An improved version is presented for analytical solution developed by the authors and the applicable ranges of the theoretical solutions for two normally intersecting cylindrical shells are successfully extended from d/D≤0.8 and λ=d/(DT)~(1/2)≤8 up to d/D ≤0.9 and λ≤2. The thin shell theoretical solution is obtained by solving a complex boundary value problem for a pair of 4-th order complex-valued partial differential equations (exact Morley equations) for the shell and the nozzle. The accuracy of results is improved by some additional terms to the expressions for resultant forces and moments in terms of complex-valued displacement-stress function. The presented theoretical stress concentration factors due to pressure are in agreement with the test results in literatures. The presented theoretical results are in good agreement with those by 3-D finite element method for all the seven load cases, I.e., internal pressure and six external branch pipe load components involving axial tension, two kinds of transverse shear forces, longitudinal and circumferential bending and torsion moments.
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机译：提出了一种改进的版本，用于作者开发的解析解，并且成功地将两个常相交的圆柱壳的理论解的适用范围从d /D≤0.8和λ= d /（DT）〜（1/2）≤ 8直到d / D≤0.9和λ≤2。薄壳理论解是通过求解壳和喷嘴的一对4阶复数值偏微分方程（精确的Morley方程）的复数边值问题而获得的。通过以复数值位移-应力函数表示的合力和力矩的表达式增加了一些附加项，从而提高了结果的准确性。提出的由于压力引起的理论应力集中系数与文献中的测试结果一致。所给出的理论结果与3-D有限元法对所有七个载荷工况即内部压力和涉及轴向拉力，两种横向剪力，纵向和周向弯曲的六个外部支管载荷分量的理论结果吻合良好。和扭转的时刻。
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