The Uncertain Analysis And Optimization Of The Composite Structure

The stochastic algorithm of the high-precise reliability has been increasingly popular and important,and as a result it leads to the emergency of the stochastic finite element method(SFEM).It emphasizes that the usage and precision strongly rely on the input random field types,their correlations as well as numerical technique used to solve the basic deterministic problem.However,considering the fact that the deterministic numerical methods have already been the unbelievably useful and powerful tool in the contemporary age,the traditional stochastic FEM has the great potential to improve in the precision and the efficiency.Thus,it is a wise way to optimize the stochastic method based on the outstanding deterministic method.Besides,the correlated relationship between the input random fields also affects the uncertain result,and now there are two main methods(Nataf and Rosenblatt transformation)to represent the correlation.Unfortunately,they both have their own limitations,so it is necessary and meaningful to develop a new method to analyze the correlation.Due to excellent properties of the composite structure,the performance prediction and optimization of the fiber-reinforced composite structure with uncertain parameters has been achieved by the improved stochastic numerical method,and the main aspects are listed as follows:(1)The generalized perturbation stochastic stable nodal-based smoothed finite element is presented for stochastic analysis of elastic-static and free vibration problems.It possesses good characters that it can be used in more flexible triangular elements and is insensitive to element distortion.More importantly,the n perturbation expansion method is deduced in this article.When the specific level of error tolerance is given,the n orders can be set to satisfy the precision for different input coefficient of variation.(2)The integration of performance prediction and optimization for the uncertain fiber-reinforced composite structure based on the transformed perturbation method,the edged-based smoothing technique and the optimization theory is presented.It proves that it is a brilliant method to explicitly predict and optimize the probability characteristic curves and reliability index.In optimization procedure,the objectives in the structural stability and maximum stiffness criteria based on the second-order perturbation expansion are proposed,and the overall uncertain condition coupled by uncertain fiber orientation,external load,material parameters and geometry sizes is analyzed and optimized using this framework.(3)The Copula function is introduced into the stochastic framework to break limitations from Nataf and Rosenblatt transformation.It could respectively describe the correlation between the fiber angles and material parameters,and show results as the means of probability density function and the cumulative distribution function.Besides,it also illustrates how the correlated parameter of Copula affects the composite structure.Compared with the traditional response surface method and surrogate modal,the present method based direct numerical simulation method is more accurate and practical.