Development of Simple Models for the Elastic Forces in the Absolute Nodal Co-Ordinate Formulation

Berzeri, Marcello; Shabana, Ahmed A.

doi:10.1006/jsvi.1999.2935

Cited by 308 publications

(128 citation statements)

References 14 publications

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“…Another method, which is used in this study, is based on a continuum mechanics approach that does not require the use of a local element coordinate system. The latter approach leads to significant simplification in the vector of elastic forces as is previously shown [3]. Furthermore, by employing a continuum mechanics approach all elastic nonlinearities are taken into consideration since nonlinear strain-displacement relationships must be used.…”

Section: Elastic Forcesmentioning

confidence: 99%

A Large Deformation Plate Element for Multibody Applications

Mikkola¹,

Shabana²

2000

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095 REPORT DOCUMENTATION PAGEThe views, opinions and/or findings contained in this report are those of the author(s) and should not be construed as an official Department of the Army position, policy or decision, unless so designated by other documentation. a. DISTRIBUTION / AVAILABILITY STATEMENTApproved for public release; distribution unlimited. 12 b. DISTRIBUTION CODE 13. ABSTRACT l In this investigation, a method for the finite rotation and large deformation analysis of plates is presented. The method, which is based on the absolute nodal coordinate formulation, leads to an isoparametric plate element capable of representing exact rigid body motion. In this method, continuity conditions on all the displacement gradients are imposed. Therefore, non-smoothness of the plate mid-surface at the nodal points is avoided. Unlike other existing finite element formulations that lead to a highly nonlinear inertial forces for three-dimensional elements, the proposed formulation leads to a constant mass matrix, and as a result, the centrifugal and Coriolis forces are identically equal to zero. Furthermore, the method relaxes some of the assumptions used in the classical and Mindlin plate theories. By using a general continuum mechanics approach, a relatively simple expression for the elastic forces is obtained. By developing such an isoparametric plate element, the development of three-dimensional shell elements becomes straightforward. Numerical results are presented in order to demonstrate the use of the proposed method in the large rotating and deformation analysis of plates. ABSTRACTIn this investigation, a method for the finite rotation and large deformation analysis of plates is presented. The method, which is based on the absolute nodal coordinate formulation, leads to an isoparametric plate element capable of representing exact rigid body motion. In this method, continuity conditions on all the displacement gradients are imposed. Therefore, non-smoothness of the plate mid-surface at the nodal points is avoided. Unlike other existing finite element formulations that lead to a highly nonlinear inertial forces for three-dimensional elements, the proposed formulation leads to a constant mass matrix, and as a result, the centrifugal and Coriolis forces are identically equal to zero. Furthermore, the method relaxes some of the assumptions used in the classical and Mindlin plate theories. By using a general continuum mechanics approach, a relatively simple expression for the elastic forces is obtained. By developing such an isoparametric plate element, the development of three-dimensional shell elements becomes straightforward. Numerical results are presented in order to demonstrate the use of the proposed method in the large rotating and deformation analysis of plates.

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Section: Elastic Forcesmentioning

confidence: 99%

A Large Deformation Plate Element for Multibody Applications

Mikkola¹,

Shabana²

2000

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“…In this paper a planar gradient deficient [25] Euler-Bernoulli beam element is used [30][31][32], Fig. 1.…”

Section: Theoretical Backgroundmentioning

confidence: 99%

Absolute Nodal Coordinate Formulation in a Pre-Stressed Large-Displacements Dynamical System

Skrinjar

Slavič

Boltežar

2017

Stroj. vest. - Jour. Mech. Eng.

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The design process for dynamical models has to consider all the properties of a mechanical system that have an effect on its dynamical response. In multi-body dynamics, flexible bodies are frequently modeled as rigid, resulting in non-valid Keywords: ANCF, pre-stress, multibody system, measurement Highlights • A numerical model of a rigid-flexible multibody system is used in the analysis of kinematic properties during switch-off. • A flexible body is modeled with the Absolute Nodal Coordinate Formulation to include the pre-stress effect. • The influence of different parameters on the switch-off time and the contact distance is investigated. • The numerical model was validated and shows good agreement with the experimental values. INTRODUCTIONWhen modeling dynamical systems the proper material and contact properties of the numerical model are crucial for simulating an accurate dynamic response. One of the properties to be considered is the effect of pre-stress on rigid and flexible bodies, as it can have a significant impact on the dynamical response of multibody mechanical systems.The modeling of deformable bodies in a multibody system can be done using a floating frame of reference (FFR) [1], which is based on the classic finite element (FE) method that is widely used in a variety of applications [2] and [3]. While in a floating frame of reference formulation a mixed set of absolute reference and local elastic coordinates are used, in the absolute nodal coordinate formulation (ANCF) only absolute coordinates are used, which include global displacement and global vector gradients [4]. The ANCF is a non-incremental method and it has been used for solving many different problems in mechanics, such as vehicle components [5] and [6], the modeling of belt drives [7], railroad applications [8], bio-mechanics [9] and also in the field of digital image correlation (DIC) [10]. The main features of the ANCF are a constant mass matrix, zero centrifugal and Coriolis inertia forces and the possibility for exact modeling of rigid-body movement.The modeling of the pre-stress effect on bodies in mechanical systems is an interesting research topic in civil-engineering applications [11], where the static [12] and dynamic responses of structural elements are considered [13]. The effect of pre-stress is introduced to the ANCF finite elements to create an accurate model of a leaf spring, where pre-stress is evaluated based on the known geometrical states in the undeformed and deformed configurations that define the vector of absolute nodal coordinates [14]. In [15] the effect of the non-dimensional axial pre-stress of eigenfrequencies on a simply supported beam is researched. The pre-stress effect is included in the model of a flexible multibody belt-drive [16], where the belt-drive is modeled with ANCF two-dimensional shear deformable beam elements that account for the longitudinal and shear deformations.When modeling mechanical systems [17-20] a validation is needed to evaluate the results from the numerical model, this can be ...

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“…Arguments in favor of the former can be found in [1-3, 6, 9]. On the other hand, in [10][11][12][13][14] the latter is treated as the better choice.…”

Section: A Remark On the Moment-curvature Relationmentioning

confidence: 99%