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Simple contact, CUBE55K1

: Problem description: Consider the two bodies shown in figure acted on by uniformly distributed pressure p. Perform a contact analysis and calculate the pressure distribution over the contact plane.

$\begin{figure} \centering\hspace{0pt} \epsfclipon\epsfxsize=6cm\epsffile{cube55k1.ps} \end{figure}$

Mesh: Two pentahedra, one hexahedron--see appendix B.6.

Material properties: $E=2\times 10^5$ MPa, $\nu=0.3$ .

Support: None. Due to symmetry only one quarter of the object is discretized, which gives rise to symmetry planes x=0 and y=0. In addition the pressure acting on the bottom face z=-1 is replaced with the surface traction indroduced by appropriate boundary conditions. The top cube (elm. 3) is suspended on regularization springs of small stiffness.


u=v=w=0 node:	 1               
w=0 nodes: 	 2 3 17 18 19 20 21                     
u=w=0 nodes: 	 4                                      
u=0 nodes: 	 5 8 9 12 13 16 20 22 25 29 34 35 38 42 
v=0 nodes: 	 5 6 9 10 13 14 17 22 23 26 31 35 36 39 


 [N/m]            nodes:                  9 10 11 12
 
Specification of contact surfaces.                                                 
Contact surface A 		 element faces: 	 1 2 S5               
Contact surface B 		 element face: 		   3 S1

Loading: p=-10MPa.

Solution: The contact search is performed at external Gauss integration points accessed by FE algorithm. Contact constraints are enforced by the penalty method. Thus, the unknown contact pressure p_IG is approximated by the penalty function as

$\begin{displaymath}p_{IG}=\xi\pi_{IG} \end{displaymath}$

where $\xi$ denotes the value of penalty parameter and $\pi_{IG}$ is the penetration determined at the Gauss integration point IG. The essential part of the analysis is a good choice of the penalty parameter $\xi$ , whose value can be estimated from the stiffness of a cubic element

$\begin{displaymath}\xi=f_s\frac{K}{\sqrt{\det{\bf J}^S}} \end{displaymath}$

where f_s is the inverse of relative displacement error, K the bulk modulus and ${\bf J}^S$ the surface Jacobian. For example, if we require the relative displacement error to be 0.01 (i.e the ratio of penetration to the displacement of the contact plane should not exceed 0.01), we set the penalty parameter to $\xi=10^{13}{\rm [N/m^3]}$ .

Execute from prompt:
>rmd3 cube55k1.I1
>rpd3 cube55k1.I2
>srh3 cube55k1.I3
>fefs cube55k1.I4
>hpp3 cube55k1.IP
>hpls cube55k1.IL
>str3 cube55k1.I5

Next: INPUT Up: Contact Problems Previous: Contact Problems