Abstract
Shakedown and ratcheting behaviour is derived for uniaxial primary membrane and thermal bending stresses both cycling strictly in-phase. The complete analytic solution for perfect plasticity is presented, including the shakedown/ratcheting diagram and the ratchet strains or cyclic plastic strains where relevant. This cyclic loading is shown to be considerably more benign than that of the original Bree problem in which the primary membrane stress does not cycle.
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