具有凸缘加劲肋圆孔的应力分析

本文讨论无限平面内具有凸缘加劲肋圆孔的应力分析问题。所谓凸缘加劲肋系指孔周用型钢或其他形状的构件加劲,进行应力分析时难以将其视为板的一部分来处理的加劲肋。文中讨论了两种荷载情形:一为薄板在无限远点处应力σ_X(∞),σ_Y(∞)及τ_XY(∞)的作用;另一为薄板受线性应力的作用。分析方法是:将加劲肋视为圆形杆件,把加劲肋与薄板间相互作用之径向力q₀(θ)及切向力t₀(θ)表示成三角级数,分别求出加劲肋轴线之位移与具有圆孔薄板孔周之位移,利用加劲肋与薄板孔周变形一致的变形协调条件,确定径向力q₀(θ)及切向力t₀(θ),从而得到加劲肋及薄板之位移和内力的算式。

Stress Analysts of Plates with a Circular Hole Reinforced by Flange Reinforcing Member

This paper deals with the problem of stress analysis of plates with a circular hole reinforced by flange reinforcing member.The so called flange reinforcing member here means that the reinforcing member is built up by setting shapes or bars with any section shape on both sides of the plates along the edge of the hole.Two cases of external loads are considered.In one case the external loads are stressesσ_X(∞),σ_Y(∞),and τ_XY(∞) acting at infinite point of the plate,and in the other the external loads are linear distributed normal stresses.The procedure of solving the problems mentioned above consists of three steps.Firstly,the reinforcing member is taken out from the plates and considered to be a circular bar being solved to determine its deformation under the action of radial force q₀(θ) and tangential force t₀(θ) which are forces acting upon each other between reinforcing member and plate.Secondly,the displacements of plate with a circular hole under the action of q₀(θ) and t₀(θ) and external loads are determined.Finally,forces q₀(θ) and t₀(θ) are obtained by the compatibility of deformations between reinforcing member and plate.Then the internal forces and displacements of reinforcing member and plate are deduced from q₀(θ) and t₀(θ) obtained.