Fig. 1. The multilayer triangular TRIC element; coordinate systems.

Fig. 2. Geometry, and material data of the cylindrical panel.

Fig. 3. Central load–displacement curve of the perfect cylindrical panel for t = 12.7 mm.

Fig. 4. One sample function of 1D initial imperfection shapes of the cylindrical panel for σ_f = 0.10 and b₁ = 50 mm.

Fig. 5. Histograms of the critical load factor P_u for 1D stochastic imperfections (σ_f = 20% and b₁ = 50 mm).

Fig. 6. 2D initial imperfection shape for σ_f = 0.20 and correlation length b₂ = 250 mm.

Fig. 7. Histograms of the critical load factor P_u for 2D stochastic imperfections (σ_f = 20% and b₁ = b₂ = 250 mm).

Fig. 8. Histograms of the critical load factor P_u for 1D variation of combined geometric, material and thickness imperfections (σ_f = 20%).

Fig. 9. Histograms of the critical load factor P_u for 2D variation of combined geometric, material and thickness imperfections (σ_f = 20%).

Fig. 10. Central load–displacement curve of the perfect cylindrical panel for t = 6.35 mm.

Fig. 11. Histograms of the critical load factor P_u for 1D variation of combined geometric, material and thickness imperfections (σ_f = 20% and t = 6.35 mm).

Fig. 12. Histogram of the critical load factor P_u for 2D variation of combined geometric, material and thickness imperfections (σ_f = 20% and t = 6.35 mm).

Fig. 13. Geometry and material data of the axially compressed cylinder.

Fig. 14. Measured initial unfolded shape of shell A-7.

Fig. 15. Ensemble average of initial imperfections.

Fig. 16. Evolutionary power spectra of (a) axial direction and (b) circumferential direction of the cylinder.

Fig. 17. Convergence behaviour of a quarter of the perfect cylinder.

Fig. 18. Half axial trace of pre-buckling deformation of the perfect cylinder.

Fig. 19. Circumferential trace of pre-buckling deformation of a quarter of the perfect cylinder for (a) 51 × 101 mesh size and (b) 51 × 401 mesh size.

Fig. 20. Sample realization of non-homogeneous geometric imperfections using evolutionary power spectra and mesh 51 × 101.

Fig. 21. Histograms of critical load factors: (a) 2D stochastic geometric imperfections; (b) experimental results (7 specimens [16]).

Fig. 22. Mean value and coefficient of variation (Cov) of the ultimate load P_u of the imperfect cylinder as a function of the correlation length parameters b₁ = b₂, for (a) 2D variation of the modulus of elasticity and (b) 2D variation of the thickness (σ_f = 10%).

Fig. 23. Histograms of critical load factors for 2D combined imperfections: (a) correlation length of additional imperfections b₁ = b₂ = 50 mm (b) correlation length of additional imperfections b₁ = b₂ = 500 mm.

Geometry, material properties and experimental buckling loads of A-shells