Simcenter 3D Solutions How to connect 2D with 3D elements for Multiphysics and SOL401 solutions

Background
A fairly common problem that reappears when performing FEM simulation is about how to connect 2D (shell) with 3D (solid) elements to maintain the propriate stiffness of the connection. This need may be caused by number of reasons where one of the most common is an optimization of solution time. Those elements have fundamental difference in the number of DoF as solid elements have only translations in X, Y and Z where shells have additionally rotation around X, Y and Z axes. As we are targeting Multiphysics solution, we are not able to use Edge-to-Surface Gluing which would be the simplest solution. This results in a risk that the model would not solve, or the results would be inaccurate due to inappropriate connection method. In this case we will also look at the temperature distribution on the connected parts as performing the Multiphysics solution with Steady-State type of thermal part of the model is our goal.

Problem description
A very simple model was prepared to better understand the problem (shown on fig.1). The model is divided in two main parts of the same length. The first is a solid body and the second one is a surface body. The surface body edge is touching the solid body face. For these studies also simple boundary conditions are defined. The model is structurally constrained on the vertical solid body face on the far end from surface body. Also, convection constrained is applied to that surface. The force in -Z direction on the surface body edge which is on the far end from solid body. Additionally, on the same edge a Heat Load was applied.

Figure 1. Problematic geometry.
To deal with that issue four approaches were tested:

1. Use of Element Edge to Element Face option in 1D Connection with Thermal Coupling.
2. Imprinting and Stitching of the surface body edge with solid body face and additionally meshing the solid body frontal surface with shell elements.
3. Extending the surface body so it will penetrate a solid body on depth of element size and Imprinting and Stitching the edges of the surface body on solid body faces.
4. Creating the frontal face for the surface body and mesh it with shell elements. Define the Gluing between frontal solid and surface faces.

Models preparation
1^st approach
This method does not require any additional geometry preparation and allows to use noncoincident meshes on surface body and solid body. At .fem level it’s needed to create 1D Connection. It is crucial to use Element Edge to Element Face option and when selecting the Source and Target it is important to use appropriate Smart Selector filter (accordingly Related Element Edge for element edges and Related Element Face for element faces). This allows the connection to update automatically when model changes. Next step is to define the Thermal Coupling between surface body edge and solid body face at .sim level. As a Primary Region a surface body edge should be selected and for a Secondary Region a solid body face (only that option was tested). Very high conductivity value should be defined. Connection zone is shown on fig.2.

Figure 2. Close-up view on connection zone for 1st approach.

2^nd approach
For this method the surface body edge should be Imprinted and Stitched with the solid body face. This can be achieved with Imprint operation at .fem level (Face Operations section under Polygon Geometry tab). It’s important to activate Stitch setting in Imprint operation options. After that the surface meshes can be created on both stitched surfaces and the solid body. The mesh should be conformal and connected (it should also be updated and maintained after model changes). It is important that the mesh of facial solid body surface would have the same properties (material and thickness) defined as the connected surface body. Connection zone is shown on fig.3.

Figure 3. Close-up view on connection zone for 2nd approach.

3^rd approach
In this case we need to Extend the surface body so it would penetrate the solid body at depth of one element size. In this method the surface body edges should be Imprinted and Stitched with the solid face. Also, the edge obtained from this operation on the frontal face of solid body needs to be Imprinted and Stitched with surface body. After that the surface meshes can be created on stitched surface body and solid body. The mesh should be conformal and connected (it should also be updated and maintained after model changes). It is important that the mesh of penetrated surface would have the same properties (material and thickness) defined as the rest of surface body mesh. Connection zone is shown on fig.4.

Figure 4.Close-up view on connection zone for 3rd approach.

4^th approach
This method is based on creation of the frontal surface face which will be part of the surface body. It should be wide as a surface body thickness to accurately represent the contacting are. In this method the surface body edges should be Imprinted and Stitched with each other. After that the surface meshes can be created on surface body. The mesh should be conformal and connected (it should also be updated and maintained after model changes). It is important that the mesh on frontal surface of surface body would have the same properties (material and thickness) defined as the rest of surface body mesh. The next step would be to define Gluing between frontal faces of solid and surface bodies. There’s no need for solid and surface body meshes to be conformal. Very high conductivity value should be defined.

Figure 5. Close-up view on connection zone for 4th approach.

Results comparison
Fully solid part was added to the comparison. This additional solid would be used as a reference model to which all the proposed solutions would be compared.
Structural results

Figure 6. Displacement contour plots.

Figure 7. Von-Mises contour plots.

Thermal results

Figure 8. Temperature contour plots.

Conclusions
From presented studies we can conclude that all four tested approaches allow to obtain very good approximation of the results comparing to the reference fully solid geometry. The deformation and temperature values are very close in each case. This means that all approaches should be appropriate to model the connection. However, all have their pros and cons.

The deviation occurs at stresses and 1st method produces biggest stress peaks at connection location. 3rd solution also shows slight jump of stresses in connection zone. 2nd and 4th solution are characterized by the smoothest stress distribution. The 1st approach doesn’t require additional geometry preparation but involves a need to define additional Thermal Couplings and causes highest local stress peaks. The 2nd approach requires very little of geometry preparation but involves adding additional meshes and adds mass which may impact transient thermal results (please see remark 1 at the end). It also shows the best correlation with reference model. The 3rd solution requires most geometry preparation and also adds additional elements and mass. The 4th approach involves relatively little additional work concerning geometry preparation and gives slightly worse results than 2nd method, however as 2nd and 3rd approach, it also adds additional elements and mass.

Due to mentioned stress inaccuracies it’s not recommended to take stress values at the connection as accurate ones. All presented methods should be created with enough distance from areas of interest, so the connection won’t affect the results in those places.

All mentioned factors should allow to select the most suitable solution for certain application. Despite the selection it is recommended to perform a validation of selected approach on larger model.

Remarks

1. In approaches with additional surfaces you can minimize the effect of additional mass by making a copy of the material of surface mesh and defining very small density value or/and specific heat. This would allow to obtain more accurate results for transient or dynamic simulations also. However, this was not tested and impact on solution stability and accuracy are not known. It may occur that Advanced Control parameter GPARAM 12 731 -1E36 may be needed to improve convergence.
2. The validation was made with FE element formulation setting.
3. To be able to use approaches 2 and 3 with CG element formulation it is possible that use of Advanced Control parameter FLAGPOLE/HINGE-DOOR EFFECT is needed to have a conduction heat path established between 2D and 3D elements.