内面近似円形, 外面正多角形なる厚肉管が内圧を受ける場合の応力分布

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(This Paper was read before the Meeting of the Japan Society of Mechanical Engineers and Applied Mechanics held in Nagoya on the 26th. Nov. 1945) The solution for an internal pressure acting at a circular hole in the center of a regular polygonal tube can be obtained from the following complex function z=C∫ (1-t^n)^n^^2 dt, z=x+iy, t=ρ (cos θ+i sin θ) using the orthogonal curvilinear coordinate. The differential equation for Airy's stress function F in this case becomes [numerical formula] where h^2=c^<-2> (1-2ρ^ncosnθ+ρ^<2n>) n^^2 The boundary conditions for this problem are σ_ρ=0,τ_<ρθ>=0 for ρ=1 σ_ρ=-p, τ_<ρθ>=0 for ρ=ρ_0,where σ_ρ, σ_θ, represent a normal stress acting a curve of ρ=const. and θ=const. on the x, y plane, and τ_<ρθ> a tangential stress acting along the both curves. Then σ_ρ, σ_θ, τ_<ρθ> and F can be write in the following form : [numerical formula] where A_o, A_s, B_s, C_o, C_s and D_s are constants and they are determined by the boundary conditions. The details are descibed in the original paper.
一般社団法人日本機械学会の論文
1952-01-20