A quadratic programming formulation for the solution of layered elastic contact problems: Example applications and experimental validation

Abstract

The development of a quadratic programming formulation for the solution of layered elastic contact problems in the presence of friction is presented in this paper. Conveyor belts, tyred wheels, composite cylinders, and conrod bearings, are classical examples of systems which can be studied using the efficient numerical methodology proposed here. In this type of mechanical assembly, micro-slip between the mating surfaces often occurs and may eventually lead to system failure. Accurately capturing the evolution of slip and stick areas using a computationally inexpensive procedure (as an alternative to full finite element analysis) is therefore key to preventing these failures and to improving the design of various engineering components. The proposed approach is first tested and validated against classical marching-in-time solutions for two-dimensional layered systems in the presence of both static and moving loads. Results are then extended to demonstrate the feasibility of the technique to study systems with multiple slip regions and to solve rolling contact problems of practical interest. Finally, the numerical methodology is successfully applied to the prediction of frictional creep of tyred cylinders. Experimental corroboration has been obtained by testing tyred discs.

Contact mechanics of frictional lap joints

“…This is similar to what is observed for the equivalent Cattaneo–Mindlin contact problem, 11 and is typical of systems which are inherently uncoupled. The reader should refer to the previous studies 12–14 for a more in-depth discussion on frictional shakedown.…”

Non-linear programming in shakedown analysis with plasticity and friction

“…The illustrative example here considered is not aimed at any technical application but is believed to be suitable to show all the key features involved in frictional problems with plasticity. Other meaningful examples in the literature investigated the shakedown occurrence in specific mechanical components (see, for instance, the frictional slipping effects in pin-loaded lugs studied by Antoni, 2014 or the layered contact problem in Reina et al, 2011), though plasticity was not taken into account.…”

The effect of friction on the stamp’s flat sole coming off the sole base

“…На теперішній час для чисельного розв'язання контактних задач теорії пружності з урахуванням тертя зазвичай використовуються методи, які базуються на варіаційній постановці задачі [1,2]. Існують також методи зведення контактних задач з урахуванням тертя до операторних рівнянь, які розв'язуються чисельно спеці-альними методами [3][4][5][6].…”