Higher-Order Plate Elements for Large Deformation Analysis in Multibody Applications

Ebel, Henrik; Matikainen, Marko K.; Hurskainen, Vesa-Ville; Mikkola, Aki

doi:10.1115/detc2016-59381

Cited by 4 publications

(5 citation statements)

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“…( 5) and ( 7), the strain vector is expressed as a function of the position gradient vectors, i.e. (11) and its variation can be related to a mid-surface quantity χ using Eq. ( 2) as…”

Section: Strains and Stressesmentioning

confidence: 99%

“…Subsequently, detailed investigations of this element focusing on the formulation of elastic forces were conducted by Yamashita et al [9] employing the continuum mechanics approach and Valkeapää et al [10] using the elastic midsurface approach. Ebel et al [11,12] developed eight-and nine-node higher-order plate elements and demonstrated the benefits of alleviating locking phenomena by introducing higher-order transverse derivatives as nodal variables. The fully parameterized elements ensure C1 continuity at neighboring element nodes, whereas the gradient-deficient elements only guarantee C0 continuity.…”

Section: Introductionmentioning

confidence: 99%

“…The fully parameterized elements ensure C1 continuity at neighboring element nodes, whereas the gradient-deficient elements only guarantee C0 continuity. Experience indicates that the satisfaction of C1 continuity has minimal impact on the accuracy of results [6], while the use of in-plane gradient vectors as node variables adversely affects element convergence [11]. Consequently, gradient-deficient elements with fewer DOFs appear to be preferable for simulations of moderately thick plates.…”

Section: Introductionmentioning

confidence: 99%

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Weak form quadrature shell elements based on absolute nodal coordinate formulation

He,

Li,

Zhong

2024

Preprint

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Weak form quadrature elements for moderately thick shells with arbitrary initial configurations are developed under the framework of continuum mechanics and the absolute nodal coordinate formulation (ANCF). Nodal variables of the element consist of the position vector, the transverse gradient vector and the transverse derivatives thereof at the shell mid-surface. In-plane gradient vectors which are not taken as nodal variables are obtained with the aid of the differential quadrature analog. Using the transverse gradient vector and one in-plane gradient vector, joint constraint equations for shells with discontinuous slopes are established. Simplified equations of motion with constant mass matrix result. The elements are applicable to analysis of shell structures undergoing large displacements and rotations. Five examples encompassing static and dynamic shell analysis, post-buckling analysis of shells, as well as analysis of shells with discontinuous mid-surface slopes are examined to assess the performance of the proposed elements. Satisfactory results are obtained, validating the efficacy of the proposed elements.

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“…( 5) and ( 7), the strain vector is expressed as a function of the position gradient vectors, i.e. (11) and its variation can be related to a mid-surface quantity χ using Eq. ( 2) as…”

Section: Strains and Stressesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Weak form quadrature shell elements based on absolute nodal coordinate formulation

He,

Li,

Zhong

2024

Preprint

View full text Add to dashboard Cite

show abstract

“…3 423 423 element and studied it intensively. 32 Ebel, Matikainen 33 34 which prevent shear locking but substantially increase the degree of freedom of the elements. Besides, Yu et al 35 proposed a quadrilateral element No.…”

Section: Ancf Plate Finite Elementsmentioning

confidence: 99%

“… 3 423 423 element and studied it intensively. 32 Ebel, Matikainen 33 synthesized three higher-order elements No. 3 433 433, No.…”

Section: Ancf Plate Finite Elementsmentioning

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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Locking alleviation in the large displacement analysis of beam elements: the strain split method

Patel

Shabana

2018

Acta Mech

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This paper proposes a new locking alleviation technique for absolute nodal coordinate formulation (ANCF) beam and plate elements based on a strain split approach. The paper also surveys classical finite element (FE) and ANCF locking alleviation techniques discussed in the literature. Because ANCF beam elements, which allow for the cross section stretch, fully capture the Poisson effect, Poisson locking is an issue when such beam elements are considered. The two-dimensional fullyparameterized ANCF beam element is primarily used in this investigation because such an element can serve as a good surrogate model for three-dimensional ANCF beams and plates as far as membrane, bending and transverse shearing behavior is concerned. In addition to proposing the strain split method (SSM) for ANCF locking alleviation, this work assesses the ANCF FE performance in the cases of higher-order interpolation, enhanced assumed strain method, elastic line method, and the enhanced continuum mechanics approach; and demonstrates the design of the enhanced strain interpolation function by using the shape functions of higher-order ANCF elements. Additionally, a new higher-order ANCF two-dimensional beam element is proposed in order to compare its performance with other finite elements that require the use of other locking alleviation techniques proposed and reviewed in the paper. Finally, several numerical examples are shown to demonstrate the effectiveness of the locking alleviation methods applied to ANCF elements. The purpose of this investigation, apart from proposing a new locking alleviation technique, a new higher-order beam element, and comparing several existing locking alleviation techniques, is to show that dealing with locking in fully-parameterized ANCF elements is feasible and that several methods exist to effectively improve the ANCF element performance without sacrificing important ANCF element properties and features including position vector gradient continuity. Because of the use of ANCF position vector gradients as nodal coordinates, complex stress-free initially-curved geometries can be systematically obtained. Such initially-curved geometries require special attention when attempting to solve locking problems, as will be discussed in this paper.

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Higher-Order Plate Elements for Large Deformation Analysis in Multibody Applications

Cited by 4 publications

References 0 publications

Weak form quadrature shell elements based on absolute nodal coordinate formulation

Weak form quadrature shell elements based on absolute nodal coordinate formulation

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

Locking alleviation in the large displacement analysis of beam elements: the strain split method

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