 # Coupled temperature-displacement

Dear CalculiX users,

recently some user had a question on the matrices in coupled temperature-displacement calculations.

In CalculiX they are symmetric, since the coupling is not taken into account in the matrix itself. The matrix in CalculiX consists indeed in a thermal conductivity matrix and a mechanical stiffness matrix, both of which are symmetric. Especially in the presence of convective networks (fluid flow adjacent to the structure) the true coupling would be very complicated. Furthermore, it may be ineffective, since convective network calculations require much more iterations than structural calculations (compressible fluid calculations are very nonlinear).

Since the calculation of an increment requires several iterations, the coupling is rather done from iteration to iteration. So after each iteration the temperature boundary conditions for the structure are updated based on the last thermal results and the pressure boundary conditions on the structure are updated based on the last network calculations. Furthermore, the displacement results from the last iteration are used in an update of the calculation of the viewfactors for thermal radiation.

In an uncoupled temperature-displacement calculation the temperatures are solved for first for the complete increment, and then the mechanical solution is obtained for the complete increment. So there is no coupling from iteration to iteration. It is as if you would have a *HEAT TRANSFER step followed by a *STATIC step.

hope this helps,

Guido

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If I understand correctly, this is referred to as a “staggered scheme”, is that correct? Where instead of having a monolithic system of equations (big stiffness matrix with coupling stiffness terms), they are decoupled, provided that the pseudo-time step is small enough. This is interesting, is there any theory that one can referr to where this implementation has been taken? Thanks!.