复合曲梁剪应力积分方程的理论解

Theoretical Solutions of Integral Equations for Shearing Stresses in Composite Curved Beams

和单层匀质曲梁相同 ,复合曲梁剪应力的计算仍然可以归结为对积分方程的求解问题 ,通过对积分方程的直接求解 ,可以导出剪应力计算的一般公式 .这些公式不仅满足该梁的平衡条件 ,同时也满足力的边界条件 .这一理论将用于研究由 2种不同材料制成的悬臂曲梁 ,以及试验轴瓦在自由端受集中力情况下的剪应力 ,经计算发现 ,理论值和按ANSYS程序的三维有限元分析结果非常接近 .理论研究表明 ,当梁的曲率半径和截面高度相差不大时 ,剪应力不容忽视 。

Following a procedure similar to that which we used i n studying shearing stresses for curved beams made of one material,the problem of evaluating shearing stresses of composite curved beams is still reduced to one of solving the integral equations.Solving directly two integral equations can de rive the formulae for shearing stresses,which satisfy not only the equilibrium e quations but also the static boundary conditions on the boundary surfaces of the beams.The present analysis will be used to investigate the shearing stresses of a cantilevered curved beam made of two materials,which is loaded by a concentra ted force at its free end.The comparison between the numerical results of sheari ng stresses obtained using the equations developed in tthis paper and a three-d imensioned finite element analysis shows excellent agreement.Theoretical researc h shows that when R is of the same order of magnitude as the depth of the be ams,the shearing stresses become more significant and they can be no longer igno red.