Boundary Value Problems of Elasticity with Unilateral Constraints

Gaetano Fichera (1)

1 University of Rome "Tor Vergeta"

In the preceding article "Existence Theorems in Elasticity", which hence forth will be cited as E.T.E., I have treated boundary value problems of Elasticity in the case when the side conditions to be associated with the differential equations of equilibrium correspond to bilateral constraints imposed upon the elastic body. In this article I will treat the analytical problems which arise when unilateral constraints are imposed. In Sect. 6 of E.T.E. it is shown that the "bilateral problems", as far as the existence theory is concerned, are founded on the solution of a system of equations of the following type $$B(u, v) =F(v),\quad u\in V,\quad \forall v\in V$$ where $B(u, v)$ is a bounded bilinear form defined in $H\times H$ ($H$=Hilbert space), $F$ is a linear functional and $V$ is a closed linear subspace of $H$. These equations, in the case when $B$ is symmetric and the space $H$ real, are easily obtained by imposing upon the energy functional $J(v) = \frac{1}{2} B(v, v)-F(v)$ the condition of attaining a minimum on $V$.

Domaines: Mécanique des structures [physics.class-ph]

Gaetano Fichera. Boundary Value Problems of Elasticity with Unilateral Constraints. Linear Theories of Elasticity and Thermoelasticity, Springer Berlin Heidelberg, pp.391-424, 1973, ⟨10.1007/978-3-662-39776-3_4⟩. ⟨hal-02183016⟩