Hi all,

I wanted to share with your a study I performed in the context of my apprenticeship that will end in August.

# Introduction

With @PP we had the idea to design a bridge structure that leverages our Generative Design solutions. In this context we decided to focus our study on the Paris Bir-Hakeim bridge which is very interesting as it is exposed to several constraints (wind, water flow, subway, vehicles, vibrations etc...)

**Note**: We used in introduction of this video a scene from **3DEXCITE **Planets Studio.

# Objectives

Our main objective is to leverage both **CATIA Functional Generative Design** and **CATIA Steel Construction Design** in order to find the best compromise between the performances and the manufacturing cost of the bridge.

# End to End Workflow

In order to perform this study we managed the following steps:

# Paris reconstruction

In this context we reproduced the Paris city with the objective to have some context in which we can design the new bridge structure with the right dimensions.

At first we used a digitalization file (.stl) of the center of Paris and then we used a manual tessellated segmentation to identify each building leveraging **CATIA Digitized Shape Preparation.** In addition we also added more than 20 remarkable buildings in the city (Eiffel Tower, Bridges, Trocadero etc...)

We reproduced the real Bir-Hakeim bridge with the right dimensions.

This bridge structure can be associated to a repeated pattern we decided to optimize 1/4 of the bridge. This considerations will be taken into account during the simulation and optimization processes through symmetry constraints.

# Generative Design

Based on the existing Bir-Hakeim bridge, we created a design space that respects all the initial dimensions and allow the River barge and vehicles to circulate in a proper manner. Then we identified the right loads and restraints that are applied over the structure.

Here we defined all the corresponding forces and restraints that are needed for the study:

__Loads - Subway: __

- We applied the pressure of the subway and an horizontal force which corresponds to the braking force of the subway.

__Loads - Wind____: __

- We defined the wind pressure on the frozen zones (for the railway and the roadway).

__Loads - Vehicles____: __

- We applied the maximum pressure that could be applied by a truck on the bridge deck.

__Loads - River ____Flow: __

- We specified the river pressure on the lower frozen zone that simulate a flood.

__Restraints____: __

- For this load case we applied symmetry constraints on one side and on the other side we allowed only the rotation in X

- At the bottom we create a pivot connection as we have on the actual bridge

(calculus in the ppt)

Then we performed the topology optimization, with the "maximize stiffness for a given volume" strategy and a targeted volume (27%) and then we managed the reconstruction leveraging **CATIA Imagine & Shape Design**.

**An important point is that we used the default mesh setting and member thickness. We could have used a reduced mesh size in order to have a more organic geometry with more arms (with a smaller section).**

# 1D Beam Reconstruction

We manually created the skeleton wireframe based on the optimized topology and we computed the equivalent beam profiles. In order to perform this computation we used the intersection between a mid plane (one per each wire of the skeleton reconstruction) and the bridge topology that gave us a surface in which we can calculate the inertia data (area, quadratic moments etc...) that allowed us to create a Beam Profile.

We performed the validation of the 3 different geometries (design space, manual reconstruction and skeleton with equivalent beam) we have seen before.

Then to minimize the overall cost of our bridge structure, we decided to perform a more manufacturable reconstruction using standards beams (such as L,U,T,W) and more specifically W beam which is Wide Flange Beam and also called H beams that are similar to I beams.

It is possible to manage either a reconstruction with the same standard beam type or with different standard type and each approach presents pros and cons.

In this context we decided to create a bridge structure using W Beams.

# Manufacturable Beam Dimension Optimization

In order to identify the right dimensions of the W Beam structure that would give us similar performances as the topology optimization or equivalent beam structure we decided to perform a parametric optimization.

We optimized the dimension of our W section using **SIMULIA Parametric Design Study**. We specified three type of W beams (based on the design space constraints and the optimization results) therefore we have 12 variables (4 variables per W beam Type).

We used a Design of Experiment in order to identify the best configuration to minimize the maximum displacement which respecting a given mass (from the topology optimization results)

At the end of the optimization we obtained a maximum displacement of 112.2mm with the optimized W beams which is lower than the maximum admissible displacement (180mm) for this bridge structure (calculus in the ppt- based on the bridge dimensions).

## Result

The W Beam reconstruction seems to have less good results than the topology optimization nevertheless it has the advantage to be more easily manufacturable and also easier to maintain (replacing elements etc...)

In addition, building bridges with a 3D Printing approach is not yet widely used as there are some limitation (size, materials, stiffness, aging etc..)

Exemple of bridge for the JO Paris 2024

# Manufacturing Reconstruction with Steel Connection Design

Leveraging the **CATIA Steel Connection Design** we can reuse the skeleton profiles and instantiate standard W Beam with the identified optimal parameters. In context we have 60 beams and 84 regular bracket connections for only 1/4 of the full bridge.

At the end we obtained the following KPIs

# xGenerative Design

We finished the project by creating a cover with the objective to hide the W beams of the bridge (with the help of @RK)

We import the external frontage of the bridge and we created a Voronoi pattern using random point placed over the surface. Then we created random holes and we obtain this modern cover.

There are variables such as the number of points that correspond to the number of Voronoi element and the number of holes.

__Final config :__

- Number of points = 600

- Number of holes= 100

# Live rendering

We applied appearance material to create a rendering scene as close as possible to the reality.

# Presentation

Thank you, please don't hesitate to share any feedback