Abstract
When exposed to cyclic quasi-static loading, elastic bodies in contact may develop a favourable condition where slip ceases after a few cycles, an occurrence commonly known as frictional shakedown. If the amplitude of the cyclic load is greater than a so-called shakedown limit, shakedown cannot occur. In this review paper, the validity of shakedown theorems in the context of conforming contacts with à la Coulomb friction is first discussed. Then, an optimisation method for determining the shakedown limit of elastic discrete three-dimensional systems is reviewed. Finally, an incremental Gauss–Seidel algorithm, extended to three-dimensional systems, is here illustrated in details for the first time. The algorithm allows us to describe the transient response of normal-tangential coupled systems under a given cyclic loading scenario, and to determine their possible shakedown depending on the initial conditions. An example concerning a discrete conforming contact problem, where either coupling or uncoupling conditions can be imposed, is illustrated.
Original language | English |
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Article number | 111470 |
Journal | International Journal of Solids and Structures |
Volume | 241 |
DOIs | |
Publication status | Published - 1 Apr 2022 |
Keywords
- Contact
- Friction
- Incremental analysis
- Limit analysis
- Linear programming
- Shakedown
ASJC Scopus subject areas
- Condensed Matter Physics
- Mechanics of Materials
- Mechanical Engineering
- Applied Mathematics
- General Materials Science
- Modelling and Simulation