A two-dimensional shear deformable beam element based on the absolute nodal coordinate formulation

Dufva, Kari; Sopanen, Jussi; Mikkola, Aki

doi:10.1016/j.jsv.2003.12.044

Cited by 96 publications

(47 citation statements)

References 16 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The beam finite element used in this study is based on a two-dimensional element originally proposed by Dufva et al [12]. This shear deformable element is based on the absolute nodal coordinate formulation and it includes an accurate expression of the elastic forces.…”

Section: Formulation Of the Finite Element Usedmentioning

confidence: 99%

“…In the element, a continuum mechanics approach is utilized in the exact displacement field of the shear deformable beam. This leads to the capability of accurately predicting the nonlinear deformations without suffering from shear or Poisson's locking [12].…”

Section: Formulation Of the Finite Element Usedmentioning

confidence: 99%

“…For this reason, it is desirable to formulate an element that allows for reducing the bending stiffness of the element. In this study, a new belt-like element is introduced by modifying the recently proposed two-dimensional shear deformable beam element, where a continuum mechanics approach is applied to the exact displacement field of the shear deformable beam [12]. This paper is organized as follows.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Modeling of Belt-Drives Using a Large Deformation Finite Element Formulation

2006

View full text Add to dashboard Cite

In this paper, the applicability of the absolute nodal coordinate formulation for the modeling of belt-drive systems is studied. A successful and effective analyzing method for belt-drive systems requires the exact modeling of the rigid body inertia during an arbitrary rigid body motion, accounting of shear deformation, description of highly nonlinear deformations, and a simple as well as realistic description of the contact. The absolute nodal coordinate formulation meets the challenge and is a promising approach for the modeling of belt-drive systems. In this study, a recently proposed two-dimensional shear deformable beam element based on the absolute nodal coordinate formulation has been modified to obtain a belt-like element. In the original element, a continuum mechanics approach is applied to the exact displacement field of the shear deformable beam. The belt-like element allows the user to control the axial and bending stiffness through the use of two parameters. In this study, the interaction between the belt and the pulleys is modeled using an elastic approach in which the contact is accounted for by the inclusion of a set of external forces that depend on the penetration between the belt and pulley. When using the absolute nodal coordinate formulation, the contact forces can be distributed over the length of the element due to the use of high-order polynomials. This is different from other approaches that are used in the modeling of belt-drives. Static and dynamic analysis are used in this study to show the performance of the distributed contact force model and the proposed belt-like element, which is able to model highly nonlinear deformations. Applying these two contributions to the modeling of belt-drive systems, instead of contact forces applied at nodes and low-order elements, leads to a considerable reduction in the degrees of freedom.

show abstract

Section: Formulation Of the Finite Element Usedmentioning

confidence: 99%

Section: Formulation Of the Finite Element Usedmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Modeling of Belt-Drives Using a Large Deformation Finite Element Formulation

2006

View full text Add to dashboard Cite

show abstract

“…can be effective in solving a class of small deformation problems Hamed et al, 2011;Shabana, 2010 Dimtrochenko and Pogorelov, 2003;Abbas et al, 2010;Dufva et al, 2005Dufva et al, , 2007Schwab and Meijaard, 2010;Shabana and Mikkola, 2003;Tian et al, 2009;Yakoub and Shabana, 2001;Omar and Shabana, 2001). ANCF finite elements can be used to model both structural and nonstructural discontinuities in a straightforward manner Hamed et al, 2011).…”

Section: Introductionmentioning

confidence: 99%

“…In addition to the high nonlinearity of the inertia forces, the joint constraints equations developed using the FFR formulation are also highly nonlinear because of the use of orientation parameters (Korkealaakso et al, 2009). Furthermore, rigid triads and unit vectors are often used in the formulation of the joints in the rigid body and FFR algorithms, and as a result, these ideal joint formulations do not capture modes of deformation.While the FFR formulation will remain an effective approach for modeling small deformation problems because it allows for filtering out high frequency modes, the more general large rotation large deformation finite element absolute nodal coordinate formulation (ANCF)can be effective in solving a class of small deformation problems Hamed et al, 2011;Shabana, 2010 Dimtrochenko and Pogorelov, 2003;Abbas et al, 2010;Dufva et al, 2005Dufva et al, , 2007Schwab and Meijaard, 2010;Shabana and Mikkola, 2003;Tian et al, 2009;Yakoub and Shabana, 2001;Omar and Shabana, 2001). ANCF finite elements can be used to model both structural and nonstructural discontinuities in a straightforward manner Hamed et al, 2011).…”

mentioning

confidence: 99%

Ideal Compliant Joints and Integration of Computer Aided Design and Analysis

Hamed¹,

Jayakumar²,

Letherwood³

et al. 2013

View full text Add to dashboard Cite

Public reporting burden for the collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing this burden, to Washington Headquarters Services, Directorate for Information Operations and Reports, 1215 Jefferson Davis Highway, Suite 1204, Arlington VA 22202-4302. Respondents should be aware that notwithstanding any other provision of law, no person shall be subject to a penalty for failing to comply with a collection of information if it does not display a currently valid OMB control number. REPORT DATE NOV 20132. REPORT TYPE Technical Report3 ; #24314 SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES) U.S. Army TARDEC, 6501 East Eleven Mile Rd, Warren, Mi, 48397-5000 SPONSOR/MONITOR'S ACRONYM(S) TARDEC SPONSOR/MONITOR'S REPORT NUMBER(S) #24314 DISTRIBUTION/AVAILABILITY STATEMENTApproved for public release; distribution unlimited 13. SUPPLEMENTARY NOTES 14. ABSTRACT This paper discusses fundamental issues related to the integration of computer aided design and analysis (I-CAD-A) by introducing a new class of ideal compliant joints that account for the distributed inertia and elasticity. The absolute nodal coordinate formulation (ANCF) degrees of freedom are used in order to capture modes of deformation that cannot be captured using existing formulations. The ideal compliant joints developed can be formulated, for the most part, using linear algebraic equations, allowing for the elimination of the dependent variables at a preprocessing stage, thereby significantly reducing the problem dimension and array storage needed. Furthermore, the constraint equations are automatically satisfied at the position, velocity, and acceleration levels. When using the proposed approach to model large scale chain systems, differences in computational efficiency between the augmented formulation and the recursive methods are eliminated, and the CPU times resulting from the use of the two formulations become similar regardless of the complexity of the system. The elimination of the joint constraint equations and the associated dependent variables also contribute to the solution of a fundamental singularity problem encountered in the analysis of closed loop chains and mechanisms by eliminating the need to repeatedly change the chain or mechanism independent coordinates. It is shown that the concept of the knot multiplicity used in computational geometry methods, such as B-spline and NURBS (Non-Uniform Rational B-Spline), to control the degree of continuity at the breakpoints is not suited for the formulation of many ideal compliant joints. As explained in this paper, this issue is closely related to the inability of B-spline and NURBS to model structural discontinuities. Another contribution of this paper is dem...

show abstract

Multibody Dynamics Modeling of Friction Winder Systems Using Absolute Nodal Coordination Formulation

Liu

Chen

et al. 2010

Advances in Intelligent and Soft Computing

View full text Add to dashboard Cite

A two-dimensional shear deformable beam element based on the absolute nodal coordinate formulation

Cited by 96 publications

References 16 publications

Modeling of Belt-Drives Using a Large Deformation Finite Element Formulation

Modeling of Belt-Drives Using a Large Deformation Finite Element Formulation

Ideal Compliant Joints and Integration of Computer Aided Design and Analysis

Multibody Dynamics Modeling of Friction Winder Systems Using Absolute Nodal Coordination Formulation

Contact Info

Product

Resources

About