How to avoid merging nodes or equivalencing meshes in Finite Element Analysis?

Merging nodes is a step common in Finite Element Analysis and is traditionally done when adding a mesh transition or connecting meshes together. Unfortunately the process of merging nodes or equivalencing nodes is a time consuming process.

In this post, an alternative to merging nodes is mentioned that is easier and can get you faster to your goal of calculating stresses, deformations, and loads.

before_after_mesh_transition_merging_nodes

To start off, why are merging nodes necessary.

Refer to the animation below. At first, the FE mesh representing the structure appears as one continuous structure, but in fact, has a piece of mesh that is disconnected from the rest of the structure. The interfaces of this separate piece contain points or nodes of its own that overlap with the nodes of the other meshe. A Finite Element Analysis (FEA) software application will be unable to perform a strength analysis on such a mesh configuration. The mesh has to be intact or one continuous piece before an FEA application can evaluate the model. For the FE mesh to be one continuous structure, the nodes at these interfaces have to be merged or equivalenced.

A mesh such as the one shown below is not suitable for most FEA software packages. Reason being, many of the nodes are unaligned and duplicate nodes exist. For clarification, such unaligned nodes and duplicate nodes have been marked in red.

region_where_merging_nodes_is_necessary

In order to evaluate this structure, the mesh must be such that all the nodes align and that nodes are not overlapping. The image below is an example of a mesh that has aligned nodes with no duplicate nodes. As mentioned at the beginning of the post, this process is quite time consuming and brings us to our alternate method of merging nodes.

mesh_transitions

For the remainder of this article, we will be focusing on this example. A plate with fillets is fixed on one end and a total load of 300 lbf is applied on the opposite end. The goal is to determine the maximum stress, which occurs at the fillets. Material properties: E = 30e6 psi; v = .3.

plate_with_fillets_fixed_total_load

Here is the example using shell elements. Since we know the maximum stress is at the fillets, the region around fillets should have a fine mesh. The rest of the plate can have a coarse mesh. Earlier I mentioned meshes should either be intact or continuous in order for an FEA application to successfully analyze.

Since this mesh is not continuous, it should be intact in order to be solved by an FE application. This is where we use Glue.

fine_mesh_for_detailed_stress_analysis

When I use Glue in this post, I am not referring to an actual adhesive used to connect physical components. Glue in MSC Apex is a virtual method of attaching FE meshes. Generally, when Glue is applied, it enforces a requirement that the interfaces of the meshes act in unison when displacing. This achieves a comparable result compared to continuous meshes that were equivalenced.

Below is a depiction of the Glue region for the bottom fillet.

glue_regions_fea_mesh

Now, how does the maximum stress of the mesh with Glue compare to a normal continuous mesh? As can be seen below, the max von Mises stress values of 2060 psi and 2070 psi are aligned with each other. This is good. It means:

  1. The stress result of the Glue mesh can be used for writing margins of safety.
  2. The process of creating a mesh with Glue is significantly faster than creating a continuous mesh that would require merging nodes or equivalencing meshes.
  3. You get to go home early since you saved yourself all the time of merging nodes.

stress_comparison

How applicable is Glue? Below are variants of the same example using a variety of different shell and solid elements. Note that the maximum stress in each example are aligned with each other. Glue can be used in many different meshing scenarios, which means you can apply Glue to many different structural models, including yours. Instead of merging nodes and equivalencing meshes, perhaps take some time and explore the use of Glue next time you have a chance. Feel free to click on the image to get a closer look.

stress_results_usinglue

 

 

Edit: After I finished this post,  I forgot to include one meshing scenario that is definitely worth mentioning. As the image below shows, meshes of different topologies can be glued together and can yield useful answers. In the image below, shell and solid elements are used. Solid elements are used in the region where accurate stress answers are necessary. Note the maximum von Mises stresses of 2080 and 2060 psi are in agreement with the results from the previous mesh examples.

global_local_stress_analysis

Watch a video demonstration on YouTube

Another tip, for more complex geometry, feel free to TET mesh portions of the geometry that are otherwise difficult to HEX mesh. Then use Glue to connect the meshes. This can help you move through your FEA workflow faster and help you write your stress margin reports sooner.

fea_mesh_tet_hex_elements

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