Unified high-order multi-scale method for mechanical behavior simulation and strength prediction of composite plate and shell structures

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.