Development of Line-to-Line Contact Formulation for Continuum Beams

2021 ◽  
Author(s):  
Babak Bozorgmehri ◽  
Marko K. Matikainen ◽  
Aki Mikkola
Keyword(s):  
Finite Element ◽  
Contact Problem ◽  
Lower Order ◽  
Beam Element ◽  
Higher Order ◽  
Line Contact ◽  
Finite Element Code ◽  
Beam Elements ◽  
Contact Formulation ◽  
Element Type

Abstract A line-to-line beam contact formulation in the framework of the absolute nodal coordinate formulation (ANCF) is introduced in this paper. Higher- and lower-order ANCF beam elements employ the introduced beam contact formulation. The higher- and lower-order ANCF beam elements are compared in terms of their accuracy and performance in a large deformation contact problem. Efficiency of numerical integration of contact energy variation contribution to the system’s equations of motion is studied. The contacting elements’ surfaces of the ANCF beam elements are parameterized by segmentation of integration over the contact patch. Numerical results investigate the accuracy, robustness and efficiency of the developed line-to-line contact formulation by comparing against a solid element type using commercial finite element code. According to the numerical results, the higher-order ANCF beam element’s solution is closer than the lower-order ANCF beam element’s in accordance with the reference solution provided by a solid element type using commercial finite element code ABAQUS. Furthermore, the higher-order beam element is found to be more efficient than the lower-order beam with respect to the numerical integration of the contact energy variation. Expectedly, the higher-order ANCF beam element is able to capture the cross-section deformation in a large deformation contact problem, while the lower-order element fails to exhibit such cross-sectional deformation.

Modeling the Dynamic Frictional Contact of Tires Using an Explicit Finite Element Code

2005 ◽  
Author(s):  
Tamer M. Wasfy ◽  
Michael J. Leamy
Keyword(s):  
Finite Element ◽  
Frictional Contact ◽  
Time Integration ◽  
Friction Model ◽  
Finite Element Code ◽  
Normal Contact ◽  
Explicit Finite Element ◽  
Beam Elements ◽  
Coulomb Friction Model ◽  
Stiffness And Damping

A time-accurate explicit time-integration finite element code is used to simulate the dynamic response of tires including tire/pavement and tire/rim frictional contact. Eight-node brick elements, which do not exhibit locking or spurious modes, are used to model the tire’s rubber. Those elements enable use of one element through the thickness for modeling the tire. The bead, tread and ply are modeled using truss or beam elements along the tire circumference and meridian directions with appropriate stiffness and damping properties. The tire wheel is modeled as a rigid cylinder. Normal contact between the tire and the wheel and between the tire and the pavement is modeled using the penalty technique. Friction is modeled using an asperity-based approximate Coulomb friction model.

Interlaminar stress analysis of multilayered composites based on the Hu-Washizu variational theorem

2017 ◽  
Vol 52 (13) ◽  
pp. 1765-1779 ◽  
Author(s):  
Wu Zhen ◽  
Chen Wanji
Keyword(s):  
Transverse Shear ◽  
Equilibrium Equation ◽  
Beam Element ◽  
Composite Beams ◽  
Higher Order ◽  
Shear Stresses ◽  
Interlaminar Stresses ◽  
Beam Elements ◽  
Transverse Shear Stresses ◽  
Derivatives Of

Up to date, accurate prediction of interlaminar stresses is still a challenging issue for two-node beam elements. The postprocessing approaches by integrating the three-dimensional equilibrium equation have to be used to obtain improved transverse shear stresses, whereas the equilibrium approach requires the first-order derivatives of in-plane stresses. In-plane stresses within two-node beam element are constant, so the first-derivatives of in-plane stresses are close to zero. Thus, two-node beam elements encounter difficulties for accurate prediction of transverse shear stresses by the constitutive equation or the equilibrium equation, so a robust two-node beam element is expected. A two-node beam element in terms of the global higher-order zig-zag model is firstly developed by employing the three-field Hu-Washizu mixed variational principle. By studying the effects of different boundary conditions, stacking sequence and loading on interlaminar stresses of multilayered composite beams, it is shown that the proposed two-node beam element yields more accurate results with lesser computational cost compared to various higher-order models. It is more important that accurate transverse shear stress has active impact on displacements and in-plane stresses of multilayered composite beams.

Nonlinear Stain of Variable Cross-Section Beam Element Based on Positional FEM

2012 ◽  
Vol 557-559 ◽  
pp. 2371-2374
Author(s):  
Lv Zhou Ma ◽  
Jian Liu ◽  
Xun Lin Diao ◽  
Xiao Dong Jia
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Cross Section ◽  
Beam Width ◽  
Variable Cross Section ◽  
Beam Element ◽  
Variable Cross ◽  
Nonlinear Fem ◽  
Beam Elements ◽  
Beam Depth

Based on positional finite element method, this paper attempts to find beam elements that can show the characteristics of the variable cross-section beam and can be practically applied. In this paper, the stain on a random point of the variable cross-section beam element is obtained when beam depth changes in a linear or quadratic parabolic way and beam width is fixed. The calculation is different and simpler than the classical nonlinear FEM.

Analysis of a PHWR Outlet Feeder Vibration Due to Random Turbulence-Induced Excitation

2007 ◽  
Author(s):  
Y. Han ◽  
V. P. Janzen ◽  
B. A. W. Smith ◽  
T. Godet
Keyword(s):  
Finite Element ◽  
Nuclear Reactor ◽  
Three Dimensional ◽  
Nuclear Industry ◽  
Finite Element Code ◽  
Two Phase ◽  
Accelerated Corrosion ◽  
Beam Elements ◽  
Vibration Tests ◽  
Flow Accelerated Corrosion

A nuclear-reactor feeder pipe has been analyzed to assess its vibration and stresses due to internal coolant random turbulence-induced excitation. The structural models were created from both isoparametric beam elements and continuum elements in the finite-element code H3DMAP, a general three-dimensional mechanics analysis package developed to solve a wide variety of problems encountered in the nuclear industry. The feeder was also modelled with beam elements in VIBIC, a finite-element code designed for the vibration assessment of beam-like structures. The excitation forces were based on recent experimental results obtained from piping-vibration tests that used two-phase air/water flow, performed at E´cole Polytechnique at Montreal. Feeder vibration levels, in terms of normalized response amplitude and velocity, and normalized vibratory stresses along the feeder are predicted for the as-designed feeder and for feeders thinned by flow-accelerated corrosion.

On Choice of Finite Element Type for the Filled Bodies in Umbilicals for Deep Water Application

2010 ◽  
Author(s):  
Naiquan Ye ◽  
Janne K. O̸. Gjo̸steen ◽  
Svein Sævik
Keyword(s):  
Finite Element ◽  
Contact Pressure ◽  
Cross Section ◽  
Contact Area ◽  
Direct Contact ◽  
Friction Stress ◽  
Shell Element ◽  
Beam Element ◽  
External Loading ◽  
Element Type

Filled bodies are often built into umbilicals to support other key components such as tubes and electric elements. These bodies play an important role in transferring the contact load between bodies when the structure is loaded. The geometrical profile can be arbitrary to fill the voids within the umbilical cross section and this causes difficulties with respect to implementation into a general finite element model. Common practice is to omit the filled bodies in cross section modeling by enabling direct contact between components. However, it has been found that the friction stress will be over estimated by this method and cause over-conservative fatigue calculations. This may be critical specially for deep water dynamic umbilicals and more accurate estimation of the friction stress is therefore needed. UFLEX2D is a non-linear finite element computer program for stress analysis of complex umbilical cross sections, see [3] and [5]. The model can handle arbitrary geometries wound in an arbitrary order including filled bodies. Contact elements are used to handle the contact between bodies due to external loading. Thin-wall shell elements were used to model the steel tubes while beam elements were used for the filled bodies in the earlier version of UFLEX2D. A beam element is treated as a rigid body incapable of deforming under external loading. It has been found that the formulation of the beam element for the filled bodies yields relatively large contact pressure for the neighboring element due to its rigidity. As a consequence, friction stress owing to the contact pressure is overestimated by the choice of the beam element for the filled bodies, however, it will be smaller than the direct contact modeling technique mentioned above. A new element type, i.e. a beam-shell element, has been developed to represent the filled bodies so as to improve the contact formulation between the filled bodies and the other surrounding structural elements. Unlike the beam element, the beam-shell element is able to deform, therefore the contact area is varying while the external load updates. The friction stress will be accordingly affected by the redistribution of the contact pressure on an updated contact area. The paper outlines how different implementations of the filled bodies will affect the distribution of the contact pressure as well as the friction stress under cyclical loading. The effect of the original contact area, as well as the development of the contact area is also a part of the study fot the three alternative models investigated.

Generalized Equations of Motion for the Dynamic Analysis of Elastic Mechanism Systems

1984 ◽  
Vol 106 (4) ◽  
pp. 243-248 ◽  
Author(s):  
D. A. Turcic ◽  
Ashok Midha
Keyword(s):  
Finite Element ◽  
High Speed ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Single Type ◽  
Generalized Equations ◽  
Element Analysis ◽  
Beam Elements ◽  
Elastic Mechanism ◽  
Element Type

Until recently, vibration effects have generally been neglected in the design of high-speed machines and mechanisms. This has been primarily due to the complexity of the mathematical analysis of mechanisms with elastic links. With the advent of high-speed computers and structural dynamics techniques, such as finite element analysis, this is no longer regarded as such a formidable task. To date, with few exceptions, the analysis of elastic mechanism systems have been limited to a single type of mechanism (i.e., a four-bar or slider-crank) modeled with a small number of simple finite elements (usually beam elements). This paper develops the generalized equations of motion for elastic mechanism systems by utilizing finite element theory. The derivation and final form of the equations of motion provide the capability to model a general two- or three-dimensional complex elastic mechanism, to include the nonlinear rigid-body and elastic motion coupling terms in a general representation, and to allow any finite element type to be utilized in the model. A discussion of a solution method, applications, as well as an experimental investigation of an elastic four-bar mechanism will be presented in subsequent publications.

Efficient Finite Element Modeling of Marine Riser Systems

2003 ◽  
Author(s):  
Yousun Li
Keyword(s):  
Finite Element ◽  
Finite Element Modeling ◽  
Higher Order ◽  
Wave Loads ◽  
Marine Riser ◽  
Time Duration ◽  
Lagrangian Multipliers ◽  
Cross Sectional ◽  
Element Modeling ◽  
Beam Elements

During the time domain simulation of a marine riser under stochastic wave loads, the small time increment and long time duration require efficiency in the finite element modeling. It is expected that the riser system can be modeled by larger elements, or fewer degrees of freedom. In this presentation, higher-order beam elements are introduced, with their tensions treated as Lagrangian multipliers. Each element can have zero, one, or two mid-nodes with varying geometry. Relatively few high-order elements can produce the same accuracy as a large number of conventional beam elements. Normally, the constraints have to be imposed to the element nodes. When a large number of constraints are involved, such as in the multitube analyses, the higher-order elements alone cannot reduce the number of elements. In the present methodology, this difficulty is also circumvented. A constraint is allowed to be applied to any location within an element. Even it is possible to model a lateral constraint sliding along a riser. The cross-sectional forces and moments can be output at any location along the riser. They are continuous within and across the elements by a special interpolation technique. These techniques help to enhance computational efficiency in the riser analyses, especially for the long-duration time simulation of the riser motions.

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