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Axisymmetric thermal stress, TUBE7TS1

Problem description: A thick-wall tube is to be analyzed for the static and thermal loadings shown in picture. Calculate the temperature distribution, displacement and stresses under plane strain conditions providing the top and bottom faces of the tube are insulated. In this example T₁ and T₂ represent the wall temperatures (as if the surface coefficients were very high).

Mesh: Ten quadrilaterals--see appendix A.3.

Material properties: $\lambda=20$ W/mK, $\alpha=10^{-5}$ 1/K, $E=2\times 10^5$ MPa, $\nu=0.3$.

Boundary conditions: $T_1=100^\circ$C, $T_2=0^\circ$C.

Support: The plane strain condition is enforced by setting v=0 for all the nodes 1 to 53, where v is the displacement component parallel to the axis of revolution.

Static loading: The internal pressure p=287.47075 MPa.

Solution: The steady-state temperature field is first calculated following the procedures described in section III. The internal temperature $T_1=100^\circ$C is assigned to nodes 1, 2, 3 and the external temperature $T_2=0^\circ$C to nodes 50, 52, 53. Subsequently the internal pressure is added by indroducing the surface traction

$$q_n(\verb*\vert S1\vert)=-p=-287.47075\times10^6\,\mbox{[Pa]}$$

that acts on face S1 of element 1.
 

Execute from prompt:
>xrm2 tube7ts1.I1
>xrpd tube7ts1.IB
>xt2s tube7ts1
>rmd2 tube7ts1.I1
>rpd2 tube7ts1.I2
>srh2 tube7ts1.I3
>fefs tube7ts1.I4
>str2 tube7ts1.I5