Mindlin板弯曲和振动分析的高阶杂交应力三角形单元  

HIGH-ORDER HYBRID STRESS TRIANGULAR 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]大连理工大学工程力学系,大连116024 [2]沈阳航空航天大学航空宇航工程学院,沈阳110136

出　　处：《工程力学》2015年第10期31-37,共7页Engineering Mechanics

基　　金：国家自然科学基金项目(11072156;11102037)

摘　　要：现有的Mindlin板单元只能通过零剪力分片检验,而不能通过非零常剪力分片检验。该文根据ReissnerMindlin一阶剪切变形理论,基于余能原理,提出了一种高阶杂交应力六节点三角形Mindlin板单元。该单元特点是不仅能通过零剪力分片检验,而且能通过严格的非零常剪力增强型分片检验。构造单元时特别注意了单元边界位移以及域内应力的插值函数的选取。采用任意阶Timoshenko梁函数作为边界位移插值函数,应力插值函数选取为满足平衡方程的多项式。对不同厚度不同边界条件的方板进行弯曲和自由振动分析,质量矩阵采用集中质量阵。数值结果表明无论对薄板还是中厚板,该单元均是准确有效的。Current patch test for Mindlin plate element only satisfies the zero shear deformation condition, while the non-zero constant shear condition cannot be satisfied. Based on the Reissner-Mindlin theory, i.e. first-order shear deformable theory and complementary energy principle, a 6-node higher-order hybrid stress triangular element is presented for Mindlin plates to pass both the zero shear patch test and the non-zero constant shear enhanced patch test. For this purpose, special attention is devoted to selecting boundary displacement interpolation and stress approximation in domain. The arbitrary order Timoshenko beam function is used successfully to derive the boundary displacement interpolation. According to the equilibrium equations, an appropriate stress approximation is rationally derived. This paper discusses the application of the proposed element to the bending and free vibration of plates with different boundary conditions and thicknesses, and the lumped mass matrix is adopted. Numerical results show that the element can be used to analyze both moderately thick and thin plates efficiently and accurately.

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：O242.21[理学—计算数学]