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The vector Signorini contact set and variational inequality

Definition

Let $ψ \in C (Γ_{C}; R)$ satisfy $ψ \leq 0$ . Define the unilateral frictionless contact set $K : = {v \in V : T_{C} v \cdot n \geq ψ for arclength-almost every point of Γ_{C}} .$ Given the elasticity form $a$ and bounded load $F$ of Small-strain elasticity with a frictionless contact gap, the contact variational inequality is to find $u \in K$ such that $a (u, v - u) \geq F (v - u) for every v \in K .$ The set $K$ is nonempty, closed and convex by The Signorini contact set is nonempty, closed, and convex ↗.

Remarks

The published scalar obstacle definition has a full-zero-boundary $H_{0}^{1}$ interface. This item instead defines the vector boundary-gap set on the stated partial-trace polygon; the scalar interface is used only by the one-dimensional example on the companion page.

Depends on

Used by

Dependency tree · two levels

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Sources

John Andersson, The Obstacle Problem, complete 52-page KTH lecture notes (standard reference, not scraped)
Richard S. Falk, Error Estimates for the Approximation of a Class of Variational Inequalities, complete 10-page paper (standard reference, not scraped)