High-order three-scale computational method for elastic behavior analysis and strength prediction of axisymmetric composite structures with multiple spatial scales

A novel high-order three-scale (HOTS) computational method for elastic behavior analysis and strength prediction of axisymmetric composite structures with multiple spatial scales is developed in this paper. The multiple heterogeneities of axisymmetric composite structures we investigated are taken into account by periodic distributions of representative unit cells on the mesoscale and microscale. First, the new micro–meso–macro coupled HOTS computational model for elastic problems of axisymmetric composite structures is established based on multiscale asymptotic analysis, which breaks through the traditional multiscale assumptions and includes three main components. Two classes of mesoscopic and microscopic auxiliary cell functions are constructed on the mesoscale and microscale, respectively. The macroscopic homogenization problems are defined on global axisymmetric structures by twice up-scaling procedures from microscale to mesoscale and then from mesoscale to macroscale. Moreover, the asymptotic HOTS solutions are constructed for approximating multiscale elastic problems of axisymmetric structures and the numerical accuracy analysis of the HOTS solutions is given in detail. Then, the strength prediction formulas for axisymmetric composite structures with multiple spatial scales are presented based on the high-accuracy elastic behavior analysis from the proposed HOTS computational model. Furthermore, the corresponding HOTS numerical algorithm based on the finite element method (FEM) is presented for analyzing the mechanical behaviors and predicting the strength of axisymmetric composite structures with multiple spatial scales in detail. Finally, some numerical examples are reported to verify the feasibility and effectiveness of the proposed HOTS computational method. In this study, a unified three-scale computational framework is offered, which enables the simulation of mechanical behaviors of axisymmetric composite structures with multiple spatial scales.