Beam Element for Creep Analysis for a Large Displacement Regime

2009 ◽  
Author(s):  
D. Lanc ◽  
G. Turkalj ◽  
J. Brnic
Keyword(s):  
Beam Element ◽  
Large Displacement ◽  
Creep Analysis ◽  
Displacement Regime

Performance of Curved Beam Elements Using the Absolute Nodal Coordinate Formulation

2009 ◽  
Author(s):  
Hiroyuki Sugiyama ◽  
Hirohisa Koyama ◽  
Hiroki Yamashita
Keyword(s):  
Absolute Nodal Coordinate Formulation ◽  
Beam Element ◽  
Solution Procedure ◽  
Large Displacement ◽  
Curved Beam ◽  
Absolute Nodal Coordinate ◽  
Curved Beam Element ◽  
Strain Components ◽  
The Absolute ◽  
Longitudinal Stretch

In this investigation, a gradient deficient beam element of the absolute nodal coordinate formulation is generalized to a curved beam for the analysis of multibody systems and the performance of the proposed element is discussed by comparing with the fully parameterized curved beam element and the classical large displacement beam element with incremental solution procedures. Strain components are defined with respect to the initially curved configuration and described by the arc-length coordinate. The Green strain is used for the longitudinal stretch, while the material measure of curvature is used for bending. It is shown that strains of the curved beam can be expressed with respect to those defined in the element coordinate system using the gradient transformation and the effect of strains at the initially curved configuration is eliminated using one-dimensional Almansi strain. This property can be effectively used with non-incremental solution procedure employed for the absolute nodal coordinate formulation. Several numerical examples are presented in order to demonstrate the performance of the gradient deficient curved beam element developed in this investigation. It is shown that the use of the proposed element leads to better element convergence as compared to that of the fully parameterized element and the classical large displacement beam element with incremental solution procedures.

Curvature Expressions for the Large Displacement Analysis of Planar Beam Motions

2017 ◽  
Vol 13 (1) ◽  
Author(s):  
Yinhuan Zheng ◽  
Ahmed A. Shabana ◽  
Dayu Zhang
Keyword(s):  
Differential Geometry ◽  
Finite Element ◽  
Beam Element ◽  
Elastic Force ◽  
Large Displacement ◽  
Displacement Analysis ◽  
The Third ◽  
Shear Deformable Beam ◽  
Approach Method ◽  
Shear Deformable

While several curvature expressions have been used in the literature, some of these expressions differ from basic geometry definitions and lead to kinematic coupling between bending and shear deformations. This paper uses three different elastic force formulations in order to examine the effect of the curvature definition in the large displacement analysis of beams. In the first elastic force formulation, a general continuum mechanics approach (method 1) based on the nonlinear strain–displacement relationship is used. The second approach (method 2) is based on a classical nonlinear beam theory, in which a curvature expression consistent with differential geometry and independent of the shear deformation is used. The third elastic force formulation (method 3) employs a curvature expression that depends on the shear angle. In order to examine numerically the effect of using different curvature definitions, three different planar beam elements are used. The first element (element I) is the fully parameterized absolute nodal coordinate formulation (ANCF) shear deformable beam element. The second element (element II) is an ANCF consistent rotation-based formulation (CRBF) shear deformable beam element obtained from element I by consistently replacing the position gradient vectors by rotation parameters. The third element (element III) is a low-order bilinear ANCF/CRBF finite element in which nonzero differential geometry-based curvature definition cannot be obtained because of the low order of interpolation. Numerical results are obtained using the three elastic force formulations and the three finite elements in order to shed light on the definition of bending and shear in the large displacement analysis of beams. The results obtained in this investigation show that the use of method 2, with a penalty formulation that restricts the excessive cross section deformation, can improve significantly the convergence of the ANCF finite element.

scholarly journals Beam element for large displacement analysis of elasto-plastic frames

2004 ◽  
Vol 26 (1) ◽  
pp. 39-54
Author(s):  
Nguyen Dinh Kien ◽  
Do Quoc Quang
Keyword(s):  
Virtual Work ◽  
Internal Force ◽  
Beam Element ◽  
Large Displacement ◽  
Isotropic Hardening ◽  
Arc Length ◽  
Tangent Stiffness Matrix ◽  
Strain Relationship ◽  
Internal Force Vector ◽  
Finite Element Formulations

The present paper develops a non-linear beam element for analysis of elastoplastic frames under large displacements. The finite element formulations are derived by using the co-rotational approach and expression of the virtual work. The Gauss quadrature is employed for numerically computing the element tangent stiffness matrix and internal force vector. A bilinear stress-strain relationship with isotropic hardening is adopted to update the stress. The arc-length technique based on the Newton-Raphson iterative method is employed to compute the equilibrium paths. A number of numerical examples is employed to assess the performance of the developed element. The effects of plastic action on the large displacement behavior of the structures as well as the expansion of plastic zones in the loading process are discussed.

A TIMOSHENKO BEAM ELEMENT FOR LARGE DISPLACEMENT ANALYSIS OF PLANAR BEAMS AND FRAMES

2012 ◽  
Vol 12 (06) ◽  
pp. 1250048 ◽  
Author(s):  
NGUYEN DINH KIEN
Keyword(s):  
Timoshenko Beam ◽  
Local Strain ◽  
Beam Element ◽  
Large Displacement ◽  
Frame Structures ◽  
Quadratic Polynomials ◽  
Displacement Analysis ◽  
Transversal Displacement ◽  
Rotational Method ◽  
Timoshenko Beam Element

A Timoshenko beam element for large displacement analysis of planar beam and frame structures is formulated in the context of the co-rotational method. The shallow arch expression is adopted for the local strain, and cubic and quadratic polynomials obtained from the field consistence approach are respectively employed to interpolate the transversal displacement and rotation. The numerical examples show that the proposed element is capable of furnishing accurate results with a smaller number of elements as compared to the elements previously used in the examples. It has also shown that the nonlinear term in the expression of the local strain plays an important role in the accuracy of the element in the large displacement analysis of beam and frame structures.

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.

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