CQUAD4 Formulation

LuisPiccino

Hello everyone,

 

By looking at OptiStruct Manual, I found that CQUAD4 Elements are formulated considering 'bubble shape functions' instead of the commonly used bi linear shape functions, and for this reason 5 integrations points are considered (in contrast with 4 points for the bi linear functions).

 

Does anyone know what are the main differences of these two sets of shape functions and how exactly the bubble shape functions can deliver a high order approximation of the displacement/stress fields without the addition of a node?

 

Thank you.

FaroukM

Hi Luis,

 

In general, the Hierarchical Bases produce, for the interpolation, an algebraic systems which are more robust and less susceptible to round-off error accumulation at high order.

 

I don't know the optistruct implementation. But let me tell you, that HB or the use of bubble functions enhance  the flexibility of the finite element especially in the bending behaviour. 

 

But you have to pay attention when you use this implementation for the large displacement - almost incompressible problem (think about the U-P hybrid formulation).

 

Good luck.