Tamtam Proceedings - lamsin

critical state of unilateral buckling 553Figure 1. A unit length beam is in presence of an obstacle.Furthermore, for the sake of simplicity, the beam is supposed to have a Young’s modulusE and a thickness 2ε such that 2 3 Eε3 = 1.Let n ∈ N ∗ , h = 1 n and x i = i.h, for 0 ≤ i ≤ n, be a regular subdivision of the interval[0, 1]. A continuous differentiable finite element (Hermite’s finite element) is used, so thatthe space W is approximated by the 2n − 1 finite dimensional subspaceW h = {v h ∈ C 1 [0, 1] : v h[xi,x i+1] ∈ R 3 [X] and v h (0) = v h ( 1 2 ) = v h(1) = 0}.We likewise approximate the convex setK = {v ∈ W : v(x) ≤ 0, a ≤ x ≤ b} by K h = {v h ∈ W h : v h (x i ) ≤ 0, k ≤ i ≤ l}and obtain the following results:Figure 2. The buckling mode of the beam in the absence and in the presence of theobstacle respectively.TAMTAM –Tunis– 2005