基于点基局部光滑点插值法的结构动力分析  

Structural dynamic analysis using NPSPIM

作　　者：张桂勇[1,2,3] 鲁欢 王海英[4] 于大鹏 孙铁志[1] ZHANG Guiyong;LU Huan;WANG Haiying;YU Dapeng;SUN Tiezhi(Liaoning Engineering Lab for Deep-Sea Floating Structures,School of Naval Architecture Engineering,Dalian University of Technology,Dalian 116024,China;State Key Lab of Structural Analysis for Industrial Equipment,Dalian University of Technology,Dalian 116024,China;Collaborative Innovation Center for Advanced Ship and Deep-Sea Exploration,Shanghai 200240,China;School of Navigation and Marine Engineering,Dalian Ocean University,Dalian 116023,China)

机构地区：[1]大连理工大学船舶工程学院辽宁省深海浮动结构工程实验室,大连116024 [2]大连理工大学工业装备与结构分析国家重点实验室,大连116024 [3]高新船舶与深海开发装备协同创新中心,上海200240 [4]大连海洋大学航海与船舶工程学院,大连116023

出　　处：《振动与冲击》2018年第17期241-248,共8页Journal of Vibration and Shock

基　　金：国家自然科学基金项目(51579042;51639003);青年千人项目(D1007001);中央高校基本科研业务费专项资金(DUT16ZD218)

摘　　要：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.

关 键 词：动力响应 有限元 点基光滑点插值法 局部应变光滑 

分 类 号：O327[理学—一般力学与力学基础]