The analysis of elastic, perfectly plastic compressible materials under the assumption of plane strain is a statically indeterminate problem. In the present paper, by introducing a perturbation parameter ε = 1/2−ν, the problem can be changed into a series of statically determinate ones. The first-order approximation yields the solution for the incompressible material. In order to show the details of this method, the second-order approximation for the problem of the thick-walled cylinder under internal pressure is obtained.

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