10.2 LAME’S THEOREM
Lame’s theorem gives the solution to thick cylinder problem. The theorem is based on the following assumptions:
- Material of the cylinder is homogeneous and isotropic.
- Plane sections of the cylinder perpendicular to the longitudinal axis remain plane under the pressure.
The second assumption implies that the longitudinal strain is same at all points, i.e., the strain is independent of the radius.
Let us consider a thick cylinder subjected to internal and external pressures (Figure 10.1(a)).
Fig. 10.1 Stress condition in thick cylinder.
Let an annular ring of the cylinder (Figure 10.1(b)) with internal radius r, thickness ...
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