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工程力学  2014 

一种基于四边形面积坐标的四结点平面参变量单元

, PP. 15-22

Keywords: 四边形面积坐标,广义协调,四结点四边形单元,分片检验,网格畸变,有限元

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Abstract:

基于四边形面积坐标和广义协调原理,通过投影技术,并引入0~1区间上可连续变化的罚因子,构造了一款具有统一格式的四结点平面参变量单元AQGβ6-I。通过4组数值算例测试了单元性能,并将计算结果与许多著名单元对比表明:时,单元退化为原始格式,具有原始单元的全部优良性能;时,单元可以精确通过强分片检验,此时性能与许多著名单元基本相当,显著优于传统平面四结点等参单元(Q4);时,单元兼具较好的抗网格畸变能力和收敛速度。单元的构造方式对缓解一个有限元难题(通过常分片检验的四结点单元在弯曲问题中表现欠佳,而在弯曲问题中表现非常好的单元无法通过强分片检验)提供了有益思路。

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