Prediction of Reliable Load for Thin Plates with Random Geometrical Imperfections Using Pseudo Random Numbers

The initial geometrical imperfections present in the thin plate structures play a vital role in determining the load carrying capacity, especially when they are subjected under axial compression. Moreover, it is impossible to manufacture thin plates without geometrical imperfections. Prediction of the reliable load is imperative because the failure of plate structures under buckling is catastrophic. The strength distribution will also be random because these initial geometric imperfections are random in nature. Hence, a probabilistic approach is pursued. In this work, 64 random geometrical imperfect plate models are generated by the linear combination of the first six Eigen affine mode shapes using 2k factorial design and by keeping the variance of imperfections of all the models at assumed manufacturing tolerance of 2 mm. Moreover, the maximum amplitude of imperfections is maintained within ±8 mm. These imperfect models are analyzed using ANSYS nonlinear Finite Element (FE) buckling analysis, including both geometrical and material nonlinearities. With the help of pseudo random numbers, the strength distribution of the plate is obtained from the results of this FE analysis. Then, by using the Mean Value First Order Second Moment (MVFOSM) method, reliability analysis of the thin plate is carried out.

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