曲梁剪应力的积分方程解

直接对曲梁剪应力的积分方程求解 ,导出了曲梁剪应力和径向应力的计算公式 .这些公式不仅满足平衡方程 ,而且满足曲梁上、下表面处力的边界条件 .将该理论用于研究悬臂曲梁在自由端受集中力作用的情况 ,计算结果表明 ,与其他采用附加假设的近似解相比 ,据此得到的应力解具有很高精度 ,同弹性理论解和有限元解非常接近 .

Solution of Integral Equation for Shearing Stresses in Curved Beams

The shearing-stress formula in curved beams can be derived by solving directly an integral equation,and the formula for radial stresses is also presented in this paper.These formulae satisfy not only the equilibrium equations but also the static boundary conditions at the top and bottom surfaces of the beams.The present analysis will be used to investigate the shearing and radial stresses of a cantilevered curved beam,which is loaded by a concentrated force at its free end.The comparison between the results of theory of elasticity and the numerical results obtained by solving the present equations shows excellent agreement,and this agreement is much better than the agreement between the results of theory of elasticity and the numerical results obtained by solving the other approximate formulae included in this paper.