Mindlin板理论高阶精化杂交应力元及稳定性分析  

High order refined hybrid stress element and stability analysis of Mindlin plate theory

作　　者：马旭 闫守浩 李坦 MA Xu;YAN Shouhao;LI Tan(College of Science,Yanshan University,Qinhuangdao 066004,China)

机构地区：[1]燕山大学理学院,河北秦皇岛066004

出　　处：《浙江工业大学学报》2024年第2期172-179,共8页Journal of Zhejiang University of Technology

基　　金：国家自然科学基金资助项目(11702242);河北省自然科学基金资助项目(A2019203403)。

摘　　要：基于Mindlin板理论,构造了杂交应力四边形8节点单元QA8-R。采用任意阶的Timoshenko梁函数构造了三阶边界位移插值函数,该函数确保单元能通过严格的收敛检验。利用Airy应力函数构造了单元域内应力插值函数,该函数包含21个最优选择的应力项。通过精化元方法构造了组合几何刚度矩阵,建立了屈曲分析的有限元列式。数值算例结果表明:QA8-R单元不仅可以通过C^(0-1)分片检验,保证了单元的严格收敛性,而且在不同边界条件下对中厚板的计算精度较高,更易于工程应用。Based on the Mindlin plate theory,the hybrid stress quadrilateral 8-node element(QA8-R)is constructed.The 3rd-order boundary displacement interpolation function is constructed using the arbitrary-order Timoshenko beam function,which ensures that the element can pass the strict convergence test.The Airy stress function is used to construct the intra-domain stress interpolation function,which contains 21 optimally selected stress terms.The combined geometric stiffness matrix is constructed by the refined element method,and the finite element column formula for buckling analysis is established.The numerical example results show that the QA8-R element can not only pass the C^(0-1)patch test,ensure the strict convergence of the element,but also have high calculation accuracy for moderately thick plates under different boundary conditions,which is easier for engineering application.

关 键 词：MINDLIN板理论 杂交应力元 Ariy应力函数 任意阶的Timoshenko梁函数 

分 类 号：O242.21[理学—计算数学] TU311.2[理学—数学]