摘要
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。
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 β∈[0,1]. The element performance has been tested by four numerical examples and compared with many famous elements. The results show that: when β=0 the element degenerates into its original formulation with all excellent performances; when β=1 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 β=0.5 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).
出处
《工程力学》
EI
CSCD
北大核心
2014年第7期15-22,共8页
Engineering Mechanics
基金
国家自然科学基金项目(51309261
51108472
41030747)
广东省自然科学基金项目(S2013040016764
S2011040005172
S2012010010446)
中山大学青年教师起步项目(39000-1188140)
关键词
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
quadrilateral area coordinate
generalized conforming
4-node quadrilateral element
patch test
mesh distortion
finite element
