# Fender Design Testing and Optimization with FEM

A **fender** can be defined as a bumper that absorbs kinetic energy during contact between berthing vessel and harbour jetty. Fenders are used to protect vessels and jetty of destruction during parking in the harbour and are produced from rubber or other elastomers. The main function of rubber fender is to absorb kinetic energy and lower reaction force.

The main goal of the analysis presented in this article was to perform structural analyses with SimScale to check the contact between a rubber fender and a yacht hull. The vessel has a speed of 1,5m/s and is pushing the fender connected to the jetty.

## Simulation Steps

The geometry of the model was created with a CAD software and imported to the SimScale CAE platform, where the meshing and definition of the model and material properties were done. This was done easily as SimScale supports several geometry formats: .STEP,. IGES, .BREP, .STL.

Besides the user-friendly interface which makes the simulation process faster, the documentation and public projects library definitely helped with questions and learning. As I already had experience with other commercial software, adapting to SimScale didn’t take long.

SimScale divides the analysis into three parts: mesh generator, simulation designer, and post-processor:

- Mesh generator – the user will import, modify, and create the geometry. In this step, the engineer will also create a mesh based on the geometry.
- Simulation designer – choosing the solver and analysis type, defining domain and contact type, and choosing contact areas. This step allows also to define the material and assign it to the geometry. The basic information used in simulations such as boundary conditions and initial conditions are defined in this part. At the end, the user runs the analysis.
- Post-processor – in the last step, the user is able to see the completed analysis and plot the needed results. I could plot the solver information such as the number of iterations and residuals. SimScale allows plotting simulation fields such as displacement, stress fields, etc.

## Structural Analysis of the Fender

The model was built from three parts: part of the vessel(1), fender(2), and jetty(3).

For this situation, some analytical calculations should be performed to select the type of fender. Below, you can see the analytical calculations of the fender with a picture of the vessel used for calculations.

The first step for the structural analysis is to find the stiffness of the fender and its energy absorption. For this, it is necessary to analyze it with a load of 1N. To continue it is needed to check the fender’s deflection, which is shown in the picture below.

The stiffness of the fender can be calculated as follows:

A contact analysis between the fender and vessel was done as well:

For numerical calculations, it is necessary to make some assumptions. Because only a part of the vessel is modelled, I needed to change the material’s density to keep a correct mass of the structure.

Next step is meshing the structure. For model discretization, 3D elements were used. The meshed model can be seen below:

The model was built from three elements and in this case, it is necessary to use contact definition for the connected parts. Contact between fender and jetty is defined as bonded contact. The connection between vessel and fender is defined as a physical connection with no friction.

The model was created with three types of material: fender – rubber, jetty – concrete, and vessel – steel (density 7,81 t/m^{3}).

The vessel’s velocity is defined as an initial condition with a value of 1,5m/s. The model is constrained on the sides of the jetty as fixed.

The next step of the analysis is to plot the stress fields, displacements, and deformation fields.

To be sure my calculations were correct, I prepared analytical calculations.

For verification of our results, we compared the kinetic energy between results of the numerical calculations with the kinetic energy received from analytical formulas.

Numerical calculations:

Analytical calculations can be found below:

The difference between the two results is 16%.

## Conclusion

During this **structural analysis**, a self-modelled shape of the fender was used. I did not have any specific information about energy absorption. Normally, fender producers will use specialized laboratories to find out more about the product’s properties, but in most of the times, this solution is quite expensive.

In my analysis, I used SimScale as a lab to find out more about the shape and its parameters. Deformation results of the fender gave possibilities to check energy absorption of the structure. By using **numerical analysis** (or CAE), engineers can analyze and optimize many shapes before the final one will be chosen and tested with a physical prototype.

This simulation was performed by Pawel Dereszewski from FEM NEWS.