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A three-dimensional (3D) fiber stress formula was developed to reduce the deviation of the two-dimensional (2D) fiber stress formula in calculating the 3D stress. The on-axis and off-axis stress–strain relationship was first presented. The 3D fiber stress formula was then derived analytically. Finite element method (FEM) of filament-wound (FW) thick-walled cylinders with symmetrical/balanced-layers was built, and numeric results were calculated and analyzed. Good agreement of the fiber stresses in the fiber direction and the strength ratios were achieved. It was found that the 3D fiber stress formula yields more accurate stress and lower strength ratio than the 2D formula in the triaxial stress state.

Three-dimensional stress formula in fiber direction and its application under internal and external pressure