弹性力学中某些问题的探讨

Some Researches on Flasticity

本文从按应力求解半无限体边界上受均布法向载荷的问题得出:对于平面弹性应力边界问题,即便是单连体情形,应力分量满足了平衡衡分方程和相容方程,也满足了应力边界条件,但应力分量并不一定是正确解答。因此,经典弹性力学[1]、[2]关于平面弹性单连体应力边界问题中应力分量由平衡分方程、相容方程和应力边界条件完全确定的提法,应力分量σ_x、σ_y、τ_(xy)与弹性常数无关的结论具有局限性,必须加以修正。

This paper concludes that for stress boundary value problems in plane elasticity,even in case of unipath body,the stress compon- ents which satisfy oquilibrium differential oquations,the equation of compatibility and stress boundary condi tionts may not be the correct solutions for resolving the semi-infinite objebt subjected to uniform normal luad on the boundary on the basis of stress.Therefore,for stress boundary value problem of unipath boay in plane elasticity,the formulation in classic elasticity that strtss components are completely determined by equilibrium differential equations,the equation of compatibility and stress boundary conditions and the conclusion that the stress components σ_x,σ_y,τ_(xy),are not related to elastic constants have a certein limitation and hence must be revised.