中厚圆柱壳振型的有限元超收敛拼片恢复解和网格自适应分析  

Superconvergent patch recovery solutions and adaptive mesh refinement analysis of finite element method for vibration modes of moderately thick circular cylindrical shells

作　　者：王永亮[1,2] WANG Yongliang(School of Mechanical&Civil Engineering,China University of Mining and Technology(Beijing),Beijing 100083,China;State Key Laboratory of Coal Resources and Safe Mining,China University of Mining and Technology(Beijing),Beijing 100083,China)

机构地区：[1]中国矿业大学(北京)力学与建筑工程学院,北京100083 [2]中国矿业大学(北京)煤炭资源与安全开采国家重点实验室,北京100083

出　　处：《振动与冲击》2021年第18期112-118,147,共8页Journal of Vibration and Shock

基　　金：国家自然科学基金项目(41877275,51608301);中央高校基本科研业务费专项资金项目(2019QL02);天津市重点实验室开放课题基金项目(2017SCEEKL003);中国矿业大学(北京)越崎青年学者计划项目(2019QN14)。

摘　　要：该研究提出中厚圆柱壳振型的有限元(FE)位移超收敛拼片恢复方法,建立各阶振型的超收敛解,并基于振型超收敛解进行中厚圆柱壳自由振动的网格自适应分析。在给定有限元网格下,先应用常规有限元法(FEM)得到该网格下中厚圆柱壳频率和振型的有限元解,再引入超收敛拼片恢复方法和高阶形函数插值技术获得振型(位移)的超收敛解、通过计算Rayleigh商获得频率的超收敛解,随后利用振型超收敛解估计有限元解在能量模形式下的误差,根据误差进行网格细分加密并生成新网格,重复该过程,直到获得优化的网格和满足预设误差限的高精度解答。数值算例表明,该算法适于求解多类边界条件、环向波数和厚长比的中厚圆柱壳连续阶频率和振型,求解过程可靠有效、解答精确。A superconvergent patch recovery method was presented for superconvergent solutions of the vibration mode of each order in the finite element(FE)post-processing stage of moderately thick circular cylindrical shells,and the adaptive mesh refinement analysis for free vibration based on the superconvergent solution was implemented.On a given finite element mesh,the FE solutions of frequency and mode of the moderately thick circular cylindrical shell were obtained by the conventional finite element method(FEM).Then the superconvergent patch recovery displacement method and high-order shape function interpolation technique were introduced to obtain the superconvergent solution of mode(displacement),while the superconvergent solution of frequency was obtained by Rayleigh quotient computation.Finally,the superconvergent solution of mode was used to estimate the errors of FE solutions in energy norm,furthermore,the mesh was subdivided to generate a new mesh in accordance with the errors.The above procedure was repeated until the optimized mesh was derived and the accuracy of FE solutions met the preset error tolerance.The numerical examples show that the proposed algorithm is suitable for solving the continuous orders of frequencies and modes under different kinds of boundary conditions,different circumferential wave number and different thickness to length ratio of moderately thick circular cylindrical shells.The computation procedure is reliable and effective and can provide accurate solutions.

关 键 词：中厚圆柱壳 自由振动 振型 位移超收敛拼片恢复 网格自适应划分 有限元法(FEM) 

分 类 号：O242.21[理学—计算数学]