 # Tmms20 Structural Optimization Assignment 2

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Shape Optimization using TRINITAS

TMMS20 Structural Optimization

Assignment 2

Chen Baocheng – Baoch894@student.liu.se

Sergio Fernández Blanco  serfe814@student.liu.se

## Introduction

The purpose of this project is to model a road pole and use the finite element software TRINITAS to do a shape optimization. The process and results are shown in this report.

[pic 2]

Figure 1: Original design of the road pole. A car passing the bridge would drive into the paper.

We want to find the shape that has the lightest weight. In this case where the density of the structure is constant, it is equivalent to do a volume minimization. The original design of the road pole is shown in the figure 1. To simplify the model, we will just take advantage of the symmetry of the road pole and model half of it.

There are some design constraints that we need to consider modelling the structure:

1. The maximum Von Misses stress must not increase compared to the original design. We will need to check the Von Misses stress in the original structure and then restrict our optimization according to that value.
2. The line between A and B must not change in length or position. We should not set any design point in the A-B line.
3. The angle ϕ must be 90º. We need to specify that A and B are rigid connections.

## Procedure

To model and then optimize the shape of the structure, we use the TRINITAS software. the following steps are taken in sequence:

1. First of all, we start adding the points that will form the road pole. This is shown in figure 2.

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Figure 2: Points of the road pole

We just model half of the structure, as it was explained in the introduction.

1. Now we join the points and create the splines. As it is said in the instructions, we approximate the circular arc with four splines while, for the “legs” we create four splines on the outer side and two splines in the inner side, as can be seen in figure 3.

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Figure 3: Splines created

1. All the splines form the half road pole that we are modeling. Now we need to create a surface and then we create a volume with constant thickness. When the volume has been created, this symbol appears:[pic 5], as shown in figure 4.

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Figure 4: Volume created

1. Now we set the boundary conditions and constraints of the road pole:
1. First, we create the “Line Load” (figure 5) whose magnitude of force is (0, -2,0) but it is of no importance for the optimization, as the corresponding response of the structure is linear in the load.
2. Now we need to fix two lines (fixed displacements): the one which is in contact with the ground (we fix it in the X and Y directions) and also the one that sets the symmetry of the road pole (we fix it in only in the X direction. This can be seen in the figure 6.

[pic 7][pic 8]

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1. We create the Lagrange type Mesh and we scale it to be 810 quadratic triangular elements. The mesh can be seen in figure 7.

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Figure 7: Mesh

1. We can now analyze the model before the optimization and get the default values of our structure. The result of our analysis is shown in figure 8.

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Figure 8: Analysis

Its volume is 0.05204 and its maximum Von Misses stress is 9.128. We will configure our shape optimization to reduce the maximum the volume while keeping the maximum Von Misses stress value constant.

1. To configure the design parameters of the simulation, we go to the 2D shape optimization options and start configuring it.
1. First, we set the design points and their span. The outline of the road pole will be controlled by these points. The span will limit the range that the design points can move during optimization. This will let the shape of the road pole change inside our requirement. Our design points can be seen in figure 9 don’t exist near A points because one of the design constraints is that angle ϕ must be 90,[pic 14]

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Figure 9: Design points

1. Then we go to constraints and configure them as we need:
1. We create the C1 continuity in all the structure except the 6 corners. The C1 continuity can improve the smoothness between the connection of two splines.
2. Like we modeled half of the road pole, we need to set a constraint in the arc to make its two last points move the same amount in the vertical direction, and this way avoid having a sharp edge. To do that we use the “Couple Design Points in Global Y Direction”.
3. The maximum Von Misses stress of the optimized road pole should not increase beyond the limit. so, we set the Von Misses limit to 9.128.

The constraints of our structure can be seen in figure 10.

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Figure 10: C1 continuity and Couple in Y direction constraints

We can now run the optimization.

## Results

As seen in figure 11, the structure meets all the optimization requirements and the volume of our structure (previously 0.05204) turns into 0.03302. This represents a 36.55% volume reduction.

A good result is already obtained without modifying the default tolerance (0.01). Since we limited the maximum Von Misses stress, so it cannot exceed this limit in the optimized structure compared to the original design (9.128). As the optimized road pole reaches the maximum allowed value in its lower part, its thickness can´t be reduced furtherly due to the limit of maximum stress. For the top left part of the road pole, the volume is difficult to change because of the fixed height and 90 angle restriction. And for the right part which is the symmetrical line for the entire road pole, we avoid putting any design points on it because holes or sharp edge can be formed. Therefore, the optimal result has been achieved in the current design. However, to see if we can optimize the result further, we repeat the optimization by decreasing the tolerance to 0.0001. The result is the same, we get a volume of 0.03302, a volume reduction of 36.55%.[pic 17]

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