Abstract

This paper presents a novel approach for assessing the uncertainty in vibration and static responses of laminated composite beams resulting from uncertainty in material properties and distributed loads. The proposed method utilizes surrogate models developed using polynomial chaos expansion (PCE) based on a relatively small sample size. These training samples are computed using a high-order shear beam model in which the governing equations are derived using Hamilton's principle, and solved by Ritz’s approach using a trigonometric series approximation. The proposed PCE model's coefficients are estimated using the spectral projection and linear regression techniques. The first four statistical moments and probability distributions of the mid-span displacement and the fundamental frequency of laminated composite beams are predicted. Global sensitivity analysis is also conducted to assess how material property variation and stochastic loads affect the beam's deflection and the fundamental frequency. The accuracy and efficiency of the proposed PCE models are compared with those from Monte Carlo simulation (MCS). A remarkable reduction in the computational cost of PCE models compared to MCS is observed without compromising the predictions' accuracy. As most real-world systems are subjected to multiple sources of uncertainty, this study provides a state-of-the-art method to quantify such uncertain parameters more efficiently and allow for a better reliability assessment in composite beam design.

中文翻译：

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用于层合复合梁随机弯曲和振动分析的谱投影和线性回归方法

摘要

本文提出了一种新方法，用于评估由于材料特性和分布载荷的不确定性而导致的层合复合材料梁的振动和静态响应的不确定性。所提出的方法利用基于相对较小样本量的多项式混沌展开（PCE）开发的代理模型。这些训练样本使用高阶剪切梁模型进行计算，其中使用哈密尔顿原理导出控制方程，并使用三角级数近似通过 Ritz 方法进行求解。所提出的 PCE 模型的系数是使用谱投影和线性回归技术来估计的。预测了层合组合梁跨中位移和基频的前四个统计矩和概率分布。还进行了全局灵敏度分析，以评估材料特性变化和随机载荷如何影响梁的偏转和基频。将所提出的 PCE 模型的准确性和效率与蒙特卡罗模拟 (MCS) 的模型进行了比较。与 MCS 相比，PCE 模型的计算成本显着降低，而不会影响预测的准确性。由于大多数现实世界的系统都受到多种不确定性来源的影响，这项研究提供了一种最先进的方法来更有效地量化这些不确定性参数，并在组合梁设计中进行更好的可靠性评估。