A Weak Formulation of Constraints to Couple Rigid and Elastic Bodies  a Study with FEniCS
(2018) In Master's Theses in Mathematical Sciences FMNM01 20181Mathematics (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 welldefined 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 jointelastic 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 twobody 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 welldefined 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 jointelastic 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 twobody system of an elastic and a rigid body, connected by a small rigid joint. During deformation the jointbody 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 semitrailer 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 semitrailer 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 timeconsuming 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 socalled 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 semitrailer connected to a truck through an undeformable joint. If the interest is to estimate the weight the semitrailer 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 backwheels, 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 welldefined 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 welldefined way, with respect to both the undeformable joint and the deformable body.
In contrast to a more common joint model, the examined model is welldefined. To apply a satisfactory welldefined 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 semitrailer, and thereby overestimate the corresponding stresses. In the study, the model distortion is clearly illustrated for a basic twobody 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 abovementioned semitrailer truck, as well as for slidercrank mechanisms in an engine and the rotor blade configurations on a helicopter. (Less)
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/studentpapers/record/8959850
 author
 Södersten, Axel ^{LU}
 supervisor

 Claus Führer ^{LU}
 organization
 course
 FMNM01 20181
 year
 2018
 type
 H2  Master's Degree (Two Years)
 subject
 keywords
 Flexible multibody dynamics, differentialalgebraic equations, interconnecting rigid joints
 publication/series
 Master's Theses in Mathematical Sciences
 report number
 LUTFNA30462018
 ISSN
 14046342
 other publication id
 2018:E56
 language
 English
 id
 8959850
 date added to LUP
 20181009 14:42:06
 date last changed
 20181011 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 welldefined 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 jointelastic 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 twobody system of an elastic and a rigid body, connected by a small rigid joint. During deformation the jointbody 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 = {14046342}, keyword = {Flexible multibody dynamics,differentialalgebraic 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}, }