Integration of localized surface geometry in fully parameterized ANCF finite elements

He, Gang; Patel, Mohil; Shabana, Ahmed A.

doi:10.1016/j.cma.2016.10.016

Cited by 19 publications

(7 citation statements)

References 34 publications

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“…Each subdomain has 3 integration points in both the x and y directions. Since the local geometry is described more accurately by locally placing the integration point, more accurate results of the dynamic analysis will be obtained through numerical integration without considerable increasing the computational cost (He et al, 2017).…”

Section: Subdomain Integration Methodsmentioning

confidence: 99%

“…For dealing with a protrusion feature such as a rib on an ANCF element, the overlapping method is used in this investigation. The basic principle of the overlapping method is to add a height value to the basic element shape to describe the protrusion feature (He et al, 2017). Because ANCF geometry is expressed by ANCF shape functions and the element nodal coordinates, the modified position field with a protrusion feature can be defined as (He et al, 2017)…”

Section: Overlapping Local Shape Featurementioning

confidence: 99%

“…, respectively. However, the function defining the geometry may change with y only (He et al, 2017).…”

Section: Overlapping Local Shape Featurementioning

confidence: 99%

“…Therefore, it is important to consider the effect of localized surface geometry in the implementation of finite element analysis. Recently, a new method proposed by He and Shabana (He et al, 2017) successfully described localized surface geometry by using NURBS; this method can accurately capture the surface geometry without significantly increasing the computational cost caused by mesh refinement.…”

Section: Introductionmentioning

confidence: 99%

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Shape optimization of a flexible beam with a local shape feature based on ANCF

Gao

Jiang

et al. 2019

JAMDSM

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This paper proposes a shape optimization method of local shape features on a flexible beam modeled with the absolute nodal coordinate formulation (ANCF). A fully parameterized ANCF beam element is used to model the global geometry for flexible body dynamics analysis. The local shape feature of the ANCF element surfaces can be described by a nonuniform rational B-spline (NURBS) without the need for mesh refinement by changing the distribution of the integration points. A mapping between the ANCF element local coordinates and the NURBS localized geometric parameters is used for the consistent implementation of the overlapping methods. The selected shape parameters of the localized surface geometry are taken as the design variables for beam shape optimization, and the weighted summation of the compliance of the beam is taken as the objective to evaluate the influence of the dynamic response. Different weighting schemes are used to compare the effects of weighting. An example of an ANCF beam with a rib is given to validate our method. A two-stage shape optimization method based on SQP (Sequence quadratic program) is run to reduce the compliance of the beam. Because few design variables are used to represent the local and global shapes of the beam geometry, our shape optimization method based on the localized surface geometry has a significantly reduced computational burden and improved optimization efficiency.

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Section: Subdomain Integration Methodsmentioning

confidence: 99%

Section: Overlapping Local Shape Featurementioning

confidence: 99%

“…, respectively. However, the function defining the geometry may change with y only (He et al, 2017).…”

Section: Overlapping Local Shape Featurementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Shape optimization of a flexible beam with a local shape feature based on ANCF

Gao

Jiang

et al. 2019

JAMDSM

Self Cite

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“…For the problem of variable thickness, firstly, Abbas and Rui et al proposed a variable-thickness quadrilateral plate element 48 based on the fully parameterized element, which is suitable for regions where the thickness does not vary greatly. Later, He et al 94 proposed a modeling method for the local features in elements, which can be used to study the mechanical effects of protruding features on large plates, 95 which has been applied to the study of the effect of tire treads. 96 In another research direction, when the sheet-like structure is continuously thinned in thickness, it can be converted to a membrane structure.…”

Section: Structural Thicknessmentioning

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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On the Lagrange multipliers of the intrinsic constraint equations of rigid multibody mechanical systems

Pappalardo

Guida

2017

Arch Appl Mech

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This paper deals with the Lagrange multipliers corresponding to the intrinsic constraint equations of rigid multibody mechanical systems. The intrinsic constraint equations are algebraic equations that are associated with nonminimal sets of orientation parameters employed for the kinematic representation of large finite rotations. Two coordinate formulations are analyzed in this investigation, namely the reference point coordinate formulation (RPCF) with Euler parameters and the natural absolute coordinate formulation (NACF). While the RPCF with Euler parameters employs the four components of a unit quaternion as rotational coordinates, the NACF directly uses the orthonormal set of nine direction cosines for describing the orientation of a rigid body in the three-dimensional space. In the multibody approaches based on the RPCF with Euler parameters and on the NACF, the use of a nonminimal set of rotational coordinates facilitates a general and systematic formulation of the differentialâ\u80\u93algebraic equations of motion. Considering the basic equations of classical mechanics, the fundamental problem of constrained motion is formalized and solved in this paper by using a special form of the Udwadiaâ\u80\u93Kalaba method. By doing so, the Udwadiaâ\u80\u93Kalaba equations are employed for obtaining closed-form analytical solutions for the Lagrange multipliers associated with the intrinsic constraint equations that appear in the differentialâ\u80\u93algebraic dynamic equations developed by using the RPCF with Euler parameters and the NACF multibody approaches. Two simple numerical examples support the analytical results found in this paper

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Integration of localized surface geometry in fully parameterized ANCF finite elements

Cited by 19 publications

References 34 publications

Shape optimization of a flexible beam with a local shape feature based on ANCF

Shape optimization of a flexible beam with a local shape feature based on ANCF

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

On the Lagrange multipliers of the intrinsic constraint equations of rigid multibody mechanical systems

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