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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。
Using the complex variable function method, the stress solution of the plane problem when the outer wall of a double-walled thick-walled cylinder is subjected to a kind of two-direction unequal-pressure radial pressure and the inner wall under uniform pressure is given. Under the assumption of smooth contact between two cylinders, a stress analytical solution of a double-walled thick-walled cylinder is obtained. The distribution of tangential stress and radial stress in different sections of cylinder with different modulus of elasticity is analyzed through numerical examples. The results show that when the uniform pressure of the inner wall is small, the tangential stress along the inner wall of the two layers of cylinder All of them have cosine distribution in the circumferential direction, and they are both subjected to the maximum compressive stress in the direction of the minimum stress of the inner wall and the maximum tensile stress in the direction of the maximum geostress. The radial stress is distributed along the radial direction at 0 °, 45 ° and 90 ° They are distributed in the approximate shape of “M”, “rhombus” and “W” respectively. With the increase of the ratio of the elastic modulus of the inner and outer layers, the tangential stress near the inner wall of the inner cylinder increases, The stress increases in the direction of the minimum stress and decreases in the direction of the maximum stress, while the distribution in the outer layer tube is opposite. The use of soft and flexible inner combination of elastic modulus, can effectively reduce the inner cylinder wall stress concentration.