Abstract
Based on the simplification of the cylindrical axisymmetric problem and the favorable properties of modified Bessel functions, a displacement harmonic function containing undetermined functions was constructed. Applying the constructed displacement harmonic function, stress expressions containing undetermined functions were derived for an infinitely long cylinder under locally uniform pressure on its inner wall, and by substituting these stress expressions into the corresponding boundary conditions and employing inverse Fourier transform, the undetermined functions in the displacement harmonic function were solved, ultimately obtaining a three-dimensional analytical stress solution that satisfies the boundary conditions. Using ANSYS finite element software, a parametric axisymmetric stress analysis simulation model was established to simulate the stress distribution characteristics under typical conditions. Through a method combining theoretical analysis and numerical simulation, the influence law of geometric dimension variations on the triaxial stress state was analyzed, and by comparing theoretical calculations with numerical simulations, good agreement was obtained, demonstrating that the three-dimensional analytical solution and finite element simulation established in this study are fundamentally accurate and reliable.
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