Three new triangular shell elements of ANCF represented by Bézier triangles

Chang, Hanjiang; Liu, Cheng; Tian, Qiang; Hu, Haiyan; Mikkola, Aki

doi:10.1007/s11044-015-9462-y

Cited by 26 publications

(11 citation statements)

References 41 publications

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“…Gantoi, Brown 65 parametrized the method of B-spline surface. Chang et al 41 proposed an element that can directly convert to Bézier triangles by adding a control point inside the triangular element of both thin and thick elements. Then, to avoid the problem of stress and strain discontinuities at end nodes, 43 Wang Tengfei introduced the triangular element 44 into the Beizer surface 66 so that the model can be conducted directly for any initial surface model.…”

Section: Arbitrary Surfacesmentioning

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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Section: Arbitrary Surfacesmentioning

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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“…7,8 Therefore, it has natural advantages to investigate the integration of computer-aided design and analysis (I-CAD-A) based on ANCF elements. ANCF is treated as crucial research progresses in the field of flexible MBS dynamics in recent years, 9,10 and a complete set of ANCF elements, such as the beam, 11–14 the plate/shell 15–19 and the solid elements, 20,21 has been developed and successfully used in modeling complex MBS applications. 22–26…”

Section: Introductionmentioning

confidence: 99%

Development and implementation of model smoothing method in the framework of absolute nodal coordinate formulation

Zhang

Mao

Hou

et al. 2021

Proceedings of the Institution of Mechanical Engineers, Part K:

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A model smoothing formulation used to filter out the high-frequency components in the dynamical modeling process is developed and implemented in the framework of absolute nodal coordinate formulation (ANCF). Unlike the conventional method which employs stiff ordinary differential equation (ODE) solvers with numerical damping to calculate the dynamic responses of the ANCF model, a new formulation with the controlled high frequency is proposed in this paper. Using the average stress defined in a time interval to replace the instant stress in the virtual power of the internal force, the additional inertial and damping terms are introduced to the equations of motion of the ANCF element. It is proved that the highest frequency magnitude of the modified ANCF model can be adjusted by changing the length parameter of the time interval. As the high-frequency components are filtered out in the process of the model development, the traditional stiff problems of ANCF elements can be solved by using well-developed explicit integration algorithms, particularly in the very stiff and thin structures. Dynamic analysis of the classic examples including the pendulum beam and plate are performed to evaluate the performance of the model smoothing formulation of ANCF elements. Numerical results show that the proposed method can greatly improve the calculation efficiency of ANCF models, and the calculation accuracy can be also guaranteed.

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“…Besides the transformation method from the conventional finite element, three ANCF triangular shell elements represented by basis functions of the Be´zier triangle patch were proposed. 15 They are the thin triangular plate element, the low order thick triangular plate element, and the high order thick triangular plate element. Since the shape functions are independent of the Cartesian nodal coordinates in parametric domain, concise shape functions are obtained compared with the element constructed based on the conventional FE.…”

Section: Introductionmentioning

confidence: 99%

“…However, the clear physical interpretation of the gradient vectors associated with the area coordinates is not obtained. 15 To address the problems above, Pappalardo et al 16 derived two new planar triangular elements using both Cartesian and area coordinate parameter sets. By introducing the concept of independent area gradient coordinate vector, which has a clear physical interpretation, concise shape functions are obtained.…”

Section: Introductionmentioning

confidence: 99%

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A new planar triangular element based on the absolute nodal coordinate formulation

Peng

Wang

2018

Proceedings of the Institution of Mechanical Engineers, Part K:

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In this paper, an improved three-node incomplete cubic planar triangular element is proposed based on the two recently reported absolute nodal coordinate formulation triangular elements. Compared with the existing absolute nodal coordinate formulation elements, a different set of polynomial basis is used to develop the new element using the method analogous to the one used in the conventional Zienkiewicz triangular element. Concise shape functions are obtained by employing both Cartesian and area coordinate sets and the concept of independent area gradient coordinate vector. From the view of the order of the polynomial basis, the criterion for developing incomplete cubic absolute nodal coordinate formulation triangular element that captures the quadratic accuracy is presented. Additionally, the algebraic constraint method used in developing the incomplete cubic triangular element is discussed. Based on the criterion, the proposed element is compared analytically with the previous incomplete cubic element. On the other hand, the proposed element is evaluated using both the static and dynamic numerical examples. The element successfully passes the patch test. The results obtained by the proposed element in this paper agree well with analytical solutions or those given by the full cubic element/general commercial finite element software. The higher accuracy, better convergence of the proposed element and the criterion are verified.

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Three new triangular shell elements of ANCF represented by Bézier triangles

Cited by 26 publications

References 41 publications

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

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

Development and implementation of model smoothing method in the framework of absolute nodal coordinate formulation

A new planar triangular element based on the absolute nodal coordinate formulation

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