Slope discontinuities in the finite element absolute nodal coordinate formulation: gradient deficient elements

Shabana, Ahmed A.; Maqueda, Luis G.

doi:10.1007/s11044-008-9111-9

Cited by 29 publications

(20 citation statements)

References 5 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In the case of fully parameterized finite elements, a constant gradient transformation can be obtained and effectively used in the analysis of complex structures with slope discontinuities, as described in the literature [16,17]. This can be accomplished since having a full set of parameters allows defining tangent vectors with arbitrary orientations.…”

Section: Introductionmentioning

confidence: 99%

“…For such lower order gradient deficient elements, which can be more efficient in many applications, defining a constant gradient transformation in the case of structures with slope discontinuities can be difficult. Nonetheless, a constant transformation can always be obtained for these gradient deficient elements in the case of commutative rotations [16]. This is the special case in which the discontinuity rotation and the structure finite rotation are commutative, as in the case of rotations about the same axis.…”

Section: Introductionmentioning

confidence: 99%

“…Therefore, the procedure described in this paper is applicable to all planar gradient deficient ANCF finite elements. In order to develop the gradient transformation for gradient deficient elements, one needs to invoke the concept of the intermediate finite element coordinate system, which has been successfully used in the case of the small deformation finite element floating frame of reference formulation [14,16].…”

Section: Introductionmentioning

confidence: 99%

“…It is the objective of this study to provide a numerical investigation of a new procedure that can be used to model finite elements with slope discontinuities [16]. For each finite element, an intermediate finite element coordinate system is introduced.…”

Section: Introductionmentioning

confidence: 99%

“…4, an example of the ANCF gradient deficient three-dimensional elements is discussed. The new constant orthogonal element transformation [16] that can be used in the case of commutative rotations of structures with slope discontinuities is discussed in Sect. 5.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Numerical investigation of the slope discontinuities in large deformation finite element formulations

Maqueda

Shabana

2008

Nonlinear Dyn

Self Cite

View full text Add to dashboard Cite

In many multibody system applications, the system components are made of structural elements that can have different orientations, leading to slope discontinuities. In this paper, a numerical investigation of a new procedure that can be used to model structures with slope discontinuities in the finite element absolute nodal coordinate formulation (ANCF) is presented. This procedure can be applied to model slope discontinuities in the case of commutative rotations of gradient deficient elements that are used for modeling thin beam and plate structures. An important special case to which the proposed procedure can be applied is the case of all planar gradient deficient ANCF finite elements. The use of the proposed method leads to a constant orthogonal element transformation that describes an arbitrary initial configuration. As a consequence, one obtains, in the case of large commutative rotations and large deformations, a constant mass matrix for structures which have complex geometry. The procedure used in this investigation to model slope discontinuities requires the use of the concept of the intermediate finite element coordinate system. For each finite element, a new set of gradient coordinates that define, at the discontinuity node, the element deformation with respect to the intermediate element coordinate system is introduced. These new gradient coordinates are assumed to be equal for the two finite elements at the point of intersection. That is, the change of the gradients of two elements at the intersection point from their respective intermediate initial reference configuration is assumed to be the same. This procedure leads to a set of linear algebraic equations that define the orthogonal transformation matrix for the finite element. Numerical examples are presented in order to demonstrate the use of the proposed procedure for modeling slope discontinuities.

show abstract

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Numerical investigation of the slope discontinuities in large deformation finite element formulations

Maqueda

Shabana

2008

Nonlinear Dyn

Self Cite

View full text Add to dashboard Cite

show abstract

Application of stable inversion to flexible manipulators modeled by the absolute nodal coordinate formulation

Drücker

Seifried

2023

GAMM-Mitteilungen

View full text Add to dashboard Cite

Compared to conventional robots, flexible manipulators offer many advantages, such as faster end‐effector velocities and less energy consumption. However, their flexible structure can lead to undesired oscillations. Therefore, the applied control strategy should account for these elasticities. A feedforward controller based on an inverse model of the system is an efficient way to improve the performance. However, unstable internal dynamics arise for many common flexible robots and stable inversion must be applied. In this contribution, an approximation of the original stable inversion approach is proposed. The approximation simplifies the problem setup, since the internal dynamics do not need to be derived explicitly for the definition of the boundary conditions. From a practical point of view, this makes the method applicable to more complex systems with many unactuated degrees of freedom. Flexible manipulators modeled by the absolute nodal coordinate formulation (ANCF) are considered as an application example.

show abstract

Effect of carbon black components on rolling mechanical properties of tread rubber material by using improved digital image correlation

et al. 2023

View full text Add to dashboard Cite

The rolling and sliding state of the tread rubber material within contact patch was very important to the handling stability and safety of the vehicle. In this paper, first, the absolute coordinate system was introduced into the digital image correlation method, which improved the ability of the traditional digital image correlation method to solve the large deformation of polymer material surface. Second, a new calculation method of rolling friction coefficient based on the brush model was proposed. Third, a non‐contact full‐field rolling dynamics experimental device was developed to study the effects of carbon black components, rotational speed and vertical load on the rolling mechanical characteristics of tread rubber material. On this basis, the rolling mechanical characteristics of tread rubber material with different formulations were obtained by analyzing the distribution properties of global strain rate, full‐field longitudinal speed and full‐field longitudinal acceleration and the variation laws of transverse/longitudinal strain rate, trajectory of marked points, stress‐strain hysteresis curve and rolling friction coefficient. Finally, the influence mechanism of carbon black composition on rolling mechanical properties of tread rubber material was revealed.

show abstract

Slope discontinuities in the finite element absolute nodal coordinate formulation: gradient deficient elements

Cited by 29 publications

References 5 publications

Numerical investigation of the slope discontinuities in large deformation finite element formulations

Numerical investigation of the slope discontinuities in large deformation finite element formulations

Application of stable inversion to flexible manipulators modeled by the absolute nodal coordinate formulation

Effect of carbon black components on rolling mechanical properties of tread rubber material by using improved digital image correlation

Contact Info

Product

Resources

About