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工程力学  2015 

Mindlin板弯曲和振动分析的高阶杂交应力三角形单元

DOI: 10.6052/j.issn.1000-4750.2014.03.0153, PP. 31-37

Keywords: 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

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Abstract:

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Reissner-Mindlin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。

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