible structures, or crash simulations. In all these use cases, the toolbox allows the user to facilitate their well-known modeling and simulation environment. Only the critical MOR process during preprocessing is performed with Morembs, which helps to compare the various MOR techniques to find the most suited one.

Implementation and validation of the extended Hill-type muscle model with robust routing capabilities in LS-DYNA for active human body models

BackgroundIn the state of the art finite element AHBMs for car crash analysis in the LS-DYNA software material named *MAT_MUSCLE (*MAT_156) is used for active muscles modeling. It has three elements in parallel configuration, which has several major drawbacks: restraint approximation of the physical reality, complicated parameterization and absence of the integrated activation dynamics. This study presents implementation of the extended four element Hill-type muscle model with serial damping and eccentric force–velocity relation including

Greedy‐based approximation of frequency‐weighted Gramian matrices for model reduction in multibody dynamics

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