Mindlin板弯曲和振动分析的高阶杂交应力四边形单元  

High-order hybrid stress quadrilateral element for Mindlin plate bending and vibration analysis

作　　者：李坦[1] 齐朝晖[1] 马旭[1] 陈万吉[1,2] 

机构地区：[1]大连理工大学工业装备结构分析国家重点实验室,辽宁大连116024 [2]沈阳航空航天大学辽宁省飞行器复合材料结构分析与仿真重点实验室,辽宁沈阳110136

出　　处：《大连理工大学学报》2014年第5期491-498,共8页Journal of Dalian University of Technology

基　　金：国家自然科学基金资助项目(11072156;11102037)

摘　　要：基于Mindlin板理论提出了一种高阶八节点杂交应力四边形单元.该单元不仅能通过零剪力分片检验,而且能通过非零常剪力增强型分片检验.单元边界位移插值采用任意阶Timoshenko梁函数,对不同厚跨比的四边简支、固支方板,以及圆板进行了弯曲和自由振动分析,数值结果表明无论对薄板还是中厚板,该单元均是准确和有效的,并且具有几何不变性.Based on the Mindlin plate theory,a high-order 8-node hybrid stress quadrilateral element is presented.The proposed element can pass not only the zero shear stress patch test,but also the non-zero constant shear stress enhanced patch test.The element boundary displacement is interpolated by arbitrary order Timoshenko beam function.The bending and free vibration of the simply-supported and clamped square and circular plate with different thickness and span ratios are investigated. Numerical results show that the element can be used to analyze both moderately thick and thin plates and it is efficient,accurate and geometric invariant.

关 键 词：杂交应力元 MINDLIN板 增强型分片检验 任意阶Timoshenko梁函数 集中质量矩阵 

分 类 号：O241.82[理学—计算数学] TU311.2[理学—数学]