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对单侧承受双曲余弦分布压力的含损伤缺陷矩形截面悬臂梁,用弹性理论进行了应力分析。应用叠加原理,将构件分解为无损伤缺陷构件和含损伤缺陷的半无限平面分别求解,将外载荷根据其特点展开成三角级数形式,采用半逆解法求出了满足边界条件的近似解析解,得到了构件的应力状态。实例计算结果表明:损伤缺陷附近将产生较大的应力集中,且应力值随损伤缺陷尺寸的减小而增大。
For a cantilever beam with a damaged rectangular cross section subjected to hyperbolic cosine distribution pressure on one side, the stress analysis was carried out using elastic theory. Applying the principle of superposition, the component is decomposed into the non-damage component and the semi-infinite plane containing the damage defect respectively. The external load is developed into a triangular series according to its characteristics. The approximate analytical solution satisfying the boundary condition , Get the component’s stress state. The calculated results show that the stress concentration will increase near the defect, and the stress value will increase with the decrease of defect size.