基于渐近均匀化方法的准周期梁结构等效刚度数值实现方法研究

Numerical implementation method of quasi periodic beam based on asymptotic homogenization method

相比周期梁结构,准周期梁结构沿轴向梯度变化,具有更大的设计自由度,能够获得更好的结构性能。由于其非均质性,一般将其均匀化为具有等效性质的均质梁结构,但现有工作很少涉及准周期梁结构等效性质的计算。本文针对由周期梁结构映射而成的准周期梁结构,通过引入雅可比矩阵,基于渐近均匀化方法推导的单胞方程及其等效性质计算列式,并建立了其单胞方程及等效刚度的有限元求解列式。该方法可以处理沿轴向变形的任意微单胞构型,数值算例验证了其正确性和有效性。

Compared with a periodic beam structure,a quasi-periodic beam structure has greater design freedom and better structural performance.Due to its heterogeneity,a quasi periodic beam is generally homogenized into a homogeneous beam with equivalent properties,but the current methodology rarely involves the effective properties of quasi-periodic beam structures.In this paper,for the quasi-periodic beam structure mapped from a periodic beam structure,by introducing the Jacobian matrix,the unit cell equation and its effective property calculation formula are derived based on the asymptotic homogenization method.Based on the calculation formula,the finite element solution formula of the unit cell equation and effective stiffness are established.This method can deal with any micro cell deformed along the axial direction.The numerical examples verify its correctness and effectiveness.