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Research Papers

On the Development of Incomplete Cubic Tetrahedral Element Based on the Absolute Nodal Coordinate Formulation

[+] Author and Article Information
Tengfei Wang

School of Mechatronics Engineering,
Harbin Institute of Technology,
92, West Dazhi Street,
Harbin 150001, Heilongjiang Province, China
e-mail: tfwangsme@hit.edu.cn

Zuqing Yu

School of Mechatronics Engineering,
Harbin Institute of Technology,
92, West Dazhi Street,
Harbin 150001, Heilongjiang Province, China
e-mail: zuqingyu@hit.edu.cn

Peng Lan

School of Mechatronics Engineering,
Harbin Institute of Technology,
92, West Dazhi Street,
Harbin 150001, Heilongjiang Province, China
e-mail: lan_p@sina.com

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received February 3, 2018; final manuscript received September 3, 2018; published online February 6, 2019. Assoc. Editor: Zdravko Terze.

J. Comput. Nonlinear Dynam 14(4), 041001 (Feb 06, 2019) (11 pages) Paper No: CND-18-1055; doi: 10.1115/1.4041416 History: Received February 03, 2018; Revised September 03, 2018

In this paper, a new four-node incomplete cubic tetrahedral element (ICTE) based on the absolute nodal coordinate formulation (ANCF) is developed employing both volume coordinate and Cartesian coordinate parameter set. From the view of the order of interpolation polynomial basis, a criterion to develop the incomplete cubic ANCF tetrahedral element that can guarantee the quadratic accuracy is proposed. Based on the criterion, the new element and the other two existing incomplete cubic ANCF tetrahedral elements are compared analytically. The three elements are evaluated by both the static and dynamic numerical simulations. The new element successfully passes the patch test. The solutions of the proposed element in this paper agree well with analytical solutions or those given by the full cubic tetrahedral element/general commercial FE software. The higher accuracy and better convergence of the new element are verified. In addition, the method to develop incomplete cubic element by applying position constraints on the face center points and other corresponding material points of the full cubic element is discussed.

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References

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Figures

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Fig. 1

Standard basis of vector space Pn(R3) associated with Cartesian coordinate

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Fig. 2

ANCF tetrahedral elements: (a) full cubic element and (b) incomplete cubic element

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Fig. 3

Containing relationship among Vi,i=1,2,3, P2(R3) and P3(R3)

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Fig. 4

Unit cube meshed by tetrahedral elements: (a) first mesh type and (b) second mesh type

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Fig. 5

Patch test: (a) tested cube and (b) meshed cube, • outer nodes; inner nodes

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Fig. 6

Curved cantilever beam test: (a) curved cantilever beam and (b) mesh strategy

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Fig. 7

Twisted cantilever beam test: (a) twisted cantilever beam and (b) mesh strategy

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Fig. 8

Beam mesh in the small deformation static analysis

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Fig. 9

Tip vertical displacement of the cantilever

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Fig. 10

Beam mesh in the large deformation static analysis and dynamic simulation

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Fig. 11

Tip vertical displacement of the cantilever

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Fig. 12

Pendulum in the dynamic analysis

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Fig. 13

Vertical displacement of tip point B of the pendulum

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Fig. 14

Strain εxx of center point C of the pendulum

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Fig. 15

x-coorindate of the mass center of one face of the element near the joint

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