薄膜横向振动的有限元分析  

A triangle element for finite element analysis of membranes

作　　者：林文静[1] 陈树辉[1] 

机构地区：[1]中山大学工学院应用力学与工程系,广州510275

出　　处：《应用力学学报》2011年第1期44-49,109,共6页Chinese Journal of Applied Mechanics

基　　金：国家自然科学基金(10972240)

摘　　要：构造了一种3节点三角形膜单元,以适用于平面薄膜横向振动的有限元分析。在给出单元形函数的基础上,根据最小势能原理建立了薄膜自由振动方程,并推导了单元刚度矩阵和单元质量矩阵。研究结果表明,单元刚度矩阵和单元质量矩阵形式简单,且自由度少;通过两个典型算例,证明3节点三角形膜单元的计算结果非常接近理论解,同时可以达到很高的精度。A pre-tensioned 3-node triangular element is constructed for the free vibration analysis of membranes by finite element.The shape functions are given to derive the element stiffness and mass matrices in accordance with the minimum potential energy principle.The element stiffness and mass matrices are very simple in form with few degree-of-freedoms.Two typical examples show that the calculation results by the 3-node triangular element is very close to those of theoretical solution.It has high accuracy.

关 键 词：薄膜横向振动 有限元分析 3节点三角形膜单元 固有频率 固有振型 

分 类 号：O327[理学—一般力学与力学基础] TU311.3[理学—力学]