abaqus自带的帮助文档(Getting started with abaqus-4.1)对沙漏的解释很清楚(这个是缩减积分单元自带的bug),大家可以细致评读、慢慢体会:
Linear reduced-integration elements tend to be too flexible because they suffer from their own numerical problem called hourglassing. Again, consider a single reduced-integration element modeling a small piece of material subjected to pure bending (see Figure 4–8).
Figure 4–8 Deformation of a linear element with reduced integration subjected to bending moment M.
Neither of the dotted visualization lines has changed in length, and the angle between them is also unchanged, which means that all components of stress at the element's single integration point are zero. This bending mode of deformation is thus a zero-energy mode because no strain energy is generated by this element distortion. The element is unable to resist this type of deformation since it has no stiffness in this mode. In coarse meshes this zero-energy mode can propagate through the mesh, producing meaningless results.
In Abaqus a small amount of artificial “hourglass stiffness” is introduced in first-order reduced-integration elements to limit the propagation of hourglass modes. This stiffness is more effective at limiting the hourglass modes when more elements are used in the model, which means that linear reduced-integration elements can give acceptable results as long as a reasonably fine mesh is used.