The complicated mesoscopic configurations of composite plate and shell structures requires a huge amount of computational overhead for directly simulating their mechanical problems. In this paper, a unified high-order multi-scale method, which can effectively simulate the mechanical behavior and predict yield strength of composite plates and shells, is developed. Firstly, through the multiscale asymptotic analysis of multi-scale elastic equations in the orthogonal curvilinear coordinate system, a high-order multi-scale model is established, which can uniformly and effectively analyze the mechanical behavior of composite plate and shell structures. Moreover, the error estimation of the high-order multi-scale solutions is derived. Then, combining with the material strength theory, a high-order multi-scale model for the strength prediction of composite plate and shell structures is established. Next, based on the established high-order multi-scale model, a multi-scale algorithm is developed which can not only efficiently and accurately simulate the mechanical behaviors of composite plate and shell structures, but also predict their yield strength. Finally, the effectiveness of the established high-order multi-scale method is verified by extensive numerical experiments. The numerical experimental results indicate that the high-order multi-scale method can more accurately capture the meso-scale oscillatory behaviors of composite plate and shell structures. The unified high-order multi-scale method established in this paper is not only suitable for the prediction of mechanical properties of composite plate and shell structures, but also can be further extended to the prediction of multi-field coupling properties of composite plate and shell structures.

翻译：复合材料板壳结构复杂的细观构型使得直接模拟其力学问题需要巨大的计算开销。本文发展了一种能够有效模拟复合材料板壳力学行为并预测其屈服强度的统一高阶多尺度方法。首先，通过对正交曲线坐标系下的多尺度弹性方程进行多尺度渐近分析，建立了高阶多尺度模型，该模型能够统一且有效地分析复合材料板壳结构的力学行为。此外，推导了高阶多尺度解的误差估计。然后，结合材料强度理论，建立了用于复合材料板壳结构强度预测的高阶多尺度模型。接下来，基于所建立的高阶多尺度模型，发展了一种多尺度算法，该算法不仅能高效准确地模拟复合材料板壳结构的力学行为，还能预测其屈服强度。最后，通过大量数值实验验证了所建立的高阶多尺度方法的有效性。数值实验结果表明，高阶多尺度方法能够更准确地捕捉复合材料板壳结构的细观振荡行为。本文建立的统一高阶多尺度方法不仅适用于复合材料板壳结构力学性能的预测，还可进一步推广至复合材料板壳结构多场耦合性能的预测。