Clamped end conditions and cross section deformation in the finite element absolute nodal coordinate formulation

Hussein, Bassam A.; Weed, David; Shabana, Ahmed A.

doi:10.1007/s11044-009-9146-6

Cited by 16 publications

(6 citation statements)

References 14 publications

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“…In the case of the fully parameterized ANCF beam element considered in this investigation, one can show that the preceding equation reduces to the simple form (ds/dS) = |r y × r z | [6].…”

Section: Ligament Cross Section Deformationmentioning

confidence: 94%

A new nonlinear multibody/finite element formulation for knee joint ligaments

Weed

Maqueda²,

Brown

et al. 2009

Nonlinear Dyn

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The focus of this investigation is to study the mechanics of the human knee using a new method that integrates multibody system and large deformation finite element algorithms. The major bones in the knee joint consisting of the femur, tibia, and fibula are modeled as rigid bodies. The ligaments structures are modeled using the large displacement finite element absolute nodal coordinate formulation (ANCF) with an implementation of a Neo-Hookean constitutive model that allows for large change in the configuration as experienced in knee flexion, extension, and rotation. The Neo-Hookean strain energy function used in this study takes into consideration the near incompressibility of the ligaments. The ANCF is used in the formulation of the algebraic equations that define the ligament/bone rigid connection. A unique feature of the ANCF model developed in this investigation is that it captures the deformation of the ligament cross section using structural finite elements such as beams. At the ligament/bone insertion site, the ANCF is used to define a fully constrained joint. This model will reflect the fact that the geometry, placement and attachment of the two collateral ligaments (the LCL and MCL), are significantly different from what has been used in most knee models developed in previous investigations. The approach described in this paper will provide a more realistic model of the knee and thus more applicable to future research studies on ligaments, muscles and soft tissues (LMST). Current finite element models are limited due to simplified assumptions for the spatial and time dependent material properties inherent in the anisotropic and anatomic constraints associated with joint stability, and the static conditions inherent in the analysis. The ANCF analysis is not limited to static conditions and results in a fully dynamic model that accounts for the distributed inertia and elasticity of the ligaments. The results obtained in this investigation show that the ANCF finite elements can be an effective tool for modeling very flexible structures like ligaments subjected to large flexion and extension. In the future, the more realistic ANCF models could assist in examining the mechanics of the knee to study knee injuries and possible prevention means, as well as an improved understanding of the role of each individual ligament in the diagnosis and assessment of disease states, aging and potential therapies.

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“…In the case of the fully parameterized ANCF beam element considered in this investigation, one can show that the preceding equation reduces to the simple form (ds/dS) = |r y × r z | [6].…”

Section: Ligament Cross Section Deformationmentioning

confidence: 94%

A new nonlinear multibody/finite element formulation for knee joint ligaments

Weed

Maqueda²,

Brown

et al. 2009

Nonlinear Dyn

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“…The cross section deformation at the joint nodes can be captured using Nanson's formula which can be written as follows [6,8,16]:…”

Section: Deformation Modesmentioning

confidence: 99%

Nonstructural geometric discontinuities in finite element/multibody system analysis

et al. 2011

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Existing multibody system (MBS) algorithms treat articulated system components that are not rigidly connected as separate bodies connected by joints that are governed by nonlinear algebraic equations. As a consequence, these MBS algorithms lead to a highly nonlinear system of coupled differential and algebraic equations. Existing finite element (FE) algorithms, on the other hand, do not lead to a constant mesh inertia matrix in the case of arbitrarily large relative rigid body rotations. In this paper, new FE/MBS meshes that employ linear connectivity conditions and allow for arbitrarily large rigid body displacements between the finite elements are introduced. The large displacement FE absolute nodal coordinate formulation (ANCF) is used to obtain linear element connectivity conditions in the case of large relative rotations between the finite elements of a mesh. It is shown in this paper that a linear formulation of pin (revolute) joints that allow for finite relative rotations between two elements connected by the joint can be systematically obtained using ANCF finite elements. The algebraic joint constraint equations, which can be introduced at a preprocessing stage to efficiently eliminate redundant position coordinates, allow for deformation modes at the pin joint definition point, and therefore, this new joint formulation can be considered as a generalization of the pin joint formulation used in rigid MBS analysis. The new pin joint deformation modes that are the result of C 0 continuity conditions, allow for the calculations of the pin joint strains which can be discontinuous as the result of the finite relative rotation between the elements. This type of discontinuity is referred to in this paper as nonstructural discontinuity in order to distinguish it from the case of structural discontinuity in which the elements are rigidly connected. Because ANCF finite elements lead to a constant mass matrix, an identity generalized mass matrix can be obtained for the FE mesh despite the fact that the finite elements of the mesh are not rigidly connected. The relationship between the nonrational ANCF finite elements and the B-spline representation is used to shed light on the potential of using ANCF as the basis for the integration of computer aided design and analysis (I-CAD-A). When cubic interpolation is used in the FE/ANCF representation, C 0 continuity is equivalent to a knot multiplicity of three when computational geometry methods such as B-splines are used. C 2 ANCF models which ensure the continuity of the curvature and correspond to B-spline knot multiplicity of one can also be obtained. Nonetheless, B-spline and NURBS representations cannot be used to effectively model T-junctions that can be systematically modeled using ANCF finite elements which employ gradient 810 A.M. Hamed et al.coordinates that can be conveniently used to define element orientations in the reference configuration. Numerical results are presented in order to demonstrate the use of the new formulation in developing new chain models.

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“…The global position vector of a point on the beam is represented using the global shape function and absolute coordinates as [17,18] …”

Section: Equations Of Motion Of An Ancf Beam Elementmentioning

confidence: 99%

Dynamic analysis of rubber-like material using absolute nodal coordinate formulation based on the non-linear constitutive law

2010

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Non-linear constitutive models of the elastic forces for a hyperelastic material are presented. Three elastic force models including Neo-Hookean, Mooney-Riblin 2nd, and Yeoh models are derived based on non-linear continuum mechanics. Elastic forces are applied to the three-dimensional absolute nodal coordinate beam element, and the transient response of the cantilever beam is analyzed. Simulation results are compared to experiment data, and the dynamic characteristics of elastic force models presented in this paper are discussed.

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Clamped end conditions and cross section deformation in the finite element absolute nodal coordinate formulation

Cited by 16 publications

References 14 publications

A new nonlinear multibody/finite element formulation for knee joint ligaments

A new nonlinear multibody/finite element formulation for knee joint ligaments

Nonstructural geometric discontinuities in finite element/multibody system analysis

Dynamic analysis of rubber-like material using absolute nodal coordinate formulation based on the non-linear constitutive law

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