An Enhanced Theory of Bending of Plates
Ilie-Radu Mitric, Christian Constanda · Birkhäuser Boston eBooks · 2002
Let S be a domain in ℝ2 bounded by a simple closed C 2-curve ∂S,, and let h 0= const be such that $$0 < {h_0} \ll $$ diam S. By a thin plate we understand an elastic body that occupies the region $$ \overline {S \times \left[ { - {h_0}/2,{h_0}/2} \right]} $$ ; here h 0 is called the plate thickness. We denote by $$ x = \left( {{x_1},{x_2}} \right) $$ a generic point in ℝ2 and write ( $$ {\partial_x} = \left( {{\partial_1},{\partial_2}} \right) $$ ), where ( $$ {\partial_{\alpha }} = \partial /\partial {x_{\alpha }},\alpha = 1,2 $$ ). Also, we denote by S + and S - the domains interior and exterior to ∂S, respectively.