Generic imperfection patterns - using truncated Fourier series

Generic imperfection patterns for shell design using GMNIA
For more information see Knoedel, P., Wacker, T., Ummenhofer, T.: Generic substitute imperfection patterns for the GMNIA of tanks and silos made of steel or aluminium. NSCC Nordic Steel Construction Conference, 26-28 June 2024, Lulea, Sweden

File extensions .dat designate ASCII files

Geometrical substitute imperfections given as radial deviation from the perfect cylindrical surface.
L,strake / L describes the spacing of circumferential welds within the total length of the shell.


see Fig. 4 in the NSCC 2024 paper

1D-Fourier series - Curved plates without welds
imperfections assumed as being random

Random_collection_23-12-29.xlsx - collection of three sets of 30 random numbers
Random_collection_23-12-29.pdf

DFT_random_row_A_24-02-04.pdf - Fouerier coefficients for row A

DFT_random_row_B_24-02-04.pdf - Fouerier coefficients for row B

DFT_random_row_C_24-02-04.pdf - Fouerier coefficients for row C


see Fig. 5a in the NSCC 2024 paper

1D-Fourier series - weld depression
Rotter/Teng (1989); Teng/Rotter (1992)
see eq. 8 in the NSCC 2024 paper

norm_coeff_mat_24-02-05_Ldep010.dat - L,strake / L = 0,10
norm_coeff_mat_24-02-05_Ldep010.pdf

norm_coeff_mat_24-02-05_Ldep025.dat - L,strake / L = 0,25
norm_coeff_mat_24-02-05_Ldep025.pdf

norm_coeff_mat_24-02-05_Ldep050.dat - L,strake / L = 0,50
norm_coeff_mat_24-02-05_Ldep050.pdf

norm_coeff_mat_24-02-05_Ldep075.dat - L,strake / L = 0,75
norm_coeff_mat_24-02-05_Ldep075.pdf

norm_coeff_mat_24-02-05_Ldep100.dat - L,strake / L = 1,00
norm_coeff_mat_24-02-05_Ldep100.pdf


see Fig. 5b in the NSCC 2024 paper

2D-Fourier series - translatory weld depression
see eq. 4 in the NSCC 2024 paper

multiple weld depressions - use coefficients for 1D-Fourier series


compare Fig. 7a in the NSCC 2024 paper

2D-Fourier series - local bump
see eq. 5 in the NSCC 2024 paper

D = 15.916 mm; C = 50.002 mm; L = 20.000 mm
d,bump = 3.000 mm; Amp = 10 mm; x0/C = 0,30; y0/L = 0,30;

Coefficient matrix A
Coefficient matrix A.pdf

Coefficient matrix B
Coefficient matrix B.pdf

Coefficient matrix C
Coefficient matrix C.pdf

Coefficient matrix D
Coefficient matrix D.pdf


exemplary project

2D-Fourier series - local bump
see eq. 5 in the NSCC 2024 paper

D = 12.600 mm; C = 39.584 mm; L = 8.300 mm
d,bump = 2.000 mm; Amp = 10 mm; x0/C = 0,101; y0/L = 0,50;
.dat files are written with "9999" as separators between values
use an editor to change these into convenient delimiters, such as comma, semicolon, blank, ...

Coefficient matrix A.dat
Coefficient matrix A.xlsx

Coefficient matrix B.dat
Coefficient matrix B.xlsx

Coefficient matrix C.dat
Coefficient matrix C.xlsx

Coefficient matrix D.dat
Coefficient matrix D.xlsx

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