无限长圆筒局部受压的三维解析解及数值验证

打开文本图片集

中图分类号：0343.2 文献标志码：A 文章编号：1000-4939（2025）03-0552-07

Abstract：Based on the simplification of cylindrical axisymmetric problem and the good properties of modified Bessel functions，displacement harmonic functions with undetermined functions are constructed. Using theconstructed displacement harmonic functions，the stress expressions of infinite cylinder under local uniformly distributed pressure are derived.By substituting the stress expressions into the corresponding boundary conditions，theundetermined function in the displacement harmonic function is solved by using the inverse Fourier transform.Finally，the three-dimensional stress analytical solution satisfying the boundary conditions is obtained.Furthermore，a parametric axisymmetric stress analysis simulation model is established by using ANSYS finite element software to simulate the stress distribution characteristics of typical conditions.The influence of geometrical size change on triaxial stress state is analyzed by theory and simulation，and simulation results with theoretical analysis conclude unanimously.It shows that the three-dimensional analytical solution and finite element simulation established in this paper are accurate and reliable.

Key words：local compression；infinite cylinder；displacement harmonic function；three-dimensional analytic solution；finite element simulation

受压圆筒作为一种重要的工程结构，在压力容器[-2]、组合凹模设计[3-4]、压力管道[5]、液压致裂测试[6-7]等领域有广泛的应用。（剩余6817字）