On the Two-step Iterative Method of Solving Frictional Contact Problems in Elasticity

Unilateral contact problems in elasticity (Duvaut and Lions, 1976) have been extensively studied in the last two decades (Andersson and Klarbring, 2001; Angelov and Liolios, 2004; Cǎpǎtinǎ and Cocu, 1991; Cocu, 1984; Demkowicz and Oden, 1982; Duvaut and Lions, 1976; Hlavaček et al., 1988; Kikuchi and Oden, 1988; Klarbring et al., 1989; Lee and Oden, 1993a,1993b; Ne čas et al., 1980; Oden and Carey, 1984; Panagiotopoulos, 1975; 1985; Rabier and Oden, 1987; 1988). Special attention has been paid to static contact problems with friction, describing one step (increment) in the actual quasistatic processes (Lee and Oden, 1993a; Oden and Carey, 1984). Since the problems are nonlinear, existence and uniqueness results were obtained using fixed point methods (Andersson and Klarbring, 2001; Cǎpǎtinǎ and Cocu, 1991; Cocu, 1984; Demkowicz and Oden, 1982; Kikuchi and Oden, 1988; Klarbring et al., 1989; Ne čas et al., 1980). Based on these methods, and the finite element method, various algorithms were proposed for solving the resulting finite dimensional systems of nonlinear equations (Angelov and Liolios, 2004; Cǎpǎtinǎ and Cocu, 1991; Glowinski, 1984; Hlavaček et al., 1988; Kikuchi and Oden, 1988; Lee and Oden, 1993a; 1993b).