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目前普遍采用的传统等参元族对网格的曲边、直边畸变均十分敏感。该文在已有的采用四边形面积坐标四边形4结点膜元基础上,构造了4个新型四边形广义协调曲边膜元5结点元ACG-Q5、6结点元ACG-Q6、7结点元ACG-Q7和8结点元ACG-Q8,形成一个完整的采用面积坐标的膜元系列。这4个单元列式简单、便于应用,且位移场实现了直角坐标的二次完备,单元精度高,对网格曲边和直边畸变都不敏感。算例表明这4个单元可以有效克服MacNeal梁、薄曲梁等传统等参元无法克服的多种闭锁现象。此外,通过这4个单元的建立还提供了一种将4结点单元推广到更多结点单元的一种通用方法。
At present, the traditional isoparameters are very sensitive to the curved edges and straight-edge distortion of the grid. Based on the existing four-membered quadrilateral 4-membered membranous element, a new type of quadrilateral generalized coordinating curved-membranous membranous 5-node ACG-Q5, 6-node ACG-Q6, The ACG-Q7 element and the 8-element ACG-Q8 form a complete series of membrane elements in area coordinates. The four elements are simple and easy to apply, and the displacement field realizes the quadratic completeness of Cartesian coordinates. The element has high precision and is insensitive to the distortion of the mesh and straight edges. The examples show that these four units can effectively overcome the various blocking phenomena that can not be overcome by traditional isoparameters such as MacNeal beams and thin curved beams. In addition, a common method of extending 4-node cells to more node cells is also provided by the establishment of these 4 cells.