Abstract
Frictional contact problems in linear elasticity are considered in this paper. The contact constraint is imposed in the weak sense using the fixed point method, which leads to a variational equation problem. For solving such a nonlinear variational problem, we study two projection methods using different self-adaptive rules. Based on the self-adaptive projection method, we propose a modified self-adaptive rule which is more effective to update the parameter. The methods can be implemented easily in conjunction with the boundary element method for the solution. Numerical experiments are reported to illustrate theoretical results.
Highlights
Frictional contact phenomena among deformable bodies or between deformable and rigid bodies abound in industry and daily life; they play an important role in many fields of solid mechanics [1, 2]
We study the numerical solutions of frictional contact problems using the projection method with two self-adaptive rules for the parameter
6 Conclusion This paper provides the analysis of two projection methods for the solution of frictional contact problems
Summary
Frictional contact phenomena among deformable bodies or between deformable and rigid bodies abound in industry and daily life; they play an important role in many fields of solid mechanics [1, 2]. We study the numerical solutions of frictional contact problems using the projection method with two self-adaptive rules for the parameter. ⎧ ⎨a(u, v) – ΓC σ t · vt dsx = L(v) ∀v ∈ V, ⎩σ t + ρut = σ t + ρut – ωRρ (ut, σ t) on ΓC Using this equivalent formulation, we can suggest a self-adaptive projection method for the frictional contact problem . We obtain the projection method for the numerical solution of the frictional contact problem In this method, there are two parameters ω ∈ (0, 2) and ρ > 0 which affect the convergence speed. We present the following self-adaptive projection method for the frictional contact problem. For a given constant integer cmax > 0, it follows that the sequence {sk} satisfies Lemma 3.1 automatically
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