Dynamic analysis with linear and quadratic element

[JayEngSci]

Hi, I am simulating a bar (Abaqus implicit dynamic) which is loaded at the right end while fixed at the left end.
The displacement imposed at the right end is a cosine function, which lasts for one period.
The results were different when I used linear and quadratic elements. What may be the reason?

The peak value of the linear one will decay during wave propagation.
The following figures show the displacement when the wave reaches the left end.

Linear

Quadratic

 

[JayEngSci]

I guess this may be caused by the mesh size. When I refined the mesh size for the case of linear element, the decay is smaller.

Any guidelines on the mesh size for such problem?

 

[FEA way]

Which elements do you use, precisely ? What are their names in Abaqus nomenclature ?

 

[JayEngSci]

Linear: T2D2; Quadratic: T2D3

 

[FEA way]

The difference may be caused by the fact that first order elements use lumped mass formulation which is better able to capture wave propagation effects than consistent mass formulation used in case of second order elements. Of course mesh density may also play important role.

 

[JayEngSci]

Yes. The result by the quadratic element should be correct. The material is homogeneous and the peak value should be constant.