基于光滑有限元的加筋板静力自由振动和声辐射分析  

Static and Free Vibration Analysis of Stiffened Plates by ES-FEM with Triangular Element

作　　者：肖倩 朱仁传[1] XIAO Qian;ZHU Renchuan(State Key Laboratory of Ocean Engineering,Collaborative Innovation Center for Advanced Ship and Deep-Sea Exploration,School of Naval Architecture,Ocean and Civil Engineering,Shanghai Jiao Tong University,Shanghai 200240,China)

机构地区：[1]上海交通大学船舶海洋与建筑工程学院海洋工程国家重点实验室高新船舶与深海开发装备协同创新中心

出　　处：《中国造船》2019年第2期13-28,共16页Shipbuilding of China

摘　　要：基于光滑有限元思想给出了一个适当“软化”的有限元模型分析方法,即对原有的应变场分别运用基于边和节点的应变光滑技术进行光滑操作,构建边光滑Mindlin板单元和带权节点光滑三维简化梁单元,结合离散剪切间隙技术对加筋板的静力、自由振动和声辐射问题进行了分析.在声辐射分析中,运用瑞利积分求得结构的声辐射阻抗从而对结构进行分析.由于模型得到了适当的“软化”且成功避免了低阶Reissner-Mindlin板单元在弯曲过程中的横向剪切自锁问题,使得计算精度大大提高.数值计算结果表明,与传统的有限元相比,本模型能实现以低阶单元达到高精度的计算结果,且收敛速度更快.A relatively"softer"finite element model is presented.With application of edge and node-based strain smoothing operation,original compatible strain field is modified,and a three-node Mindlin plate element combined with a simplified three-dimensional thick beam element is constructed.Discrete shear gap(DSG)method is introduced to analyze the static,vibration and sound radiation of the stiffened plates.By using Rayleigh integral,it is possible to obtain sound radiation resistance of stiffened plates.This relatively nsofter"model is free of transverse shear-locking occurred in the low丒order Reissner-Mindlin plate element,which will greatly improve the accuracy.Improvement in accuracy and convergency compared to FEM is verified through several numerical examples.

关 键 词：加筋板结构 静力 自由振动 光滑有限元 声辐射 离散剪切技术 

分 类 号：O242.21[理学—计算数学] O312[理学—数学]