高阶等参元在薄膜结构自由振动中的应用  

Application of High-Order Isoparametric Elements in Free Vibration of Membrane Structures

作　　者：乔海青 鲍四元[1] 邓子辰[2] 王博[2] QIAO Haiqing;BAO Siyuan;DENG Zichen;WANG Bo(School of Civil Engineering,Suzhou University of Science and Technology,Suzhou,Jiangsu 215011,P.R.China;School of Mechanics and Civil Engineering,Northwestern Polytechnic University,Xi’an 710072,P.R.China)

机构地区：[1]苏州科技大学土木工程学院,江苏苏州215011 [2]西北工业大学力学与土木建筑学院,西安710072

出　　处：《应用数学和力学》2025年第2期187-198,共12页Applied Mathematics and Mechanics

基　　金：国家自然科学基金(12172282);中央高校基本科研业务费。

摘　　要：薄膜结构是工程中广泛应用的结构之一,其自振特性的理论解与三角函数族有关,采用常规低阶单元分析时,有限元解精度不高.虽然h型有限元法将结构的网格细化后可提高有限元解的精度,但是其前处理相对困难,如果细化网格时出现畸变网格,那么有限元解的精度可能降低.基于p型有限元法构造两种用于研究薄膜结构自由振动特性的四边形高阶等参元,即节点数为16的Q16等参元和节点数为13的Q13等参元.不同形状和不同边界条件的薄膜结构算例表明,所提单元较常规低阶等参元有较快的收敛速率和较高的精度及计算效率.The membrane is one of the most widely used structures in engineering.Because the theoretical solution of the structure’s natural vibration characteristics is related to the trigonometric function family,the accuracy of the finite element solution is not very high by the conventional low-order element analysis.Although the h-type finite element method can improve the accuracy of the finite element solution with refined meshing of the structure,the corresponding pre-processing is relatively difficult,and the accuracy of the finite element solution may be reduced if the refined mesh is distorted.Based on the p-type finite element method,2 quadrilateral high order isoparametric elements,i.e.,isoparametric element Q16 with 16 nodes and isoparametric element Q13 with 13 nodes,were constructed to study the free vibration characteristics of membranes.Examples of membranes with different shapes and different boundary conditions show that,the proposed elements have faster convergence rates,higher computational accuracies and efficiencies than conventional low-order isoparametric elements.

关 键 词：薄膜自由振动 p型有限元 自振特性 

分 类 号：O327[理学—一般力学与力学基础]