Universität Stuttgart
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Item Open Access A nonsmooth generalized‐alpha method for mechanical systems with frictional contact(2021) Capobianco, Giuseppe; Harsch, Jonas; Eugster, Simon R.; Leine, Remco I.In this article, the existing nonsmooth generalized‐α method for the simulation of mechanical systems with frictionless contacts, modeled as unilateral constraints, is extended to systems with frictional contacts. On that account, we complement the unilateral constraints with set‐valued Coulomb‐type friction laws. Moreover, we devise a set of benchmark systems, which can be used to validate numerical schemes for mechanical systems with frictional contacts. Finally, this set of benchmarks is used to numerically assert the properties striven for during the derivation of the presented scheme. Specifically, we show that the presented scheme can reproduce the dynamics of the frictional contact adequately and no numerical penetration of the contacting bodies arises - a big issue for most popular time‐stepping schemes such as the one of Moreau. Moreover, we demonstrate that the presented scheme performs well for multibody systems containing flexible parts and that it allows general parametrizations such as the use of unit quaternions for the rotation of rigid bodies.Item Open Access Automatische Applikation modellbasierter Diesel-Luftsystem-Funktionen in Motorsteuergeräten(2020) Xie, Yijiang; Kistner, Arnold (Prof. Dr.-Ing.)The continuous development of diesel engines for meeting the legal and functional requirements, e.g. reducing emissions and fuel consumption while taking drivability into account, has led to a significant increase in the number of sensors and actuators required for the engine. For the diesel-air system it means to introduce a turbocharger, a system for exhaust gas recirculation (EGR), an exhaust gas aftertreatment system, a variable valve control, etc. In order to control such an increasingly complex system in diesel engines, ECU-functions are developed by means of a model-based approach. The success of a model-based development methodology is based on a precise and e cient modeling of the relevant engine behavior. Because of the limited computing power of an ECU, a combination of physical models and so-called calibration parameters is usually preferred for engine modeling. The calibration parameters can be scalar or one or two-dimensional empirical models and usual ly have to be determined (calibrated) by experiments on an engine test bench. Typical examples for such calibration parameters are lookup-tables for modeling the cylinder charge (volumetric e ciency) and the e ective area of the EGR valve. In this thesis a procedure is proposed which is able to calibrate the ECU functions for stationary relationships, e.g. in the diesel-air system, automatically and with as little measurement e ort as possible in terms of the number of measurement points. The algorithm runs within the framework of sequential experimental planning, in which Gaussian models with non-stationary covariance functions are used to approximate the relations of interest. For adaptive experimental planning an active sampling strategy is developed based on the concept of mutual information and optimal system inputs (engine speed, fuel quantity, air actuators, etc.) and which determines the resulting operating points, with respect to the input space coverage, the inhomogeneous properties of the relations, the uncertainty of the estimated calibration parameters and the feasibility of the operating points. The method is able to predict the stationary engine behavior, which results from the selected system inputs, by means of the physical structure of the air system and the data-based models of the calibration parameters. On this basis the uncertainties of the application parameters are estimated using extended Kalman filters. The feasibility of the operating point is checked by comparing the predicted system behavior with the engine limits. For validation the developed algorithm was implemented on an engine test bench to calibrate the air system of a diesel engine equipped with high and low pressure EGR, a variable geometry turbocharger and variable valve timing. As a result, using the presented approach, using as little as approx. 130 measurement points is enough to obtain a comparable application quality to that achieved by conventional methods with more than 800 measurement points.Item Open Access Projected and partitioned Runge-Kutta methods for nonsmooth mechanical systems with frictional contact and impacts(2024) Breuling, Jonas; Leine, Remco I. (Prof. Dr. ir. habil.)Item Open Access The “Fluid Jacobian” : modeling force-motion relationships in fluid-driven soft robots(2024) Remy, C. David; Brei, Zachary; Bruder, Daniel; Remy, Jan; Buffinton, Keith; Gillespie, R. BrentIn this paper, we introduce the concept of the Fluid Jacobian, which provides a description of the power transmission that operates between the fluid and mechanical domains in soft robotic systems. It can be understood as a generalization of the traditional kinematic Jacobian that relates the joint space torques and velocities to the task space forces and velocities of a robot. In a similar way, the Fluid Jacobian relates fluid pressure to task space forces and fluid flow to task space velocities. In addition, the Fluid Jacobian can also be regarded as a generalization of the piston cross-sectional area in a fluid-driven cylinder that extends to complex geometries and multiple dimensions. In the following, we present a theoretical derivation of this framework, focus on important special cases, and illustrate the meaning and practical applicability of the Fluid Jacobian in four brief examples.Item Open Access Stability and finite element analysis of fractionally damped mechanical systems(2021) Hinze, Matthias; Leine, Remco I. (Prof. Dr. ir. habil.)Item Open Access Finite element formulations for constrained spatial nonlinear beam theories(2021) Harsch, Jonas; Capobianco, Giuseppe; Eugster, Simon R.A new director-based finite element formulation for geometrically exact beams is proposed by weak enforcement of the orthonormality constraints of the directors. In addition to an improved numerical performance, this formulation enables the development of two more beam theories by adding further constraints. Thus, the paper presents a complete intrinsic spatial nonlinear theory of three kinematically different beams which can undergo large displacements and which can have precurved reference configurations. Moreover, the hyperelastic constitutive laws allow for elastic finite strain material behavior of the beams. Furthermore, the numerical discretization using concepts of isogeometric analysis is highlighted in all clarity. Finally, all presented models are numerically validated using exclusive analytical solutions, existing finite element formulations, and a complex dynamical real-world example.Item Open Access Finite element formulation of fractional constitutive laws using the reformulated infinite state representation(2021) Hinze, Matthias; Schmidt, André; Leine, Remco IngmarIn this paper, we introduce a formulation of fractional constitutive equations for finite element analysis using the reformulated infinite state representation of fractional derivatives. Thereby, the fractional constitutive law is approximated by a high-dimensional set of ordinary differential and algebraic equations describing the relation of internal and external system states. The method is deduced for a three-dimensional linear viscoelastic continuum, for which the hydrostatic and deviatoric stress-strain relations are represented by a fractional Zener model. One- and two-dimensional finite elements are considered as benchmark problems with known closed form solutions in order to evaluate the performance of the scheme.Item Open Access State observers for the time discretization of a class of impulsive mechanical systems(2022) Preiswerk, Pascal V.; Leine, Remco I.In this work, we investigate the state observer problem for linear mechanical systems with a single unilateral constraint, for which neither the impact time instants nor the contact distance is explicitly measured. We propose to attack the observer problem by transforming and approximating the original continuous‐time system by a discrete linear complementarity system (LCS) through the use of the Schatzman-Paoli scheme. From there, we derive a deadbeat observer in the form of a linear complementarity problem. Sufficient conditions guaranteeing the uniqueness of its solution then serve as observability conditions. In addition, the discrete adaptation of an existing passivity‐based observer design for LCSs can be applied. A key point in using a time discretization is that the discretization acts as a regularization, that is, the impacts take place over multiple time steps (here two time steps). This makes it possible to render the estimation error dynamics asymptotically stable. Furthermore, the so‐called peaking phenomenon appears as singularity within the time discretization approach, posing a challenge for robust observer design.Item Open Access Nonunit quaternion parametrization of a Petrov-Galerkin Cosserat rod finite element(2023) Harsch, Jonas; Eugster, Simon R.The application of the Petrov-Galerkin projection method in Cosserat rod finite element formulations offers significant advantages in simplifying the expressions within the discrete virtual work functionals. Moreover, it enables a straight‐forward and systematic exchange of the ansatz functions, specifically for centerline positions and cross‐section orientations. In this concise communication, we present a total Lagrangian finite element formulation for Cosserat rods that attempts to minimize the number of required theoretical concepts. The chosen discretization preserves objectivity and allows for large displacements/rotations and for large strains. The orientation parametrization with nonunit quaternions results in a singularity‐free formulation.Item Open Access Mechanical systems with frictional contact : geometric theory and time discretization methods(2021) Capobianco, Giuseppe; Leine, Remco I. (Prof. Dr. ir. habil.)This dissertation deals with the mathematical description and the simulation of mechanical systems with frictional contact. First, a geometric theory for the description of smooth mechanical systems is developed, which is then extended to allow for nonsmooth motions, i.e., motions with discontinuous velocities. The developed nonsmooth theory of mechanics is used to describe mechanical systems with frictional contact. Finally, two numerical schemes for the simulation of such systems are derived by using a time finite element method and the generalized-alpha approach, respectively.