弹性地基圆形加肋板静力弯曲及弯曲自由振动分析的无网格法  

Meshless method for static bending and free bending vibration analysis of stiffened circular plates on elastic foundation

作　　者：彭林欣[1,2,3] 谌亚菁 覃霞 杨健生[1] PENG Linxin;SHEN Yajing;QIN Xia;YANG Jiansheng(School of Civil Engineering and Architecture,Guangxi University,Nanning 530004,China;Guangxi Provincial Key Lab of Disaster Prevention and Engineering Safety,Guangxi University,Nanning 530004,China;MOE Key Lab of Disaster Prevention and Structural Safety,Guangxi University,Nanning 530004,China)

机构地区：[1]广西大学土木建筑工程学院,南宁530004 [2]广西大学广西防灾减灾与工程安全重点实验室,南宁530004 [3]广西大学工程防灾与结构安全教育部重点实验室,南宁530004

出　　处：《振动与冲击》2022年第7期11-22,30,共13页Journal of Vibration and Shock

基　　金：国家自然科学基金资助项目(11562001,11102044);广西重大研究计划(桂科AA18118029)。

摘　　要：基于一阶剪切理论和移动最小二乘法,提出分析弹性地基圆形加肋板线性弯曲的静力和自由振动问题的无网格方法。对弹性地基采用Winkler地基模型,对圆形加肋板则将平板和肋条分开考虑,通过位移协调条件建立两者的参数转换方程。平板和肋条均采用一系列点来离散,用移动最小二乘法建立的形函数来分别描述两者的位移场,再分别通过最小势能原理和Hamilton原理导出弹性地基的静力弯曲和弯曲自由振动控制方程,最后采用完全转换法处理边界条件。以一系列不同基床系数、荷载、边界、肋条布置方式的弹性地基圆形加肋板为例,研究所提出方法的收敛性和稳定性,并将计算结果与有限元、文献结果对比。研究表明该方法可以有效分析弹性地基圆形加肋板线性弯曲的静力和自由振动问题,且肋条位置改变时,可避免网格重构。Here,based on the first-order shear theory and the moving least square method,a meshless method was proposed to analyze static and free vibration of stiffened circular plates on elastic foundation.Winkler foundation model was used for elastic foundation.Circular plate and rib were considered separately for a ribbed circular plate,and parameter conversion equations of both two were established with displacement coordination conditions.The plate and rib were discretized using a series of points,and shape functions established using the moving least square method were used to describe their displacement fields,respectively.Then,static bending and free bending vibration governing equations of elastic foundation were derived using the minimum potential energy principle and Hamilton principle,respectively.Finally,the complete transformation method was used to deal with boundary conditions.Taking a series of stiffened circular plates on elastic foundation with different subgrade coefficients,loads,boundaries and rib arrangements as examples,the convergence and stability of the proposed method were studied,the calculation results were compared with those obtained using finite element method and those published in literature.The results showed that the proposed method can effectively analyze static and free vibration problems of stiffened circular plates’ linear bending on elastic foundation;the grid reconstruction can be avoided when rib positions are changed.

关 键 词：弹性地基 圆形加肋板 线性弯曲 自由振动 无网格 

分 类 号：TU339[建筑科学—结构工程]