Shakedown at finite displacements; A note on Melan's theorem

Abstract

This paper outlines an elastoplastic design approach for beam and plate structures subjected to transverse pressure loads and thermal stresses. The purpose of this study is to overcome the limitations of yield-limited designs by exploiting plastic design theorems. The feasible design space of a clamped beam/plate structure subjected to combined thermomechanical loads is explored considering shakedown (stabilized plasticity) as the design criteria. Analytic and numerical solutions are developed that show that allowing shakedown to occur extends the design space and acceptable loading range. In addition, the structures considered here are also prone to buckling due to thermal loads. In this work, interactions between thermal buckling and shakedown are investigated using numerical parametric studies. It is found that buckling enhances elastoplastic shakedown performance which expands the feasible design domain significantly when high aspect ratio beams are considered. In particular it is shown that the enhancement is 2–4 times for the range of aspect ratios examined.