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.