Generalization of the strain-split method and evaluation of the nonlinear ANCF finite elements

Shabana, Ahmed A.; Desai, Chintan J.; Grossi, Emanuele; Patel, Mohil

doi:10.1007/s00707-019-02558-w

Cited by 21 publications

(5 citation statements)

References 34 publications

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“…was chosen because it also describes large deformations [26,27]. Here, I is the identity matrix, and E 11 , E 12 , and E 22 are three independent components of the Green-Lagrangian strain tensor.…”

Section: Fundamentals and Modelingmentioning

confidence: 99%

Deformation of planar ring mesh under static in-plane tensile loads

2022

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A ring mesh is a large-scale manufacturable structure with versatile applications in architecture and for protective systems. However, the static and dynamic numerical simulation of a large-scale ring mesh is a resource-intensive task due to the many nonlinear contact points between the individual rings. To characterize the rigid body behavior of the ring mesh, in this paper, a representative volume element is loaded under different in-plane directions. The Green-Lagrangian strain tensor components are obtained as a result. An implicit one-step algorithm is used for this dynamic relaxation issue, modified by the use of stiff springs. Static convergence positions of a representative volume element are determined in several multiaxial tensile directions. The obtained deformation parameters can be used to simulate large deformations of large-scaled ring meshes.

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Section: Fundamentals and Modelingmentioning

confidence: 99%

Deformation of planar ring mesh under static in-plane tensile loads

2022

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“…where K is the global stiffness matrix, U is the global vector of nodal displacements, and F is the global vector of external forces, which includes both internal forces calculated according to (34) and nodal electrostatic forces either calculated according to (17) or found from the electrostatic pressure (21), depending on the problem under consideration. On the basis of the above, the electromechanical problem is solved according to the following procedure:…”

Section: Absolute Nodal Coordinate Formulationmentioning

confidence: 99%

“…The formulation is a nonlinear finite element approach that can be used for a wide variety of applications; however, it has been mostly used for beam-and platelike structures [9]. Some of the most recent developments include enhancements in numerical performance [14,18,20,34]. Applications of the ANCF include soft machines [13], biological tissues [29,30], cables and wires [12,19], pneumatic elements [37], dielectric elastomer actuators [24], railroad track structures [33], and rotating shafts [4].…”

Section: Introductionmentioning

confidence: 99%

Analysis of electromechanical systems based on the absolute nodal coordinate formulation

et al. 2022

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The absolute nodal coordinate formulation (ANCF) approach has been successfully used to analyze bodies undergoing large deformations in multibody dynamics applications. In this study, the ANCF is extended to the analysis of coupled electromechanical systems. To this end, the electrostatic equations are solved by means of conventional plane finite elements, and the ANCF is used to describe the geometrically nonlinear elastic deformation of a thin beam. Bidirectional coupling between electrostatic and elastic domains was introduced using an iterative staggering algorithm. The results illustrate that the ANCF approach can be applied to electromechanical problems when objects are discretized using beam and plate elements. Two numerical examples of microbeams subject to an electrostatic field are used to validate the proposed solution strategy and to reveal characteristic features of fully coupled electromechanical solutions accounting for finite strain theory.

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“…However, this approach will increase the degree of freedom of the elements. Shabana 17,55 applied the Strain Split Method (SSM) by suppressing the occlusion effect in curved structures by decomposing the stress-strain tensor, and the results showed that this method can effectively reduce this deviation. However, this method has just been introduced to the calculation of plate elements and needs to be studied in more depth.…”

Section: Locking Problemsmentioning

confidence: 99%

Research status and prospect of plate elements in absolute nodal coordinate formulation

Zhang

Ren

Zhou

2022

Proceedings of the Institution of Mechanical Engineers, Part K:

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The Absolute Nodal Coordinate Formulation (ANCF) is a milestone in the study of flexible multibody dynamics and is of great significance for the study of the dynamics of multi-flexible systems, of which the plate element is an important part. In this article, the construction and principles of this type of element are systematically traced, the types of elements that have been studied are summarized, and the research history of the element locking problem and extended applications in different fields are briefly described. Through the systematic summary, the shortcomings in the current research and application of the element are identified, and some suggestions for future theoretical research on the plate element are given. The functional expansion of the plate element under the conditions of constraints, materials and physical fields as well as practical engineering applications are discussed.

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Generalization of the strain-split method and evaluation of the nonlinear ANCF finite elements

Cited by 21 publications

References 34 publications

Deformation of planar ring mesh under static in-plane tensile loads

Deformation of planar ring mesh under static in-plane tensile loads

Analysis of electromechanical systems based on the absolute nodal coordinate formulation

Research status and prospect of plate elements in absolute nodal coordinate formulation

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