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对平面内弯矩作用下的弯管的应力分析提出了一种新的计算方法,以替代现行的有限元网格法。新方法的提出基于有限弯曲单元,其位移由一系列三角函数或者五次多项式,与傅里叶级数共同计算而得。整体的壳位移由两类位移组合而成,一个是拱的弯曲位移,另一个则是环形的薄壁壳体的翘曲位移。梁模型的位移和平面内转角是不耦合的,分别应用三角函数,如Timoshenko或Mindlin梁理论计算得到。基于双曲线壳体的半膜单元概念,提出了一个简化的变形模型用于此计算方法。研究成果也与已有的试验和数值分析结果进行了对比。
A new calculation method is proposed to analyze the stress of elbow under in-plane bending moment, which replaces the current finite element method. The new method is based on finitely curved elements whose displacements are calculated by a series of trigonometric or quintic polynomials in combination with the Fourier series. The overall shell displacement is a combination of two types of displacements, one is the flexural displacement of the arch and the other is the warping displacement of the annular thin walled shell. Beam model displacement and in-plane rotation are uncoupled and are calculated using trigonometric functions such as Timoshenko or Mindlin beam theory respectively. Based on the concept of a semicircular element in a hyperbolic shell, a simplified deformation model is proposed for this method. The research results are also compared with the results of the existing experiments and numerical analysis.