内压下带径向接管圆柱壳的薄壳理论解

Thin shell theoretical solution for cylindrical shells with normally intersecting nozzles subjected to internal pressure

圆柱壳开孔接管是各种工程中常见的部件,在内压下交贯线附近有很高的应力集中,自20世纪50年代以来成为工程界与力学界关注的难题,问题的求解归结为2个8阶偏微分方程的复杂边值问题。该文在作者前20年研究基础上,从解析求解精确的圆柱壳Morley方程出发,对内力素的表达式加入修正项改善了解的精度,增大了适用范围。通过三维有限元数值验证,说明了该文所引入的修正项将薄壳理论解的参数最大适用范围由开孔率0.8增至0.93,λ=d/(DT)1/2由8增至12。据此给出了便于工程设计的内压下圆柱壳大开孔接管应力集中系数曲线。

Cylindrical shells with nozzles are commonly used in many industries. Since the 1950s, the topic has attracted much attention due to their importance in the areas of mechanics and engineering. A thin shell theoretical solution was obtained by solving a complex boundary value problem for both of the eighth-order partial differential equations. In this paper some terms are added to the formulas for the resultant forces from a theoretical solution based on the exact Morley equation to improve the accuracy of the analytical solution. The theoretical results were verified numerically by a three-dimensional finite element solution. Stress concentration curves are presented for pressurized cylindrical shells with nozzles for expanded ranges to d/D ≤ 0. 93 and λ = d/（DT）^1/2≤12.