Use of General Nonlinear Material Models in Beam Problems: Application to Belts and Rubber Chains

2010 ◽  
Vol 5 (2) ◽  
Author(s):  
Luis G. Maqueda ◽  
Abdel-Nasser A. Mohamed ◽  
Ahmed A. Shabana
Keyword(s):  
Finite Element ◽  
Large Deformation ◽  
Cross Section ◽  
Multibody System ◽  
Three Dimensional ◽  
Nonlinear Material ◽  
Tracked Vehicle ◽  
Material Models ◽  
Belt Drives ◽  
Linear And Nonlinear

Accurate modeling of many engineering systems requires the integration of multibody system and large deformation finite element algorithms that are based on general constitutive models, account for the coupling between the large rotation and deformation, and allow capturing coupled deformation modes that cannot be captured using beam formulations implemented in existing computational algorithms and computer codes. In this investigation, new three-dimensional nonlinear dynamic rubber chains and belt drives models are developed using the finite element absolute nodal coordinate formulation (ANCF) that allows for a straight forward implementation of general linear and nonlinear material models for structural elements such as beams, plates, and shells. Furthermore, this formulation, which is based on a more general kinematic description, can be used to predict the cross section deformation and its coupling with the extension and bending of the belt drives and rubber chains. The ANCF cross section deformation results are validated by comparison with the results obtained using solid finite elements in the case of a simple tension test problem. The effect of the use of different linear and nonlinear constitutive laws in modeling belt drive mechanisms is also examined in this investigation. The finite element formulation presented in this paper is implemented in a general purpose three-dimensional flexible multibody algorithm that allows for developing detailed models of mechanical systems subject to general loading conditions, nonlinear algebraic constraint equations, and arbitrary large displacements that characterize belt drives and tracked vehicle dynamics. The successful integration of large deformation finite element and multibody system algorithms is shown to be necessary in order to be able to study the dynamics of complex tracked vehicles with rubber chains. A computer simulation of a three-dimensional multibody tracked vehicle model that consists of twenty rigid bodies and two flexible rubber chains is used in order to demonstrate the use of the formulations presented in this investigation.

Use of General Nonlinear Material Models in Beam Problems: Application to Belt and Rubber Chains

2009 ◽  
Author(s):  
Luis G. Maqueda ◽  
Abdel-Nasser A. Mohamed ◽  
Ahmed A. Shabana
Keyword(s):  
Finite Element ◽  
Large Deformation ◽  
Cross Section ◽  
Multibody System ◽  
Three Dimensional ◽  
Nonlinear Material ◽  
Tracked Vehicle ◽  
Material Models ◽  
Belt Drives ◽  
Linear And Nonlinear

Accurate modeling of many engineering systems requires the integration of multibody system and large deformation finite element algorithms that are based on general constitutive models, account for the coupling between the large rotation and deformation, and allow capturing coupled deformation modes that cannot be captured using beam formulations implemented in existing computational algorithms and computer codes. In this investigation, a new nonlinear finite element dynamic model for the analysis of three-dimensional rubber chains and belt drives is developed using the finite element absolute nodal coordinate formulation (ANCF) that allows for a straight forward implementation of general linear and nonlinear material models for structural elements such as beams, plates and shells. Furthermore, this formulation, which is based on a more general kinematic description, can be used to predict the cross section deformation and its coupling with the extension and bending of the belt drives and rubber chains. The ANCF cross section deformation results are validated by comparison with the results obtained using solid finite elements in the case of a simple tension test problem. The effect of the use of different linear and nonlinear constitutive laws in modeling belt drives mechanism is also examined in this investigation. The finite element formulation presented in this paper is implemented in a general purpose three-dimensional flexible multibody algorithm that allows for developing detailed models of mechanical systems subject to general loading conditions, nonlinear algebraic constraint equations, and arbitrary large displacements that characterize belt drives and tracked vehicle dynamics. The successful integration of large deformation finite element and multibody system algorithms is shown to be necessary in order to be able to study the dynamics of complex tracked vehicles with rubber chains. A computer simulation of a three-dimensional multibody tracked vehicle model that consists of twenty rigid bodies and two flexible rubber chains is used in order to demonstrate the use of the formulations presented in this investigation.

ANCF Finite Element/Multibody System Formulation of the Ligament/Bone Insertion Site Constraints

2010 ◽  
Vol 5 (3) ◽  
Author(s):  
Florentina M. Gantoi ◽  
Michael A. Brown ◽  
Ahmed A. Shabana
Keyword(s):  
Finite Element ◽  
Finite Elements ◽  
Cross Section ◽  
Multibody System ◽  
Insertion Site ◽  
Three Dimensional ◽  
Beam Element ◽  
Large Displacement ◽  
End Conditions ◽  
The Cross

The focus of this investigation is to study the mechanics of the knee joint using new ligament/bone insertion site constraint models that require the integration of multibody system and large displacement finite element algorithms. Two different sets of clamped end conditions at the ligament/bone insertion site are examined using nonlinear large displacement absolute nodal coordinate formulation (ANCF) finite elements. The first set of end conditions, called the partially clamped joint, eliminates only the translations and rotations at a point, allowing for the cross section stretch and shear at the ligament/bone connection. The second joint, called the fully clamped joint, eliminates all the translation, rotation, and deformation degrees of freedom of the cross section at the ligament/bone insertion site. In the case of the fully clamped joint, the gradient vectors do not change their length and orientation, allowing for the use of the constant strain assumptions. The partially clamped joint, on the other hand, allows for the change in length and relative orientation of the gradient vectors at the bone/ligament insertion site, leading to the cross section deformation induced by knee movements. Nanson’s formula is applied as a measure of the deformation of the cross section in the case of the partially clamped joint. In this study, the major bones in the knee joint consisting of the femur, tibia, and fibula are modeled as rigid bodies while the ligaments structures are modeled using the large displacement ANCF finite elements. Two different ANCF finite element models are developed in this investigation: the first model employs the fully parameterized three-dimensional beam element while the second model employs the three-dimensional cable element. The three-dimensional fully parameterized beam element allows for a straight forward implementation of a neo-Hookean constitutive model that can be used to accurately predict the large displacement as experienced in knee flexation and rotation. At the ligament bone insertion site, the ANCF fully parameterized beam element is used to define a fully or partially constrained joint while the ANCF cable element can only be used to define one joint type. The fully and partially clamped joint constraints are satisfied at the position, velocity, and acceleration levels using a dynamic formulation that is based on an optimum sparse matrix structure. The approach described in this investigation can be used to develop more realistic models of the knee and is applicable to future research studies on ligaments, muscles, and soft tissues. In particular, the partially clamped joint representation of the ligament/bone insertion site constraints can be used to develop improved structural mechanics models of the knee.

scholarly journals On the Design of a Biodegradable POC-HA Polymeric Cardiovascular Stent

2012 ◽  
Author(s):  
Joonas Ponkala ◽  
Mohsin Rizwan ◽  
Panos S. Shiakolas
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Material Properties ◽  
Three Dimensional ◽  
Polymeric Composite ◽  
Coronary Stent ◽  
Element Analysis ◽  
Material Models ◽  
Solid Models ◽  
Biodegradable Stents

The current state of the art in coronary stent technology, tubular structures used to keep the lumen open, is mainly populated by metallic stents coated with certain drugs to increase biocompatibility, even though experimental biodegradable stents have appeared in the horizon. Biodegradable polymeric stent design necessitates accurate characterization of time dependent polymer material properties and mechanical behavior for analysis and optimization. This manuscript presents the process for evaluating material properties for biodegradable biocompatible polymeric composite poly(diol citrate) hydroxyapatite (POC-HA), approaches for identifying material models and three dimensional solid models for finite element analysis and fabrication of a stent. The developed material models were utilized in a nonlinear finite element analysis to evaluate the suitability of the POC-HA material for coronary stent application. In addition, the advantages of using femtosecond laser machining to fabricate the POC-HA stent are discussed showing a machined stent. The methodology presented with additional steps can be applied in the development of a biocompatible and biodegradable polymeric stents.

scholarly journals Finite Element Software for Rubber Products Design

2018 ◽  
Vol 3 (1) ◽  
pp. 13-20
Author(s):  
Dávid Huri
Keyword(s):  
Finite Element ◽  
Complex Analysis ◽  
Large Deformations ◽  
Material Behavior ◽  
Nonlinear Material ◽  
Material Models ◽  
Finite Element Software ◽  
Highly Nonlinear ◽  
Wide Range ◽  
Different Types

Automotive rubber products are subjected to large deformations during working conditions, they often contact with other parts and they show highly nonlinear material behavior. Using finite element software for complex analysis of rubber parts can be a good way, although it has to contain special modules. Different types of rubber materials require the curve fitting possibility and the wide range choice of the material models. It is also important to be able to describe the viscoelastic property and the hysteresis. The remeshing possibility can be a useful tool for large deformation and the working circumstances require the contact and self contact ability as well. This article compares some types of the finite element software available on the market based on the above mentioned features.

scholarly journals Membrane analogy for multi-material bars under torsion

2019 ◽  
Vol 475 (2225) ◽  
pp. 20190124 ◽  
Author(s):  
Laura Galuppi ◽  
Gianni Royer-Carfagni
Keyword(s):  
Finite Element ◽  
Cross Section ◽  
Cross Sections ◽  
Three Dimensional ◽  
Element Model ◽  
Elastic Problem ◽  
Two Dimensional ◽  
Torsion Problem ◽  
Linear Elastic ◽  
Physical Apparatus

Prandtl's membrane analogy for the torsion problem of prismatic homogeneous bars is extended to multi-material cross sections. The linear elastic problem is governed by the same equations describing the deformation of an inflated membrane, differently tensioned in regions that correspond to the domains hosting different materials in the bar cross section, in a way proportional to the inverse of the material shear modulus. Multi-connected cross sections correspond to materials with vanishing stiffness inside the holes, implying infinite tension in the corresponding portions of the membrane. To define the interface constrains that allow to apply such a state of prestress to the membrane, a physical apparatus is proposed, which can be numerically modelled with a two-dimensional mesh implementable in commercial finite-element model codes. This approach presents noteworthy advantages with respect to the three-dimensional modelling of the twisted bar.

Development of a Nonlinear, C1-Beam Finite-Element Code for Actuator Design of Slender Flexible Robots

2017 ◽  
Author(s):  
Hidenori Murakami ◽  
Oscar Rios ◽  
Takeyuki Ono
Keyword(s):  
Finite Element ◽  
Large Deformation ◽  
Cross Section ◽  
Beam Model ◽  
Finite Element Code ◽  
Shape Functions ◽  
Lagrange Equations ◽  
Element Discretization ◽  
Flexible Robots ◽  
Actuator Design

For actuator design and motion simulations of slender flexible robots, planar C1-beam elements are developed for Reissner’s large deformation, shear-deformable, curbed-beam model. Internal actuation is mechanically modeled by a rate-form of beam constitutive relation, where actuation curvature is prescribed at each time. Geometrically, a curbed beam is modeled as a frame bundle, whereby at each point on beam’s curve of centroids a moving orthonormal frame is attached to a cross section. After a finite element discretization, a curve of centroids is modeled as a C1-curve, employing cubic shape functions for both planar coordinates with an arc-parameter. The cubic shape functions have already been utilized in linear Euler-Bernoulli beams for the interpolation of transverse displacement. To define the rotation angle of each cross section or the attitude of the moving frame, quadratic shape functions are used introducing a middle node, resulting in three angular nodal displacements. As a result, each beam element has total eleven nodal coordinates. The implementation of a nonlinear finite element code is facilitated by the principle of virtual work, which yields Reissner’s large deformation curbed beam model as the Euler-Lagrange equations. For time integration, the Newmark method is utilized. Finally, as applications of the code, a few inchworm motions induced by different actuation curvature fields are presented.

Stress and Strength of Butt Circular Shaft With Metal Columns Subjected to Torques

2004 ◽  
Author(s):  
Jiemin Liu ◽  
Jintang Liu ◽  
Toshiyuki Sawa
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Stress Analysis ◽  
Yield Stress ◽  
Cross Section ◽  
Three Dimensional ◽  
Adhesive Layer ◽  
Circular Shaft ◽  
Dimensional Finite Element ◽  
Three Dimensional Finite Element

Stress analysis of the butt circular shaft with three uniformly distributed metal columns subjected to external torques are carried out by using three-dimensional finite element method. The loading capability of the butt circular shaft is measured. It was found that torque acting on the cross-section of adhesive layer is simultaneously withstood by the adhesive layer and the metal columns; The ratio of the torque withstood by metal columns to that withstood by adhesive layer increases with increase of the ratio of Young’s modulus of metal columns to that of the circular shaft; The metal columns enhance and improve the reliability of the joints; The strength of the butt adhesive circular shafts increases with increase of the ratio of the yield stress of the metal columns to that of circular shafts.

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