Nonlinear Finite Element Formulation for the Large Displacement Analysis of Plates

Chang, Betty; Shabana, Ahmed A.

doi:10.1115/1.2897081

Cited by 23 publications

(3 citation statements)

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“…In studying these systems, most analysts have focused on rotating beams, although some [5][6][7]101 have also considered rotating plates, and others [9, 1 I ] have incorporated the finite element method into dynamic analysis to study arbitrarily shaped bodies. The objective of this paper is to present a formulation that is applicable for arbitrarily shaped bodies but not directly dependent on the finite element method.…”

Section: And Kim [I I])mentioning

confidence: 99%

On the Dynamics of an Arbitrary Flexible Body with Large Overall Motion: An Integrated Approach

Zhang

Liu

Huston

1995

Mechanics of Structures and Machines

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This paper presents a procedure for studying flexibility effects of arbitrarily shaped bodies having large overall motion. The procedure automatically incorporates the so-called "dynamic stiffness" effects through its analysis, which is an integration of the techniques of structural dynamics and multibody dynamics. Nonlinear strain-displacement relations are used to obtain a consistent set of governing equations, which are linear in their displacements away from the: undeformed state. The governing equations themselves are developed from Kane's equations, using partial 419

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Section: And Kim [I I])mentioning

confidence: 99%

On the Dynamics of an Arbitrary Flexible Body with Large Overall Motion: An Integrated Approach

Zhang

Liu

Huston

1995

Mechanics of Structures and Machines

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“…In the past ten years, several modeling methods [2][3][4][5] have been introduced to solve the stiffening problem of flexible beams, and then the proposed methods have been extended from beams to plates. By the use of nonlinear strain-displacement relations, the geometric stiffening terms are included in the equations of motion of a plate in large overall motions [6]. Yoo and Chung presented an accurate and efficient linear-modeling method for plates undergoing prescribed overall motion in Ref.…”

Section: Introductionmentioning

confidence: 99%

Study on rigid-flexible coupling dynamics of hub-plate system

Zhao

Xie

Zhang

et al. 2007

Front. Energy Power Eng. China

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Dynamic modeling of a rotating flexible hubplate system is investigated by using Jourdain's variation principle in which the finite element method (FEM) is used as discretization method for a flexible plate. Different from the previous modeling of a plate with a prescribed large overall motion, the coupling between large overall motion of the system and elastic deformation of the flexible plate is taken into account in the proposed coupling model. The quadratic terms are included in the strain-displacement expression, such that the dynamic stiffening terms are included. Simulation of a rotating hub-plate system indicates that the linear model based on linear strain-displacement assumption may lead to erroneous results in the case of high rotation speed. Conservation of energy verifies the validity of the proposed model. Furthermore, frequency analysis of a hub-plate system shows the difference between the frequencies of the system with free and prescribed large overall motion, and parameter analysis of the system reveals the coupling characteristics of the rotational motion and the deformation.

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“…These coupling terms involve the derivation of matrices, which include the ÿnite-element shape functions that are not available in the common ÿnite-element literature. Such terms need to be derived if other types of ÿnite-elements are to be used in the exible multibody models, besides beam and eight-node plates=shell elements [10,11]. As a result, most of the exible multibody models presented in the literature are made of beam elements only.…”

Section: Introductionmentioning

confidence: 99%

Efficient kinematic joint descriptions for flexible multibody systems experiencing linear and non‐linear deformations

Ambrósio¹

2003

Numerical Meth Engineering

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SUMMARYDi erent ÿnite-element-based strategies used to represent the components' exibility in multibody systems lead to various sets of co-ordinates. For systems in which the bodies only experience small elastic deformations it is common to use mode component synthesis to reduce the number of generalized elastic co-ordinates and, consequently, the equations of motion are written in terms of modal co-ordinates. However, when the system components experience non-linear deformations the use of reduction methods is not possible, in general, and the ÿnite element nodal co-ordinates are the generalized co-ordinates used. Furthermore, depending on the type of ÿnite elements used to represent each exible body, the nodal co-ordinates may include all node rotations and translations or only some of each. Regardless of the type of generalized co-ordinates adopted it is required that kinematic joints are deÿned. The complete set of joints available in a general-purpose multibody code must include, for each particular type of joint, restrictions involving only rigid bodies, or only exible bodies, or exible and rigid bodies. Therefore, the e ort put into the development and implementation of any joint is at least three times as much as the initial work done in the implementation of joints with rigid bodies only. The concept of virtual bodies provides a general framework to develop general kinematic joints for exible multibody systems with minimal e ort, regardless of the exible co-ordinates used. Initially, only a rigid constraint between the exible and a massless rigid body is developed. Then, any kinematic joint that involves a exible body is set with the massless rigid body instead, using the regular joint library of the multibody code. The major drawback is that for each kinematic joint involving a exible body it is required to use six more co-ordinates per virtual body and six more kinematic constraints. It is shown in this work that for small elastic deformations, for which the mode component synthesis is applied, the use of sparse matrix solvers can compensate for the computational overhead of involving more co-ordinates and kinematic constraints in the system, due to the use of virtual bodies. For non-linear deformations, where the generalized co-ordinates are the global positions of the ÿnite-element nodes, the use of the virtual body concept does not require an increase in the number of system co-ordinates or kinematic constraints. By introducing the rigid joint between the exible body nodal co-ordinates and the virtual body, with the use of Lagrange multipliers, and then solving the equations explicitly for * Correspondence to: Jorge AmbrÃ osio, Instituto de Engenharia Mecânica (IDMEC), Instituto Superior TÃ ecnico, Av.Rovisco Pais, 1049-001 Lisboa, Portugal. † E-mail: jorge@lemac.ist.utl.pt these multipliers the resulting equations of motion for the subsystem have the same degrees of freedom as the original exible body alone. The di erence is that degrees of freedom associated to the virtual body are used as co-ordi...

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Nonlinear Finite Element Formulation for the Large Displacement Analysis of Plates

Cited by 23 publications

References 0 publications

On the Dynamics of an Arbitrary Flexible Body with Large Overall Motion: An Integrated Approach

On the Dynamics of an Arbitrary Flexible Body with Large Overall Motion: An Integrated Approach

Study on rigid-flexible coupling dynamics of hub-plate system

Efficient kinematic joint descriptions for flexible multibody systems experiencing linear and non‐linear deformations

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