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A Weak Formulation of Constraints to Couple Rigid and Elastic Bodies - a Study with FEniCS

Södersten, Axel LU (2018) In Master's Theses in Mathematical Sciences FMNM01 20181
Mathematics (Faculty of Engineering)
Abstract
Many complex mechanical systems are simplified by considering them as multibody systems. In recent years, flexible multibody dynamics has become more and more in demand. In~\cite{simeon2013}, a weakly constrained joint model was presented, which in a well-defined way models the interconnection of an elastic and a rigid body by a massless rigid joint. However, the joint model assumes that the orientation of the joint-elastic body interface is unaffected by the displacement field of the elastic body. The aim of this study is to highlight the limitations of the joint model due to this assumption.

In this study, the joint model was applied for two-body system of an elastic and a rigid body, connected by a small rigid joint. During... (More)
Many complex mechanical systems are simplified by considering them as multibody systems. In recent years, flexible multibody dynamics has become more and more in demand. In~\cite{simeon2013}, a weakly constrained joint model was presented, which in a well-defined way models the interconnection of an elastic and a rigid body by a massless rigid joint. However, the joint model assumes that the orientation of the joint-elastic body interface is unaffected by the displacement field of the elastic body. The aim of this study is to highlight the limitations of the joint model due to this assumption.

In this study, the joint model was applied for two-body system of an elastic and a rigid body, connected by a small rigid joint. During deformation the joint-body interface was expected to rotate due to the displacement field of the elastic body. However, due to the assumption the interface stayed fixed which distorted the displacement field of the elastic body. This assumption could be avoided if the orientation of the interface during deformation was predicted, which would be possible by the use of observer points. (Less)
Popular Abstract
In this study, model distortions, due to applying a joint model for interconnecting deformable and undeformable bodies, are highlighted. Specifically, the overall dynamics are restricted, by that the joint model prohibits any rotational component of the displacements along the interface between joint and deformable body. A stress analysis for a loaded semi-trailer hinged to a truck is a typical example where the joint model could distort the analysis.

In the design of most mechanical systems, it is key to understand the dynamics and the durability of the system. Even for many complex systems, there are both efficient and accurate ways to numerically model the dynamics. Naturally, performing numerical simulations are significantly... (More)
In this study, model distortions, due to applying a joint model for interconnecting deformable and undeformable bodies, are highlighted. Specifically, the overall dynamics are restricted, by that the joint model prohibits any rotational component of the displacements along the interface between joint and deformable body. A stress analysis for a loaded semi-trailer hinged to a truck is a typical example where the joint model could distort the analysis.

In the design of most mechanical systems, it is key to understand the dynamics and the durability of the system. Even for many complex systems, there are both efficient and accurate ways to numerically model the dynamics. Naturally, performing numerical simulations are significantly cheaper and less time-consuming than conducting prototype testing. Hence, numerical simulations has become an increasingly vital part in the development of many mechanical systems over the past decades.

For a car, a useful model simplification is to view the car as a set of body parts interconnected by springs, dampers and actuators; a so-called multibody system. In the crudest simplification, all compressions are assumed to occur over the interconnecting elements. Then, the body parts can be modeled as undeformable. The dynamics of an undeformable body can be fully described as a point mass motion at its center of mass.

Consider a loaded semi-trailer connected to a truck through an undeformable joint. If the interest is to estimate the weight the semi-trailer can withstand, it should be modeled as a deformable body. To describe the displacements of a deformable body numerically, the body is covered by finite many points, and the dynamics is solved locally through influences between adjacent points. If the joint is connected to the truck above its back-wheels, the truck can still be modeled as an undeformable multibody system.

%The joint constrains the dynamics of the system, which makes the model very sensitive to errors in displacements.
Retrieving a satisfactory and well-defined joint model, for interconnecting deformable and undeformable bodies, is still an open topic. The challenging aspect is to describe the interface, between joint and deformable body, in a well-defined way, with respect to both the undeformable joint and the deformable body.

In contrast to a more common joint model, the examined model is well-defined. To apply a satisfactory well-defined model is strongly favorable, since it increases the reliability of retrieved results. However, the examined model prohibits any rotational component of the displacements along the interface between joint and deformable body. The restricted motion slightly distorts the deformation of the semi-trailer, and thereby overestimate the corresponding stresses. In the study, the model distortion is clearly illustrated for a basic two-body system, where an undeformed body is hinged to a deformable one.

Due to the model restrictions, the examined model is expected to give less reliable results than the more common one. However, due to limitations of both models, further investigations are encouraged. To retrieve novel satisfactory joint models are important in order to retrieve more reliable results for mechanical systems, such as the above-mentioned semi-trailer truck, as well as for slider-crank mechanisms in an engine and the rotor blade configurations on a helicopter. (Less)
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author
Södersten, Axel LU
supervisor
organization
course
FMNM01 20181
year
type
H2 - Master's Degree (Two Years)
subject
keywords
Flexible multibody dynamics, differential-algebraic equations, interconnecting rigid joints
publication/series
Master's Theses in Mathematical Sciences
report number
LUTFNA-3046-2018
ISSN
1404-6342
other publication id
2018:E56
language
English
id
8959850
date added to LUP
2018-10-09 14:42:06
date last changed
2018-10-11 16:18:40
@misc{8959850,
  abstract     = {Many complex mechanical systems are simplified by considering them as multibody systems. In recent years, flexible multibody dynamics has become more and more in demand. In~\cite{simeon2013}, a weakly constrained joint model was presented, which in a well-defined way models the interconnection of an elastic and a rigid body by a massless rigid joint. However, the joint model assumes that the orientation of the joint-elastic body interface is unaffected by the displacement field of the elastic body. The aim of this study is to highlight the limitations of the joint model due to this assumption.

In this study, the joint model was applied for two-body system of an elastic and a rigid body, connected by a small rigid joint. During deformation the joint-body interface was expected to rotate due to the displacement field of the elastic body. However, due to the assumption the interface stayed fixed which distorted the displacement field of the elastic body. This assumption could be avoided if the orientation of the interface during deformation was predicted, which would be possible by the use of observer points.},
  author       = {Södersten, Axel},
  issn         = {1404-6342},
  keyword      = {Flexible multibody dynamics,differential-algebraic equations,interconnecting rigid joints},
  language     = {eng},
  note         = {Student Paper},
  series       = {Master's Theses in Mathematical Sciences},
  title        = {A Weak Formulation of Constraints to Couple Rigid and Elastic Bodies - a Study with FEniCS},
  year         = {2018},
}