复合材料壳体三维弹性力学问题的高阶多尺度方法及其误差估计  

HIGHER-ORDER MULTI-SCALE METHOD AND ITS ERROR ESTIMATION FOR THREE-DIMENSIONAL ELASTIC PROBLEMS OF COMPOSITE SHELLS

作　　者：董灏 石婕 葛步峰 高鸣远 Dong Hao;Shi Jie;Ge Bufeng;Gao Mingyuan(School of Mathematics and Statistics,Xidian University,Xi’an 710071;School of Electronic Engineering,Xidian University,Xi’an 710071;School of Artificial Intelligence,Xidian University,Xi’an 710071)

机构地区：[1]西安电子科技大学数学与统计学院,西安710071 [2]西安电子科技大学电子工程学院,西安710071 [3]西安电子科技大学人工智能学院,西安710071

出　　处：《高等学校计算数学学报》2024年第3期229-247,共19页Numerical Mathematics A Journal of Chinese Universities

基　　金：国家自然科学基金项目(12471387,12001414);陕西省科学技术协会青年人才托举计划项目(20220506);西安市科学技术协会青年人才托举计划项目(095920221338);西安电子科技大学2024年学科交叉拓展特支计划(TZJH2024008);中央高校基本科研业务费项目(ZYTS24071);陕西省创新能力支撑计划-科技创新团队计划项目(2024RS-CXTD-88)

摘　　要：1引言复合材料是由两种或多种不同性质的材料用物理或化学方法组成的新型材料,具有优良的热学和力学性能,并且集轻质、多功能及可设计性于一身,具有广阔的工程应用前景[1].在实际工程应用中,复合材料常被制造成多层壳、夹层壳、加筋壳等壳体结构.对于复合材料壳体,从力学角度来看,复合材料壳体的宏观结构整体尺寸远大于其细观结构特征尺寸,直接进行数值求解需要足够细的计算网格才能捕捉到其细观尺度的信息.In this paper,a novel higher-order multi-scale method is developed for effectively simulating the three-dimensional elastic problems of composite shells.Firstly,a higher-order multi-scale computational model is established by the multiscale asymptotic analysis of three-dimensional multi-scale elastic equations in the orthogonal curvilinear coordinate system,which can effectively analyze the mechanical behavior of composite shells.Then,the local error estimation of the higher-order multi-scale solutions is derived in the point-wise sense,which proves that only higher-order multi-scale solutions can ensure the small-scale approximation of three-dimensional mechanical equilibrium equations.Furthermore,the global error estimation of the higher-order multi-scale solutions is obtained in the energy norm sense.Next,a multi-scale algorithm is developed based on finite element method,which enables the efficient and accurate simulation of the oscillatory mechanical behaviors of composite shells.And we also derive the error estimation of the multi-scale algorithm with an explicit convergence rate.Finally,the computational accuracy and efficiency of the established higher-order multi-scale method for composite shells are verified by extensive numerical experiments.

关 键 词：误差估计 多尺度方法 复合材料壳体 新型材料 壳体结构 细观尺度 计算网格 可设计性 

分 类 号：O241.82[理学—计算数学]