Klaus Dreßler - Academia.edu (original) (raw)

Papers by Klaus Dreßler

The Rainflow Method in Fatigue, 1992

Abstract We present a new fatigue analysis data reduction concept for general multidimensional ti... more Abstract We present a new fatigue analysis data reduction concept for general multidimensional time series. The method is based on the Rainflow method, the most successful one-dimensional counting algorithm.

Mathematik Schlüsseltechnologie für die Zukunft, 1997

We propose a modification of the one-parameter multisurface Mroz- model for kinematic hardening, ... more We propose a modification of the one-parameter multisurface Mroz- model for kinematic hardening, which takes into account the phenomenon of ratchetting. We present some numerical simulations which show a certain qualitative agreement with published experimental data.

Mathematik in der Praxis, 1995

Muste man die in der Uberschrift gestellte Frage mit einem Wort beantworten, so wurde man sagen: ... more Muste man die in der Uberschrift gestellte Frage mit einem Wort beantworten, so wurde man sagen: Teilweise. Durfte man einen ganzen Satz formulieren, so konnte man etwa antworten: Nur das richtige Zusammenspiel von Tests, Rechnungen und Ingenieurerfahrung ermoglicht es gegenwartig, brauchbare Lebensdauervorhersagen bei vertretbarem Aufwand zu erstellen. Wurde man sich auf Tests beschranken, so hiese das Echtzeitfahrt auf der Strase oder auf dem Prufstand. Die Entwicklung ware dann zu teuer und zu langwierig, da fur jede Entwurfsvariante Prototypen des Fahrzeugs oder einzelner Teile desselben hergestellt werden musten. Auf der anderen Seite sind die auf dem heutigen Stand von Theorie und Algorithmik durchgefuhrten Rechnungen fur sich allein genommen nicht aussagekraftig und sicher genug. Tatsachlich sind gegenwartig in der Betriebsfestigkeitsanalyse Tests und Rechnungen an mehreren Stellen verzahnt. Eine zentrale Rolle auf der Seite der Algorithmik spielen hier — neben FE- und BE-Verfahren — Verfahren zur Datenanalyse und -aufbereitung, und zwar im Bereich der Klassierverfahren insbesondere das Rainflow-Verfahren.

SIMVEC – Simulation und Erprobung in der Fahrzeugentwicklung

SAE Technical Paper Series

Testing a new suspension based on real load data is performed on elaborate multi channel test rig... more Testing a new suspension based on real load data is performed on elaborate multi channel test rigs. Usually wheel forces and moments measured during driving maneuvers are reproduced on the rig. Because of the complicated interaction between rig and suspension each new rig configuration has to prove its efficiency with respect to the requirements and the configuration might be subject to optimization. This paper deals with modeling a new rig concept based on two hexapods. The real physical rig has been designed and meanwhile built by MOOG-FCS for VOLKSWAGEN. The aim of the simulation project reported here was twofold: First the simulation of the rig together with real VOLKSWAGEN suspension models at a time where the design was not yet finalized was used to verify and optimize the desired properties of the rig. Second the simulation environment was set up in a way that it can be used to prepare real tests on the rig. The model contains the geometric configuration as well as the hydrau...

Sicherheitsrelevante Bauteile sind in der Automobilindustrie so auszulegen, dass sie im Rahmen vo... more Sicherheitsrelevante Bauteile sind in der Automobilindustrie so auszulegen, dass sie im Rahmen von bestimmungsgemaesser Verwendung oder vorhersehbarer Fehlanwendung Sicherheit und Gesundheit nicht gefaehrden. Aufgrund der Streuungen in Beanspruchung und Beanspruchbarkeit ist dieser Nachweis mit statistischen Methoden zu fuehren. Um diesen Nachweis moeglichst effizient zu erbringen, wurden mathematisch fundierte Auswertemethoden entwickelt, die auch Durchlaeufer, Ausfaelle vor Erreichen der Solllaufzeit und Versuchsabbrueche verwerten koennen. Weiterhin ist damit eine dynamische Anpassung des Versuchsplans an diese Ereignisse moeglich. (A) ABSTRACT IN ENGLISH: In the automotive industry, safety parts must be designed according to the state of the art of science and technology in such a way that they do not fail as long as the vehicle is used according to its purpose and misuse of the vehicle does not exceed a reasonably expectable degree. Due to scatter in customer loads and componen...

Mathematical Methods in the Applied Sciences, 1987

We study stationary solutions of the Vlasov‐Fokker‐Planck Equation, a modification of the Vlasov‐... more We study stationary solutions of the Vlasov‐Fokker‐Planck Equation, a modification of the Vlasov‐Poisson Equation, obtained by adding a diffusion term with respect to velocity. From a physical point of view it describes a plasma in thermal equilibrium.We prove existence of stationary solutions; for the mollified equation even an existence‐ and uniqueness theorem holds for sufficiently high temperature.

Mathematics in Industry, 2021

Berichte des Fraunhofer …, 2009

This contribution presents a model reduction method for nonlinear problems in structural mechanic... more This contribution presents a model reduction method for nonlinear problems in structural mechanics. Emanating from a Finite Element model of the structure, a subspace and a lookup table are generated which do not require a linearisation of the equations. The method is applied to a model created with commercial FEM software. In this case, the terms describing geometrical and material nonlinearities are not explicitly known.

In this article, we present an analytic solution for Jiang's constitutive model of elastoplas... more In this article, we present an analytic solution for Jiang's constitutive model of elastoplasticity. It is considered in its stress controlled form for proportional stress loading under the assumptions that the one-to-one coupling of the yield surface radius and the memory surface radius is switched off, that the transient hardening is neglected and that the ratchetting exponents are constant.

A gradient based algorithm for parameter identification (least-squares) is applied to a multiaxia... more A gradient based algorithm for parameter identification (least-squares) is applied to a multiaxial correction method for elastic stresses and strains at notches. The correction scheme, which is numerically cheap, is based on Jiang's model of elastoplasticity. Both mathematical stress-strain analyses (nonlinear finite element method with Jiang's model of elastoplasticity) and physical strain measurements have been approximized. The gradient evaluation with respect to the parameters, which is very large in scale, is realized by the automatic forward differentiation technique.

SAE technical paper series, Mar 29, 2022

Bundesgesundheitsblatt - Gesundheitsforschung - Gesundheitsschutz, 2021

Zusammenfassung Hintergrund Gerade in der Frühphase einer Pandemie ist es schwierig, verlässliche... more Zusammenfassung Hintergrund Gerade in der Frühphase einer Pandemie ist es schwierig, verlässliche Zahlen über deren Ausbreitung zu erhalten. Die derzeitige COVID-19-Pandemie und das damit verbundene umfassende, aber nicht vollständige Datenmonitoring bieten die Möglichkeit, die Dunkelziffer der nicht erfassten Fälle zu schätzen. Ziel Vorstellung eines einfachen mathematischen Modells, welches eine frühzeitige Abschätzung der Zahl nichtregistrierter Fälle (Dunkelziffer) ermöglicht. Material und Methoden Es werden die Prävalenzen der gemeldeten Infektionen in verschiedenen Altersgruppen mit Kennzahlen der altersabhängigen Kontaktzahlen kombiniert. Daraus wird für jede Altersgruppe eine korrigierte Prävalenz abgeleitet, mit der dann die Dunkelziffer geschätzt werden kann. Ergebnisse Unser Modell berechnet für Mitte April 2020 in Deutschland insgesamt 2,8-mal so viele Infektionen wie die Zahl der registrierten Infektionen (Fälle). Für Italien ergibt sich Mitte April 2020 ein Faktor von ...

A gradient based algorithm for parameter identification (least-squares) is applied to a multiaxia... more A gradient based algorithm for parameter identification (least-squares) is applied to a multiaxial correction method for elastic stresses and strains at notches. The correction scheme, which is numerically cheap, is based on Jiang’s model of elastoplasticity. Both mathematical stress-strain analyses (nonlinear finite element method with Jiang’s model of elastoplasticity) and physical strain measurements have been approximized. The gradient evaluation with respect to the parameters, which is very large in scale, is realized by the automatic forward differentiation technique.

Input signals are needed for the numerical simulation of vehicle multibody systems. With these in... more Input signals are needed for the numerical simulation of vehicle multibody systems. With these input data, the equations of motion can be integrated numerically and some output quantities can be calculated from the simulation results. In this work we consider the corresponding inverse problem: We assume that some reference output signals are available, typically gained by measurement and focus on the task to derive the input signals that produce the desired reference output in a suitable sense. If the input data is invariant, i.e., independent of the specific system, it can be transferred and used to excite other system variants. This problem can be formulated as optimal control problem. We discuss solution approaches from optimal control theory, their applicability to this special problem class and give some simulation results.

In this article, we give some generalisations of existing Lipschitz estimates for the stop and th... more In this article, we give some generalisations of existing Lipschitz estimates for the stop and the play operator with respect to an arbitrary convex and closed characteristic a separable Hilbert space. We are especially concerned with the dependency of their outputs with respect to different scalar products.

We consider in this paper the quasistatic boundary value problems of linear elasticity and nonlin... more We consider in this paper the quasistatic boundary value problems of linear elasticity and nonlinear elastoplasticity with linear kinematic hardening material. We derive expressions and estimates for the difference of solutions (i.e. stress, strain and displacement) of both models. Further, we study the error between the elastoplastic solution and the solution of a postprocessing method, that corrects the solution of the linear elastic problem in order to approximate the elastoplastic model.

The Rainflow Method in Fatigue, 1992

Abstract We present a new fatigue analysis data reduction concept for general multidimensional ti... more Abstract We present a new fatigue analysis data reduction concept for general multidimensional time series. The method is based on the Rainflow method, the most successful one-dimensional counting algorithm.

Mathematik Schlüsseltechnologie für die Zukunft, 1997

We propose a modification of the one-parameter multisurface Mroz- model for kinematic hardening, ... more We propose a modification of the one-parameter multisurface Mroz- model for kinematic hardening, which takes into account the phenomenon of ratchetting. We present some numerical simulations which show a certain qualitative agreement with published experimental data.

Mathematik in der Praxis, 1995

Muste man die in der Uberschrift gestellte Frage mit einem Wort beantworten, so wurde man sagen: ... more Muste man die in der Uberschrift gestellte Frage mit einem Wort beantworten, so wurde man sagen: Teilweise. Durfte man einen ganzen Satz formulieren, so konnte man etwa antworten: Nur das richtige Zusammenspiel von Tests, Rechnungen und Ingenieurerfahrung ermoglicht es gegenwartig, brauchbare Lebensdauervorhersagen bei vertretbarem Aufwand zu erstellen. Wurde man sich auf Tests beschranken, so hiese das Echtzeitfahrt auf der Strase oder auf dem Prufstand. Die Entwicklung ware dann zu teuer und zu langwierig, da fur jede Entwurfsvariante Prototypen des Fahrzeugs oder einzelner Teile desselben hergestellt werden musten. Auf der anderen Seite sind die auf dem heutigen Stand von Theorie und Algorithmik durchgefuhrten Rechnungen fur sich allein genommen nicht aussagekraftig und sicher genug. Tatsachlich sind gegenwartig in der Betriebsfestigkeitsanalyse Tests und Rechnungen an mehreren Stellen verzahnt. Eine zentrale Rolle auf der Seite der Algorithmik spielen hier — neben FE- und BE-Verfahren — Verfahren zur Datenanalyse und -aufbereitung, und zwar im Bereich der Klassierverfahren insbesondere das Rainflow-Verfahren.

SIMVEC – Simulation und Erprobung in der Fahrzeugentwicklung

SAE Technical Paper Series

Testing a new suspension based on real load data is performed on elaborate multi channel test rig... more Testing a new suspension based on real load data is performed on elaborate multi channel test rigs. Usually wheel forces and moments measured during driving maneuvers are reproduced on the rig. Because of the complicated interaction between rig and suspension each new rig configuration has to prove its efficiency with respect to the requirements and the configuration might be subject to optimization. This paper deals with modeling a new rig concept based on two hexapods. The real physical rig has been designed and meanwhile built by MOOG-FCS for VOLKSWAGEN. The aim of the simulation project reported here was twofold: First the simulation of the rig together with real VOLKSWAGEN suspension models at a time where the design was not yet finalized was used to verify and optimize the desired properties of the rig. Second the simulation environment was set up in a way that it can be used to prepare real tests on the rig. The model contains the geometric configuration as well as the hydrau...

Sicherheitsrelevante Bauteile sind in der Automobilindustrie so auszulegen, dass sie im Rahmen vo... more Sicherheitsrelevante Bauteile sind in der Automobilindustrie so auszulegen, dass sie im Rahmen von bestimmungsgemaesser Verwendung oder vorhersehbarer Fehlanwendung Sicherheit und Gesundheit nicht gefaehrden. Aufgrund der Streuungen in Beanspruchung und Beanspruchbarkeit ist dieser Nachweis mit statistischen Methoden zu fuehren. Um diesen Nachweis moeglichst effizient zu erbringen, wurden mathematisch fundierte Auswertemethoden entwickelt, die auch Durchlaeufer, Ausfaelle vor Erreichen der Solllaufzeit und Versuchsabbrueche verwerten koennen. Weiterhin ist damit eine dynamische Anpassung des Versuchsplans an diese Ereignisse moeglich. (A) ABSTRACT IN ENGLISH: In the automotive industry, safety parts must be designed according to the state of the art of science and technology in such a way that they do not fail as long as the vehicle is used according to its purpose and misuse of the vehicle does not exceed a reasonably expectable degree. Due to scatter in customer loads and componen...

Mathematical Methods in the Applied Sciences, 1987

We study stationary solutions of the Vlasov‐Fokker‐Planck Equation, a modification of the Vlasov‐... more We study stationary solutions of the Vlasov‐Fokker‐Planck Equation, a modification of the Vlasov‐Poisson Equation, obtained by adding a diffusion term with respect to velocity. From a physical point of view it describes a plasma in thermal equilibrium.We prove existence of stationary solutions; for the mollified equation even an existence‐ and uniqueness theorem holds for sufficiently high temperature.

Mathematics in Industry, 2021

Berichte des Fraunhofer …, 2009

This contribution presents a model reduction method for nonlinear problems in structural mechanic... more This contribution presents a model reduction method for nonlinear problems in structural mechanics. Emanating from a Finite Element model of the structure, a subspace and a lookup table are generated which do not require a linearisation of the equations. The method is applied to a model created with commercial FEM software. In this case, the terms describing geometrical and material nonlinearities are not explicitly known.

In this article, we present an analytic solution for Jiang's constitutive model of elastoplas... more In this article, we present an analytic solution for Jiang's constitutive model of elastoplasticity. It is considered in its stress controlled form for proportional stress loading under the assumptions that the one-to-one coupling of the yield surface radius and the memory surface radius is switched off, that the transient hardening is neglected and that the ratchetting exponents are constant.

A gradient based algorithm for parameter identification (least-squares) is applied to a multiaxia... more A gradient based algorithm for parameter identification (least-squares) is applied to a multiaxial correction method for elastic stresses and strains at notches. The correction scheme, which is numerically cheap, is based on Jiang's model of elastoplasticity. Both mathematical stress-strain analyses (nonlinear finite element method with Jiang's model of elastoplasticity) and physical strain measurements have been approximized. The gradient evaluation with respect to the parameters, which is very large in scale, is realized by the automatic forward differentiation technique.

SAE technical paper series, Mar 29, 2022

Bundesgesundheitsblatt - Gesundheitsforschung - Gesundheitsschutz, 2021

Zusammenfassung Hintergrund Gerade in der Frühphase einer Pandemie ist es schwierig, verlässliche... more Zusammenfassung Hintergrund Gerade in der Frühphase einer Pandemie ist es schwierig, verlässliche Zahlen über deren Ausbreitung zu erhalten. Die derzeitige COVID-19-Pandemie und das damit verbundene umfassende, aber nicht vollständige Datenmonitoring bieten die Möglichkeit, die Dunkelziffer der nicht erfassten Fälle zu schätzen. Ziel Vorstellung eines einfachen mathematischen Modells, welches eine frühzeitige Abschätzung der Zahl nichtregistrierter Fälle (Dunkelziffer) ermöglicht. Material und Methoden Es werden die Prävalenzen der gemeldeten Infektionen in verschiedenen Altersgruppen mit Kennzahlen der altersabhängigen Kontaktzahlen kombiniert. Daraus wird für jede Altersgruppe eine korrigierte Prävalenz abgeleitet, mit der dann die Dunkelziffer geschätzt werden kann. Ergebnisse Unser Modell berechnet für Mitte April 2020 in Deutschland insgesamt 2,8-mal so viele Infektionen wie die Zahl der registrierten Infektionen (Fälle). Für Italien ergibt sich Mitte April 2020 ein Faktor von ...

A gradient based algorithm for parameter identification (least-squares) is applied to a multiaxia... more A gradient based algorithm for parameter identification (least-squares) is applied to a multiaxial correction method for elastic stresses and strains at notches. The correction scheme, which is numerically cheap, is based on Jiang’s model of elastoplasticity. Both mathematical stress-strain analyses (nonlinear finite element method with Jiang’s model of elastoplasticity) and physical strain measurements have been approximized. The gradient evaluation with respect to the parameters, which is very large in scale, is realized by the automatic forward differentiation technique.

Input signals are needed for the numerical simulation of vehicle multibody systems. With these in... more Input signals are needed for the numerical simulation of vehicle multibody systems. With these input data, the equations of motion can be integrated numerically and some output quantities can be calculated from the simulation results. In this work we consider the corresponding inverse problem: We assume that some reference output signals are available, typically gained by measurement and focus on the task to derive the input signals that produce the desired reference output in a suitable sense. If the input data is invariant, i.e., independent of the specific system, it can be transferred and used to excite other system variants. This problem can be formulated as optimal control problem. We discuss solution approaches from optimal control theory, their applicability to this special problem class and give some simulation results.

In this article, we give some generalisations of existing Lipschitz estimates for the stop and th... more In this article, we give some generalisations of existing Lipschitz estimates for the stop and the play operator with respect to an arbitrary convex and closed characteristic a separable Hilbert space. We are especially concerned with the dependency of their outputs with respect to different scalar products.

We consider in this paper the quasistatic boundary value problems of linear elasticity and nonlin... more We consider in this paper the quasistatic boundary value problems of linear elasticity and nonlinear elastoplasticity with linear kinematic hardening material. We derive expressions and estimates for the difference of solutions (i.e. stress, strain and displacement) of both models. Further, we study the error between the elastoplastic solution and the solution of a postprocessing method, that corrects the solution of the linear elastic problem in order to approximate the elastoplastic model.