基于点基局部光滑点插值法的结构动力分析

Structural dynamic analysis using NPSPIM

针对传统有限元法采用线性三角形单元刚度过硬、计算的固有频率值较大,四边形单元对复杂构件不能自动剖分,点基光滑点插值法刚度过软、会导致计算动力问题失败以及求解固有频率值过低的问题,提出了点基局部光滑点插值法(NPS-PIM)。该方法将有限元与点基光滑点插值法结合,对背景网格基础上形成的点基光滑域剖分、进行局部应变光滑,计算结构的动力问题。研究发现,该方法克服了点基光滑点插值法的时间不稳定性和求解固有频率值过低的缺陷;在采用同样线性三角形单元网格对问题域进行离散的情况下,计算得到的固有频率较传统有限元法有明显提高。该方法简便实用、易于实现,具有较好的工程应用前景。

Aiming at problems of linear triangular element used by the traditional finite element method(FEM)having an over-hard stiffness and computed structure natural frequencies being larger,while the node-based smooth point interpolation method(NS-PIM)causing over-soft stiffness and making dynamic computation failure and computed natural frequencies too smaller,a node-based partly smoothed point interpolation method(NPS-PIM)was proposed here.This new method combined FEM and NS-PIM through partly strain smoothing operation to compute structural dynamic problems.It was shown that the proposed method overcomes NS-PIM’s deficiencies of time instability and solved natural frequencies too smaller;the same linear triangular element mesh was used to discretize a problem domain,the natural frequencies computed with the new method are more accurate than those with the traditional FEM;the new method is simple and easy to implement,and it has better prospects for engineering application.