Haslinger, J.; Panagiotopoulos, P. D. The reciprocal variational approach to the Signorini problem with friction. Approximation results. (English) Zbl 0547.73096 Proc. R. Soc. Edinb., Sect. A 98, 365-383 (1984). The authors study the plane and linear-elastic contact problem with given friction on a straight-line contact segment. They derive a ”primitive variational formulation” (in terms of the displacements), a ”mixed variational formulation” (in terms of the displacements and contact stresses) and a ”reciprocal variational formulation” (in terms of the contact stresses alone) and prove the existence and uniqueness of the solution. Then they discuss the resulting finite element approximations and certain convergence results. Further the more realistic case of friction obeying Coulomb’s law is treated using the contact problem with given friction as an auxiliary problem. At last numerical results are presented for the cases ”without friction”, ”with Coulomb’s friction” and with ”given friction”. Reviewer: H.Bufler Cited in 25 Documents MSC: 74A55 Theories of friction (tribology) 74M15 Contact in solid mechanics 74S99 Numerical and other methods in solid mechanics 74S30 Other numerical methods in solid mechanics (MSC2010) 65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs 49J40 Variational inequalities Keywords:Signorini problem; plane and linear-elastic contact problem; given friction; straight-line contact segment; primitive variational formulation; mixed variational formulation; reciprocal variational formulation; existence; uniqueness; finite element approximations; convergence results; Coulomb’s law; without friction PDFBibTeX XMLCite \textit{J. Haslinger} and \textit{P. D. Panagiotopoulos}, Proc. R. Soc. Edinb., Sect. A, Math. 98, 365--383 (1984; Zbl 0547.73096) Full Text: DOI References: [1] DOI: 10.1002/mma.1670050127 · Zbl 0525.73130 · doi:10.1002/mma.1670050127 [2] Hlavaček, Apl. Mat. 22 pp 215– (1977) [3] Lions, Problems aux limites non homogenes et applications, 1 (1968) [4] DOI: 10.1016/0022-247X(82)90257-8 · Zbl 0486.73099 · doi:10.1016/0022-247X(82)90257-8 [5] Glowinski, Analyse numéerique des inéquations variationnelles (1976) [6] Oden, TICOM Report pp 79– (1979) [7] Duvaut, Les inéquations en Mécanique et en Physique (1972) [8] Sayegh, ASCE 100 pp 49– (1974) [9] DOI: 10.1016/0020-7683(80)90100-6 · Zbl 0451.73094 · doi:10.1016/0020-7683(80)90100-6 [10] Panagiotopoulos, Arch. 44 pp 421– (1975) [11] Nečas, Boll. Un. Mat. Ital. 17B pp 796– (1980) [12] Ekeland, Analyse convex et problèmes variationnelles (1974) · Zbl 0281.49001 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.