A Cauchy like problem in plane elasticity - Ang, Dang Dinh; Dung, Nguyen (Vietnam Journal of Mechanics, 2007)
Let \(Ω \) be a bounded domain in the plane, representing an elastic body. Let \(Γ_0 \) be a portion of the boundary \(Γ\) of \(Ω \), \(Γ_0 \) being assumed to be paralled to the \(x\)-axis. It is proposed to determine the stress field in \(Ω \) from the displacements and surface stresses given on \(Γ_0 \). Under the assumption of plane stress, it is shown that \(u_x + u_y\) is a harmonic function. An Airy stress function is introduced, from which the stress field is computed.