摘要
采用复变函数方法,给出了双层厚壁圆筒外壁受有一类两向不等压非均布径向压力,内壁受有均布压力作用时平面问题的应力求解方法。在两层圆筒光滑接触的假定下,获得双层厚壁圆筒的应力解析解。通过算例分析了不同弹性模量组合时圆筒内不同截面的切向应力与径向应力分布规律,研究结果表明:当内壁均布压力较小时,两层圆筒的内壁处切向应力沿环向均呈余弦分布,且都在内壁的最小地应力方向承受最大压应力,在最大地应力方向承受最大拉应力;径向应力沿径向在圆筒0°、45°、90°截面处分别呈近似"M"状、"菱形"、"W"状分布;随着内外层弹性模量比值的增大,内层圆筒内壁附近切向应力增大,径向应力在最小地应力方向增大,在最大地应力方向减小,而在外层筒分布规律相反。采用内软外硬的弹性模量组合,能有效的减小圆筒内层内壁处的应力集中程度。
The stress analytic method for the plane problem of a double-layered thick-walled cylinder subjected to a type of non-uniform pressure on the outer surface and a uniform radial pressure on the inner surface is given by the complex function method. The stress analytic solution is obtained with the assumption that the contact condition between two layers is pure slip. The distributions of tangential and radial stress along different sections are obtained through an example. The result indicates that： when the uniform radial pressure on the inner surface is small, the tangential stress along the hoop direction in the inner boundaries of two layers form a cosine distribution. The maximum compressive stress occurs in the direction of the minimum in-situ stress and the maximum tensile stress occurs in the direction of the maximum in-situ stress. The distributions of radial stresses along the radial direction at 0° 45°, 90° sections are respectively similar to ＂M＂, ＂diamond＂, ＂W＂ shape. With the increase of the ratio of the Young＇s modulus of the inner and the outer layer, for the inner layer, the tangential stress along the inner boundary increases, the radial stress increases in the direction of the minimum in-situ stressand decreases at the maximum in-situ stress direction. While the opposite stress state happens in the outer layer. If the Young＇s modulus of the inner layer is smaller than that of the outer layer, the stress concentration at the inner surface of the inner layer can be alleviated effectively.
出处
《工程力学》
EI
CSCD
北大核心
2013年第10期93-99,共7页
Engineering Mechanics
基金
长江学者和创新团队发展计划项目(IRT0950)
国家自然科学基金项目(50874047)
关键词
厚壁圆筒
应力解析解
复变函数
非均布荷载
不同弹性模量组合
thick-walled cylinder
stress analytic solution
complex variable function
non-uniform pressure
combination of different elastic modulus
