摘要
论文提出一种周期性点阵桁架材料力学性能分析的新的多尺度方法.方法的主要思想是通过数值构造能反映周期性桁架材料单胞内部非均质性的多尺度基函数,从而在大尺度上求得单胞的等效刚度阵,大大减小了模型计算量.通过引入基函数的耦合附加项,以考虑多维矢量场问题不同方向间的耦合作用.数值研究表明,采用线性边界条件构造基函数有时会产生较强的边界效应,而超样本技术的振荡边界和周期性边界条件能很大程度地减少单胞边界强制变形产生的误差.特别是对于非均质特征尺度跟宏观单元尺度相近的单胞,论文提出的周期性边界条件具有很好的效果.所提出的方法的优点是,在所构造的多尺度有限元法的基础上,能较容易地进行降尺度计算,较准确地得到单胞内部小尺度上的应力应变信息,为材料强度分析的多尺度计算打下基础.
A new multiscale computational method is developed to study the mechanical properties of periodic lattice truss materials.The underlying idea is to construct numerically the multiscale base functions to reflect the heterogeneities of the unit cells and obtain the equivalent stiffness matrix of the unit cells of periodic truss materials.Then the problems only need to be solved on the large-scale meshes and the computational cost can be dramatically reduced.To consider the coupled effect among different directions in the multi-dimensional problems,the coupled additional terms of base functions for the interpolation of the vector fields are introduced.Numerical experiments show that the base functions constructed by the linear boundary conditions sometimes will have a strong boundary effect.While the oscillatory boundary conditions obtained by the oversampling technique and the periodic boundary conditions can greatly reduce the errors induced by the forcible deformations of the unit cells.Especially for the unit cells whose coarse-mesh scales are close to the small scales of heterogeneities,the periodic boundary conditions proposed can improve greatly the accuracy of the results.The advantage of the method developed is that the downscaling computation could be realized easily and the stress and strain in the unit cell can be obtained simultaneously in the multiscale computation.Thus the multiscale method studied here has good potential in the strength analysis of heterogeneous materials.
出处
《固体力学学报》
CAS
CSCD
北大核心
2011年第2期109-118,共10页
Chinese Journal of Solid Mechanics
基金
国家自然科学基金项目(11072051,90715037,91015003,10728205,51021140004)
国家基础性发展规划项目(2010CB832704)资助
关键词
多尺度计算方法
桁架材料
降尺度计算
基函数
multiscale computational method
truss material
downscaling computation
base function
