Joint modeling techniques using finite element analysis
Kazunori Shinohara 1 and Ryoji Takaki 211

JAXA's Engineering Digital Innovation Center (JEDI), Japan Aerospace Exploration Agency (JAXA), Japan2
Institute of Space and Astronautical Science (ISAS), Japan Aerospace Exploration Agency (JAXA), Japan

Introduction

This year, Failures due to joints between parts have becomeapparent, as high-precision equipment of space structures aredemanded. Various contaminants in the air on the ground adhere
to the contacting parts of metal surfaces. These contaminants, inturn, act as a lubricant, thereby reducing the coefficient offriction. Therefore, the frictional force on the contact surface isnaturally decreased on the ground. Space, however, is a vacuum,and because metal contamination does not occur in space, thefriction coefficient between the metals in space increases toabout 100 times that on the ground. In space, the friction force
causes incomplete movement at joints because of the lack oflubrication.
In this study, to develop the high-precision space structure,
we construct a simulation based on contact-friction finite
element analysis (FEM) using Advance/FrontSTR [1] [2] [3].
The accuracy of the calculated results using Advance/FrontSTR
is verified by comparison with the contact force in [4]. Using thereliable simulation, the non-reversible behavior by contact
friction is verified by comparison to the hysteresis of thedisplacement in the literature.

2

Computer model for contact force
A computer model consists of a reinforcing ring and circularcylinder that are in contact with each other. The internal
diameter and the outer diameter of the reinforcing ring are99.825 (mm) and 200.0 (mm), respectively. The diameter of thecircular cylinder is 100.0 (mm). With respect to the radial
direction in the initial condition, the distance of interference
between the reinforcing ring and the circular cylinder is δ =0.175 (mm). The number of nodes and the number of elements
are 10159 and 8360, respectively. The element type is applied to
the first order hexahedral element. The material properties are
set to a Young’s modulus of 210.0 (GPa) and a Poisson ratio of0.3. The symmetry condition is set as the boundary conditions.

Algorithm of Contact-Friction Analysis

In this study, the Advance/FrontSTR and JAXA
supercomputer system (JSS) are applied to solve the contactfriction problem. Advance/FrontSTR was jointly-developed aspart of a government project (Ministry of Education, Culture,Sports, Science and Technology) by the University of Tokyo(Prof. Hiroshi Okuda) and Advance Soft Co. Ltd. Presently,
Advance Soft Co. Ltd. provides commercial versions of thesoftware and is responsible for upgrades. The software cancalculate the geometric non-linearity, the material non-linearity,and the contact non-linearity. The JSS consists of a massively
parallel supercomputing system, a storage system, a large-scale
shared memory system, and a remote access system. We
attempted to realize a large-scale FEM analysis of the highefficient parallel supercomputing system by Advance/FrontSTRand JSS. The increments of displacements are unknown
variables at the nodes in the FEM model. The displacement canbe obtained by the increments of displacements. The strain canbe subsequently calculated by the displacement. Then, the stresscan be calculated by the stress-strain relationship.
Advance/REVOCAP is applied for the pre-processing and thepost-processing. Advance/REVOCAP can easily make FEM
meshes, set calculation conditions, and visualize results fromAdvance/FrontSTR [1] [2].

3

3.1

Calculated Results of Contact-Friction Analysis

To verify the distribution of the contact force and theirreversible behavior, the contact problem in 3D FEM analysis issolved using Advance/FrontSTR.

Figure 1 Computer model (by Advance/REVOCAP [1]).
3.2

Contact pressure distribution
The horizontal and vertical axes of Fig. 2 represent thenormalized distance and the normalized stress with respect tothe z axis, respectively. The distance in Fig. 2 represents thelength from the node N1(0,0,99.825) to the node N2(50,0,99.825)
and is located on the contact surface of the reinforcing ring. The
four curves represent the distribution of the contact force withthe friction (the coefficient of friction is 0.2) in [4], thedistribution of the contact force without the friction in [4], thedistribution of the contact force with the friction (the coefficientof friction is 0.2) using Advance/FrontSTR, and the distributionof the contact force without the friction using
Advance/FrontSTR. Using Advance/FrontSTR, the stress
distribution in the frictionless case is almost in agreement withthat in the friction case. Compared to the friction case in [4], thenormalized stress of the frictionless case in [4] sharply increases
around the node N2(50,0,99.825). It is considered that thisdifference depends on the friction computational model.
Advance/FrontSTR evaluates the occurrence of the friction on
the contact surface by the relative displacement between two
nodes located on both sides of the contact surface. In classicalfriction theory (coulomb friction), the friction (= coefficient offriction × surface force) occurs on the contact surface, even if
small relative displacement occurs. However, in the numericalalgorithm, the steepest friction forces cause numerical error andnumerical instability. To obtain a stable solution numerically,
the friction force should increase gradually according to theincrement of time when a small relative displacement occurs.
When a large relative displacement on the contact surface occurs,
the maximum frictional force (friction coefficient × surfaceforces) is better seen on the contact surface. In the literature [4],the coulomb friction is implemented in the computer model. In
Advance/FrontSTR, to obtain numerical stabilization, a small
force below the friction force occurs with respect to the small
relative displacement. It may be impossible for theAdvance/FrontSTR to reproduce the difference between theresults of the friction and frictionless cases for small relativedisplacements.

(hysteresis), which cannot be recovered to the initialdisplacement, the displacement at point A is larger than that at
point B.
3.5

Hysteresis of displacement
The vertical and horizontal axes in Fig. 4 represent the force
and the displacement at point A with respect to the y direction(radial direction), respectively. Using Advance/FrontSTR, thedisplacements with friction and without friction are calculated.
Before loading, the displacement at point A increases by theinterference between structure A and structure B. After thesedeformations of both structure A and structure B, a force (35kN) is applied at structure A. When the friction coefficient is set
to 0.0 (frictionless case), the displacement at point A returns to
the initial position before application of the loading force when
the force is removed. When the friction coefficient is set to 0.2,
the displacement at point A cannot recover to the initial positionby the same operation. This phenomenon is known as
irreversible behaviors. Compared to the irreversible behaviors in
the literature [4], hysteresis displacement by Advance/FrontSTR
is almost in agreement. The curves between the force and thedisplacement by Advance/FrontSTR do not agree with those in
the literature [4]. The contact stiffness cannot be sufficiently
evaluated because the contact stiffness depends on the contact
state identified in various unknown parameters.

Figure 2 Stress distribution on contact surface.

3.3
Computer model to reproduce irreversible
behaviors
We make the one-quarter FEM model. The structures A andB contact each other. The initial interference with respect to theradial direction is δ = 0.0875 (mm). The number of nodes andelements are set to 390 and 156, respectively. The element typeis applied to the first order hexahedral element. The material
properties are set to a Young’s modulus of 210.0 (GPa) and aPoisson ratio of 0.3, respectively.

Figure 4 Hysteresis of displacement.

4Conclusion

To verify the accuracy of the contact-friction analysis for astructure containing interference between two circular rings, thedistribution of the contact force by Advance/FrontSTR wascompared to that in the literature. In the literature, the radiuscontact force is minimized at the center of the contact force. The
contact force increases sharply as it nears the edge of the contact
force. The results by Advance/FrontSTR are qualitatively inagreement with the results in the literature. The irreversible
behavior can also be reproduced by Advance/FrontSTR.
Figure 3 Contour of displacement difference between theinitial shape and the deformed shape (coefficient of contact
friction is 0.2) (by Advance/REVOCAP [1]).
3.4

Displacement contour map
The displacement contour map under a loading force isshown in Fig. 3. The red area and the blue area represent thelarge deformation and the small deformation, respectively. Theinterference between structure A and structure B causes thedeformation. Subsequently, the force is loaded at structure A.
Then, the force is removed. In the displacement residual

References[1][2]

AdvanceSoft. Co., Ltd., http://www.advancesoft.jp/.

[3]
[4]

FrontISTR, http://www.ciss.iis.u-tokyo.ac.jp/dl/.

[5]K.J. Bathe, Finite Element Procedures, New Jersey, Prentice Hall, 1995.

X. Yuan, “Theory reference on nonlinear analysis of Advance/FrontSTR
Ver.3.0,” Advance Simulation, vol. 4, pp. 6–59, 2010.
N. Okamoto and M. Nakazawa, “Finite element incremental contact analysis
with various frictional conditions,” International Journal for Numerical
Methods in Engineering, vol. 14, pp. 337–357, 1979.