周期结构后屈曲新算法及其应用

A novel algorithm for post-buckling analysis of periodic structures and its application

提出了周期结构后屈曲分析的一种新算法。在屈曲点附近,通过加载模型和诱导后屈曲边值问题之间的相互切换,避开屈曲点附近刚度矩阵的奇异性,并诱导结构产生预期的后屈曲变形,避免了以往后屈曲算法中引入几何初始缺陷后对系统带来的可能影响。通过对三种由超弹性材料所构成的周期孔隙结构的后屈曲分析,验证了本文所提出的后屈曲算法的有效性和灵活性。分析了周期孔隙材料多向加载对屈曲模式转换的影响,以及后屈曲变形对弹性波传播带隙的影响,为周期结构中弹性波传播的调控提供良好的基础。

In this paper,a novel algorithm is proposed to simulate the post-buckling deformation of perio- dic structures under mechanical loadings. By switching between loading model and corresponding bound- ary condition model to induce the post-buckling deformation, the singularity of stiffness matrix around the buckling point is effectively avoided, and the post-buckling deformation can be triggered, which could eliminate the effect of geometric imperfections introduced by previous post-buckling algorithms. Through simulations of three 2D cellular solids made of hyperelastic materials,the validity and robustness of the new algorithm is verified. The transition among buckling modes through the control of bi-axial loading conditions is also discussed. It is further shown that the dynamic properties of the elastic wave propagation through the periodic structures can be tuned hy the control of the post-buckling deformation.