Ponter, Alan R. S.; Chen, H. F.; Ciavarella, M.; Specchia, G. Shakedown analyses for rolling and sliding contact problems. (English) Zbl 1120.74668 Int. J. Solids Struct. 43, No. 14-15, 4201-4219 (2006). Summary: There is a range of problems where repeated rolling and sliding contact occurs over a half space of an elastic-perfectly plastic material. For such problems shakedown and limit analysis provide significant advantages over other forms of analysis when a global understanding of deformation behaviour is required. In this paper, a recently developed numerical upper bound method, the Linear Matching Method (LMM), for shakedown analyses is applied to the solution of a problem previously considered by Ponter et al. [Ponter, A.R.S., Hearle, A.D., Johnson, K.L., 1985. J. Mech. Phys. Solids 33 (4), 339-362] for a moving Hertzian contact, with sliding friction. This semi-analytic solution is an upper bound based on certain specific kinematic assumptions. We show that the Ponter, Hearle and Johnson solution is a reasonable approximate solution for a circular contact area but is less accurate for an elliptic contact area. For an elliptic contact area LLM solutions converge to the line contact solution. The effect of the non-coincidence of the direction of travel and slide is also investigated. Cited in 2 Documents MSC: 74M15 Contact in solid mechanics 74C05 Small-strain, rate-independent theories of plasticity (including rigid-plastic and elasto-plastic materials) Keywords:Plasticity; limit loads; shakedown; Hertzian contact PDFBibTeX XMLCite \textit{A. R. S. Ponter} et al., Int. J. Solids Struct. 43, No. 14--15, 4201--4219 (2006; Zbl 1120.74668) Full Text: DOI Link