# DIRECT COMPUTATION OF STRESSES IN PLANAR LINEARIZED ELASTICITY

@article{Ciarlet2009DIRECTCO, title={DIRECT COMPUTATION OF STRESSES IN PLANAR LINEARIZED ELASTICITY}, author={Philippe G. Ciarlet and Patrick Ciarlet}, journal={Mathematical Models and Methods in Applied Sciences}, year={2009}, volume={19}, pages={1043-1064} }

Given a simply-connected domain Ω in ℝ2, consider a linearly elastic body with Ω as its reference configuration, and define the Hilbert space E(Ω)={e(eαβ) ∈ L2s (Ω) ∂11e22- 2∂12e12}+∂22e11 = 0 in H-2(Ω)}. Then we recently showed that the associated pure traction problem is equivalent to finding a 2 × 2 matrix field = (∈αβ) ∈E(Ω) that satisfies j(∈)= inf e∈E(Ω) j(e), where j(e) = 1/2 ∫Ω Aαβστ eστ eαβ dx - l(e), where (A αβστ ) is the elasticity tensor, and l is a continuous linear form over E… Expand

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