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Using the penalty method

: Problem description: Consider a creep analysis of the thick-wall tube shown. Compute the relaxation history of stress under plane strain conditions using i) the axisymmetric 8-node elements and ii) the 3D elements with the symmetry condition enforced by the penalty method. Compare the results.

$\begin{figure} \centering\hspace{0pt} \epsfclipon\epsfxsize=6cm\epsffile{tubec1.ps} \end{figure}$

Mesh: Use the following element types:
ITE=7--see appendix A.3, ten quadrilaterals
ITE=56--see appendix B.5, ten hexahedra.

Material properties: $\alpha=10^{-5}$ 1/K, $E=2\times 10^5$ MPa, $\nu=0.3$ .


Norton's law:

Support: Plane strain condition.

Loading: The internal pressure p=100 MPa, $T=600^\circ$ C.

Solution: Material description is included in the input files as in example VI.2, i.e.

$\begin{displaymath}\dot\epsilon_c=a_1 +a_2\sigma_e+a_3\sigma_e^2+a_4\sigma_e^3 \end{displaymath}$

where

$\begin{displaymath}a_1=a_2=a_3=0~,~~~a_4=2\times 10^{-28}\,\mbox{1/h} \end{displaymath}$

The process of relaxation is studied under steady-state conditions (p,T) for 10 hours with the elastic solution being the initial stress state. It should be noted that the automatic integration step control causes the time increments to increase as relaxation proceeds--see the OL protocols.