Analytic Solution for an Enhanced Theory of Bending of Plates

Abstract

Let S be a domain in ℝ² bounded by a simple closed C ²-curve ∂S, and let h ₀ = const be such that 0 < h ₀ ≪ diam S. By a thin plate we understand an elastic body that occupies the region $\bar S x [ - h_0 /2,h_0 /2];$; here h ₀ is called the plate thickness. We denote by x = (x ₁, x ₂) a generic point in ℝ², and write z = x ₁ + ix ₂ ∈ ℂ, ∂_α = ∂/∂x _α, α = 1,2, and ∂ _z = ∂/∂z. Also, we denote by S ⁺ and S ^- the domains interior and exterior to ∂S, respectively.