一种基于四边形面积坐标的四结点平面参变量单元

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。

A 4-NODE PLANE PARAMETERIZED ELEMENT BASED ON QUADRILATERAL AREA COORDINATE

A 4-node plane parameterized element named AQGβ6-I is constructed based on quadrilateral area coordinate, a generalized conforming principle and projection technique with variable. The element performance has been tested by four numerical examples and compared with many famous elements. The results show that: when the element degenerates into its original formulation with all excellent performances; when the element can accurately pass strong patch test, its performance is same as that of many famous elements and significantly better than a bilinear-displacement quads isoparametric element (Q4); when the element is both well insensitive to distortion and convergence speed. It has also provided a useful method to alleviate a finite element trouble (The 4-node element has poor performance in bending problem but can pass the strong patch test. Conversely, it has excellent performance in bending problem but cannot pass the strong patch test).