NDLI: Definition of the Elastic Forces in the Finite-Element Absolute Nodal Coordinate Formulation and the Floating Frame of Reference Formulation

Content Provider	Springer Nature Link
Author	Berzeri, Marcello Campanelli, Marcello Shabana, Ahmed A.
Copyright Year	2001
Abstract	The equivalence of the finite-element formulations used inflexible multibody dynamics is the focus of this investigation. Thisequivalence will be used to address several fundamental issues related tothe deformations, flexible body coordinate systems, and the geometriccentrifugal stiffening effect. Two conceptually different finite-elementformulations that lead to exact modeling of the rigid body dynamics will beused. The first one is the absolute nodal coordinateformulation in which beams and plates can be treated as isoparametricelements. This formulation leads to a constant and symmetric mass matrix andhighly nonlinear elastic forces. In this study, it is demonstrated thatdifferent element coordinate systems which are used for the convenience ofdescribing the element deformations lead to similar results as the elementsize is reduced. In particular, two element frames are used;the pinned and the tangent frames. The pinned frame has one ofits axes passing through two nodes of the element, while the tangent frame isrigidly attached to one of the ends of the element. Numerical resultsobtained using these two different frames are found tobe in good agreement as the element size decreases. The relationshipbetween the coordinates used in the absolute nodal coordinate formulationand the floating frame of reference formulation is presented. Thisrelationship can be used to obtain the highly nonlinear expression of thestrain energy used in the absolute nodal coordinate formulation from thesimple energy expression used in the floating frame of referenceformulation. It is also shown that the source of the nonlinearityis due to the finite rotation of the element. The result of the analysispresented clearly demonstrates that the instability observedin high-speed rotor analytical models due to the neglect of the geometriccentrifugal stiffening is not a problem inherent to a particular finite-element formulation. Such a problem can only be avoided by considering the known linear effect of the geometric centrifugal stiffening or by using a nonlinear elastic model as recently demonstrated. Fourier analysis of the solutions obtained in this investigation also sheds new light on the fundamental problem of the choice of the deformable body coordinate system in the floating frame of reference formulation. Another method forformulating the elastic forces in the absolute nodal coordinate formulationbased on a continuum mechanics approach is also presented.
Starting Page	21
Ending Page	54
Page Count	34
File Format	PDF
ISSN	13845640
Journal	Multibody System Dynamics
Volume Number	5
Issue Number	1
e-ISSN	1573272X
Language	English
Publisher	Kluwer Academic Publishers
Publisher Date	2001-01-01
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Optimization Vibration, Dynamical Systems, Control Mechanical Engineering Automotive and Aerospace Engineering Electronic and Computer Engineering
Content Type	Text
Resource Type	Article
Subject	Control and Optimization Mechanical Engineering Aerospace Engineering Modeling and Simulation Computer Science Applications

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in

Definition of the Slopes and the Finite Element Absolute Nodal Coordinate Formulation

Slope discontinuities in the finite element absolute nodal coordinate formulation: gradient deficient elements

Clamped end conditions and cross section deformation in the finite element absolute nodal coordinate formulation

A geometrically exact beam element based on the absolute nodal coordinate formulation

On the integration of computer aided design and analysis using the finite element absolute nodal coordinate formulation

Three- and four-noded planar elements using absolute nodal coordinate formulation

Study of the Centrifugal Stiffening Effect Using the Finite Element Absolute Nodal Coordinate Formulation

Effect of the centrifugal forces on the finite element eigenvalue solution of a rotating blade: a comparative study

Absolute nodal coordinate plane beam formulation for multibody systems dynamics

Definition of the Elastic Forces in the Finite-Element Absolute Nodal Coordinate Formulation and the Floating Frame of Reference Formulation

Similar Documents

Definition of the Slopes and the Finite Element Absolute Nodal Coordinate Formulation

Slope discontinuities in the finite element absolute nodal coordinate formulation: gradient deficient elements

Clamped end conditions and cross section deformation in the finite element absolute nodal coordinate formulation

A geometrically exact beam element based on the absolute nodal coordinate formulation

On the integration of computer aided design and analysis using the finite element absolute nodal coordinate formulation

Three- and four-noded planar elements using absolute nodal coordinate formulation

Study of the Centrifugal Stiffening Effect Using the Finite Element Absolute Nodal Coordinate Formulation

Effect of the centrifugal forces on the finite element eigenvalue solution of a rotating blade: a comparative study

Absolute nodal coordinate plane beam formulation for multibody systems dynamics

Definition of the Elastic Forces in the Finite-Element Absolute Nodal Coordinate Formulation and the Floating Frame of Reference Formulation