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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β,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:β=0时,单元退化为原始格式,具有原始单元的全部优良性能;β=1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);β=0.5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。
Based on the quadrilateral area coordinates and the generalized coordination principle, a four-node planar parametric unit AQGβ6-I with a uniform format was constructed by introducing projection technique and introducing penalty factor β, which can vary continuously from 0 to 1. The performance of the element is tested by four numerical examples. The comparison between the calculated result and many well-known elements shows that when β = 0, the element degenerates into the original form and has all the good properties of the original element. When β = 1, the element can accurately pass Strong fragment inspection, performance at this time and many well-known unit is basically the same, significantly better than the traditional planar four-node isoparametric unit (Q4); β = 0.5, the unit has both good anti-grid distortion ability and convergence speed. The construction of elements provides a useful way to alleviate a finite element problem (the four-node element of a regular piece-piece test does not perform well in bending problems and the unit that performs very well in bending problems fails strong piece-wise testing) .