Analytic Solution for an Enhanced Theory of Bending of Plates
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.
KeywordsDisplacement Boundary Finite Energy Vertical Translation Domain Interior Rigid Displacement
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