  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.
