【作者】 徐亮； 程耿东；

【Author】 Xu Liang;Cheng Gengdong;Dalian University of Technology;

【机构】 大连理工大学；

【摘要】 具有周期非均匀微结构的宏观结构在工业中有着广泛的应用。在分析其力学性能时,我们往往利用均匀化方法将其简化为具有等效性质的连续体结构。具有严谨数学基础的渐近均匀化方法就是其中的一种,但该方法不易有限元实现。程耿东等采用等效位移场代替单位广义应变场的新数值求解方法,使其能在商业有限元软件中实现,并推广至具有周期非均匀微结构的细长梁式结构。但是,这一算法只能将这类结构简化为Bernoulli-Euler梁,无法求得剪切刚度而将其简化为Timoshenko梁。本文以渐近均匀化方法的新数值求解方法为基础,构造和广义线性弯曲应变对应的、满足单胞周期边界条件的复合位移场,采用能量等效的方法推导得到具有周期微结构的梁的剪切刚度,并利用商用有限元软件进行二次开发实现这些计算。这一算法在实现周期微结构均匀化的同时,实现了由三维结构降阶为Timoshenko梁结构,可以利用商用有限元程序的多种单元和模型化能力,将具有周期微结构的非均匀梁式结构简化为Timoshenko梁。最后给出了一些算例来证明该数值方法求解剪切刚度的有效性。更多还原

【Abstract】 Periodic heterogeneous structures are widely used in industrial applications.In mechanical analysis,these structures are often treated as homogeneous beam structures with effective mechanical properties by homogenization method.Asymptotic homogenization(AH) method is one of them with rigorous mathematical theory,but poor usability in FEA.Cheng.et al.proposed a new numerical implementation which replaces unit strain field with equivalent displacement field,and realized AH method in commercial software.However,this method can only deal with Bernoulli-Euler beam,and it can’t deal with Timoshenko beam because shear stiffness can’t be obtained with this method.In this paper,the authors use a displacement field,which is equivalent to linear bending curvatures and satisfies periodic boundary conditions,to calculate shear stiffness through energy method,based on the new numerical implementation.This method can be easily implemented in commercial software,and different kinds of elements and modeling techniques can be used.At last,several examples are given to validate the effectiveness of this method.更多还原