基于六面体体积坐标的新型8结点实体单元

8-node solid element based on the hexahedral volume coordinate method

六面体体积坐标方法是构造高性能三维实体单元的新工具。基于六面体体积坐标方法,构造了含有内参的8结点实体单元HV3D8。其基本位移场的形函数由点协调广义协调条件精确确定,并按照Wilson非协调元的模式进一步建立了单元内部位移场,这样使得该单元的位移场对整体坐标是二次完备的。数值算例表明:该单元在各种弯曲问题中不仅计算精度高,而且抗网格畸变能力优于其他同类等参元,显示了六面体体积坐标和广义协调理论相结合的特有优点。

The hexahedral volume coordinate method is a new tool for developing high-performance 3D solid finite element models. An 8-node hexahedral element HV3D8 containing internal parameters was successfully formulated using the hexahedral volume coordinate method. The shape functions for the fundamental displacement field of the element are exactly determined by the nodal-version generalized conforming conditions, while the internal displacement field is constructed using the Wilson＇s nonconforming element method. Thus, the entire displacement field for the element possesses second-order completeness in the global coordinates. Numerical results indicate that the element exhibits better performance than other conventional isoparametric models for various bending problems with mesh distortion. The results demonstrate efficiency of the HVCM and the generalized conforming theory for developing simple, effective and reliable finite elements.