Lumped-parameter modelling of elastically coupled bodies: Derivation of constitutive equations and determination of stiffness matrices

Persistent Link:
http://hdl.handle.net/10150/284462
Title:
Lumped-parameter modelling of elastically coupled bodies: Derivation of constitutive equations and determination of stiffness matrices
Author:
Zhang, Shilong
Issue Date:
1999
Publisher:
The University of Arizona.
Rights:
Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.
Abstract:
Modelling of elastically coupled rigid bodies is an important research topic in multibody dynamics. We consider the problem of modelling what can be called flexural joints, where two essentially rigid bodies are coupled by a substantially more elastic body. For modelling general elastic couplings one would like to have generically applicable, lumped parameter, intuitive, Euclidean geometric, accurate models with desirable physical symmetries. The model constitutive equations should be easily and quickly computable. For purely elastic coupling the constitutive equations should be truly energy conservative: the configuration-wrench equations should be derivable from a potential function. Linear and angular momentum should be conserved. Quaternion-based and twist-based modelling methods are presented. The constitutive equations to calculate the configuration-wrench behavior are derived via geometric potential energy functions. Wrenches are computable given the configurations of the rigid bodies and all the stiffness matrices of the compliant element. For an arbitrary pair of elastically coupled rigid bodies there exist coincident, unique points on the bodies known as centers of stiffness at which translation and rotation are minimally coupled. At the center of stiffness there exist three sets of orthonormal principal axes and corresponding principal stiffnesses. These parameters are useful in both analysis and numerical simulation. A finite-element-based method for computing canonical stiffness parameters of elastically coupled rigid bodies is presented. The method is applied to notch hinges and Remote Center of Compliance (RCC) hinges. Standard procedures are presented on how to determine canonical stiffness parameters at the center of stiffness of a spatial compliance. Series of canonical stiffness parameters can be generated automatically using the methods provided. Key program listings are provided which can be used to duplicate the results presented.
Type:
text; Dissertation-Reproduction (electronic)
Keywords:
Applied Mechanics.; Engineering, Mechanical.
Degree Name:
Ph.D.
Degree Level:
doctoral
Degree Program:
Graduate College; Aerospace and Mechanical Engineering
Degree Grantor:
University of Arizona
Advisor:
Fasse, Ernest

Full metadata record

DC FieldValue Language
dc.language.isoen_USen_US
dc.titleLumped-parameter modelling of elastically coupled bodies: Derivation of constitutive equations and determination of stiffness matricesen_US
dc.creatorZhang, Shilongen_US
dc.contributor.authorZhang, Shilongen_US
dc.date.issued1999en_US
dc.publisherThe University of Arizona.en_US
dc.rightsCopyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.en_US
dc.description.abstractModelling of elastically coupled rigid bodies is an important research topic in multibody dynamics. We consider the problem of modelling what can be called flexural joints, where two essentially rigid bodies are coupled by a substantially more elastic body. For modelling general elastic couplings one would like to have generically applicable, lumped parameter, intuitive, Euclidean geometric, accurate models with desirable physical symmetries. The model constitutive equations should be easily and quickly computable. For purely elastic coupling the constitutive equations should be truly energy conservative: the configuration-wrench equations should be derivable from a potential function. Linear and angular momentum should be conserved. Quaternion-based and twist-based modelling methods are presented. The constitutive equations to calculate the configuration-wrench behavior are derived via geometric potential energy functions. Wrenches are computable given the configurations of the rigid bodies and all the stiffness matrices of the compliant element. For an arbitrary pair of elastically coupled rigid bodies there exist coincident, unique points on the bodies known as centers of stiffness at which translation and rotation are minimally coupled. At the center of stiffness there exist three sets of orthonormal principal axes and corresponding principal stiffnesses. These parameters are useful in both analysis and numerical simulation. A finite-element-based method for computing canonical stiffness parameters of elastically coupled rigid bodies is presented. The method is applied to notch hinges and Remote Center of Compliance (RCC) hinges. Standard procedures are presented on how to determine canonical stiffness parameters at the center of stiffness of a spatial compliance. Series of canonical stiffness parameters can be generated automatically using the methods provided. Key program listings are provided which can be used to duplicate the results presented.en_US
dc.typetexten_US
dc.typeDissertation-Reproduction (electronic)en_US
dc.subjectApplied Mechanics.en_US
dc.subjectEngineering, Mechanical.en_US
thesis.degree.namePh.D.en_US
thesis.degree.leveldoctoralen_US
thesis.degree.disciplineGraduate Collegeen_US
thesis.degree.disciplineAerospace and Mechanical Engineeringen_US
thesis.degree.grantorUniversity of Arizonaen_US
dc.contributor.advisorFasse, Ernesten_US
dc.identifier.proquest9934844en_US
dc.identifier.bibrecord.b3964845xen_US
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