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Due to the uncertainty of the initial geometrical imperfection, it is difficult to evaluate its influence on bucking behavior of structures. In this study, the double trigonometric series is adopted to describe the initial geometric imperfection and the deformed deflection, and then the relation between them is deduced from the bending equilibrium equation. Therefore, the total displacement can be obtained by superposing these two deflections. Based on this analytical model, the range of the maximum deformation is determined by Monte Carlo simulation. The analysis provides a new analytical model for the buckling problem of plate with uncertain initial geometrical imperfection. INTRODUCTION Previously reported experimental studies [1] show that the experimental values of critical load are much lower and the data has a larger scatter band when compared with the results predicted by the linear theories of buckling. It is widely accepted that the result is caused by the original defects of structures. These original defects mainly include the thickness imperfection [2, 3], misalignment in the loading [4], non-perfect boundary conditions [5], fluctuations in material properties [6], impact of residual stress [7] and the initial geometrical imperfection [8-13], and among which the initial geometrical imperfection is the major one whose influence on buckling has become a very important issue [14]. Flügge [15] firstly studied the effect of initial geometrical imperfection on the shell stability based on linear buckling equations, however, he could not make reasonable explanations because that equation can not describe the deformation of post-buckling. Donnell studied the post-buckling equilibrium path of cylindrical shell by assuming the initial geometrical imperfection as a slight deviation from the ideal cylindrical shell and is of the same shape with the buckling deflection [16], and described the impact of the initial geometrical imperfection on buckling load by proposing an initial defect factor. Later Koiter [17] put forward a post-buckling theory to depict the initial post-buckling behavior with imperfection sensitivity and introduced a precise theory which results in an asymptotically solution. Hutchinson presented a two equivalent description of initial post-buckling theory based on the energy principle and the virtual work principle [18, 19], which extended the application scope of Koiter theory. However the initial geometrical imperfection is of random shape and random amplitude in engineering application, the aforementioned theory can not take the uncertainty of initial geometrical imperfection into account. There are two methods to solve this problem, one is that calculate the buckling load through harmonic analysis based on the deflection distribution measured by actual measurement, and the other is that establish an appropriate criterion for buckling by analyzing the effect of the random initial geometrical imperfection on buckling behavior via stochastic theory. Since the former method needs plenty of measurement data, more research focuses on the latter. The stochastic theory includes non-probability convex model method and probability method. Convex model method is adopted to analyze the problem of structure with 738 5th International Conference on Frontiers of Manufacturing Science and Measuring Technology (FMSMT 2017) Advances in Engineering Research (AER), volume 130

Analytical Model and Numerical Simulation for the Effect of Uncertain Initial Geometrical Imperfection on the Buckling of Thin Plate