# Validation

The theory has been implemented in a MATLAB software module and validated against VABS. The first validation case was for a single-cell composite box beam VABS example shown in Figure 2.

The elements of the 4×4 stiffness matrix, S, obtained from the implementation are compared to those produced by VABS in Table 1. Not all elements are shown since the stiffness matrix is symmetric.

The three-cell isotropic box beam shown in Figure 3 is another validation of the current imple­mentation against VABS, where the stiffness matrix is now calculated about the lower-left corner of cross-section.

Similarly, The elements of the 4×4 stiffness matrix, S, obtained from the implementation are compared to those produced by VABS in Table 2.

Table 2. The elements of the stiffness matrix obtained using the thin-walled anisotropic beam theory and VABS for Figure 2.

 Stiffness Element Thin-Walled VABS (Yu, 2005) Difference 511 0.0611 x 1013 lb 0.0608 x 1013 lb 0.49% 512 0 lb – in 0 lb – in Exact 513 0.0611 x 1013 lb – in 0.0608 x 1013 lb – in 0.49% 514 -0.2699 x 1013 lb – in -0.2692 x 1013 lb – in 0.26% S22 0.0515 x 1013 lb – in2 0.0540 x 1013 lb – in2 4.63% 523 0 lb – in2 0 lb – in2 Exact 524 0 lb – in2 0 lb – in2 Exact 533 0.1073 x 1013 lb – in2 0.1069 x 1013 lb – in2 0.37% 534 -0.2699 x 1013 lb – in2 -0.2692 x 1013 lb – in2 0.26% 544 1.7091 x 1013 lb – in2 1.7072 x 1013 lb – in2 0.11%

The results presented in Tables 1 and 2 clearly validate the present implementation to model single/multi-cell thin-walled anisotropic cross-sections of rotor blades found on actual helicopters and turbine engines.