PSI - Issue 34

C. Becker et al. / Procedia Structural Integrity 34 (2021) 99–104 Author name / Structural Integrity Procedia 00 (2019) 000–000

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The CGSM is valid for low and high variability levels of the input parameters. A Gaussian distribution (± 3σ) of the uncertain parameter is considered. A range of values for the c.o.v. from 5% to 30% is also considered. A c.o.v. of 30% corresponds to an extremely high variability of the Young’s modulus, which then ranges from 10% to 190% of the nominal value. A Young’s modulus value of E = 60GPa is used for a continuous carbon fiber composite in the longitudinal direction. The finite element analyses are performed with Abaqus, one finite element being used for each truss member, as the axial force is considered to be constant in a given member. We further assume that the Young’s modulus of the truss members varies, but stays constant within each member. In general, different cases for the correlation between the uncertain parameters can be considered. The uncertain parameters can be assumed as independent, partially correlated or completely dependent. Here, a fully independent case is considered, leading to a number of uncertain parameters equal to the number of truss members in a given design. For the optimized structures, which we compare here, the number of uncertain parameters ranges from 12 to 161. The variability of the displacement at point P, which depends on the uncertain Young’s modulus, is evaluated using Matlab. Once the uncertain parameters are introduced, the influence on the displacement can be evaluated using the CGSM. Almost no difference is found between the designs for the mean value of the displacement, for all levels of variability. In contrast to the mean value, the standard deviation shows a clear difference between the designs. Fig. 5 shows the variability of displacement c.o.v.(U) for all studied designs. For a c.o.v.(E) of 10%, the variability of the displacement ranges from 1.97% to 3.34%. For an extremely high variability level (c.o.v.(E) = 30%), the variability of displacement ranges from 9.09% to 15.44%. In summary, uncertainty in the material properties (in this case Young’s modulus) affects the variability of the displacement at point P. In all cases, the displacement variability level is smaller than the input parameters variability level. The findings suggest a correlation between the number of cantilever truss members and the variability of the displacement. The lowest value for the output variability is obtained for a truss structure with 161 members, while the four highest values of output variability are obtained for designs with 32 or fewer members. Thus, the designs with more elements are more robust to the variability of the Young’s modulus. This is due to a compensation phenomenon, which often occurs when the number of uncertain parameters increases, which is the case here when the number of members increases.

Fig. 5. Cantilever structure with 2 loads: variability of the maximum displacement for different levels of variability of Young’s modulus.