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工程力学  2015 

基于单元应力级数展开的下限原理有限元法

DOI: 10.6052/j.issn.1000-4750.2014.02.0104

Keywords: 下限分析,有限元法,Taylor级数,稳定性,极限荷载

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Abstract:

基于Taylor级数,将三角形单元内的应力场在三角形单元中心点处展开,从而可以借助于中心点应力及应力场梯度来表达整个单元应力场,再利用平衡方程中应力场梯度之间的线性关系,使单元中未知量的个数从9个减少到7个。由于已经满足了平衡方程,因此得到下限问题的数学规划模型不仅减少了变量的个数,而且也减少了等式约束的个数,从而降低了模型的规模。该方法丰富了下限原理有限元法的理论,为进一步提高求解效率打下了基础。计算结果表明与经典Sloan方法得到的结果完全一致。

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