What is in this Article?

1. Introduction

2. Problem Description

3. Before We Start

4. Implementation

5. Results Verification

Figure 1.1. 1D cantilever beam problem workflow

Figure 2.1. Cantilever beam with a uniformly distributed load

The beam geometry and beam properties used in this example model are as follows:

• Total length (L) is 2 (m)
• Beam cross-section (mm): B = 37.5, b = 4.525, H = 65 and h = 4.525
• Young’s modulus (E) of material is 200e9 (Pa), Poisson (ν) is 0.3
• Mass density: 7850 kg/m³

Figure 2.2. The beam Cross-section

• A new collection in your Organization is required to store this model on Akselos Customer Dashboard (https://dashboard.akselos.com). Don’t know how? Read more Start building your asset with a new collection.
• Akselos Modeler – our simulation is required to build this model.
• A sample collection has been prepared for you to use as a reference. Find the Steel-Beams here on Akselos Dashboard.
• By default, you can use Akselos Cloud (available in Akselos Modeler).
  
  

Note: If you have trouble accessing to any of those prerequisites. Please contact us at: support @akselos.com

Follow the steps below to import the Steel-Beams collection into Akselos Modeler:

• In Akselos Modeler, click on the Cloud tab on Ribbons → Authentication → Enter your username and (password or token) → Click on the Check button and wait for Authentication status to turn green and show Authentication successful.

Figure 3.1. Checking authentication

• On the File tab, click on Import Collection… → On the Import Collection window, find and select Steel-Beams collection → Double-click on it or click on the Import button to pull the collection into your computer. You will receive a success message when the collection is successfully imported. 

Figure 3.2. Importing Steel-Beams collection into the local machine

• On the File tab, click on New Model → From Current Collection. The collection is ready to use after this step.

Figure 3.3. Opening the Steel-Beams collection

4. Implementation

In the Implementation section, we will show you a step-by-step in detail guide on how to analyze the basic 1D beam problem in Akselos Modeler.

Figure 4.1. 1D cantilever beam problem workflow

Step 1: Create Nodes

Figure 4.2. Create Model – Create Nodes

In Akselos Modeler, we use the Edit Beams tool to create the 1D beam. It is located on the Right Panel.

Figure 4.3. Edit Beams tool interface

Figure 4.4. Adding nodes' coordinates

Figure 4.5. Creating a beam from two nodes

A single beam may not give us good results compared to theoretical results. To increase accuracy, we should split the beam into several sub-beams.

Figure 4.7. Steps to split beam

Figure 4.8. A beam with four equal elements after splitting

Figure 4.9. Steps to merge beams

Figure 4.10. A beam after merging two elements

In this step, we will guide you to create and define cross-section. Then the process of applying it to the beam model.

• In the Model ribbon on the left panel, right-click on Model → Add Property → Cross-Sections. The group of cross-sections will be created with one default item. You can add more Cross-sections in the group by right-clicking on the group → Add Property → Crosssectiongroupitem or delete them by clicking on then pressing the Delete button. Each item has an ID number on the right, it starts from 1 with the default item. The ID number is used to assign the cross-section to the model.

Figure 4.12. Creating CrossSectionGroup

Figure 4.13. Defining Cross-section properties

Figure 4.14. Assigning cross-section to model

• In the Model ribbon on the left panel, right-click on Model → Add Property → Materials. The group of materials will be created with one default item. You can add more Materials by right-clicking on the group → Insert Property → Materialgroupitem or delete them by clicking on then pressing the Delete button. Each item has an ID number on the right, it starts from 1 with the default item. The ID number is used to assign the material to the model.

Figure 4.16. Creating MaterialGroup

Figure 4.17. Defining material properties

Figure 4.18. Assigning material to model

Once you have defined and assigned the material and cross-section to the beam, you can visualize it in the Graphic Window by enabling Show Beam Cross-section in the Configure view settings. Note that you need to assign both properties to the model for the Show Beam Cross-section tool to work properly. After viewing the cross-section, you should disable it to make it easier to work in the next step.

Figure 4.19. Showing beam model with cross-section on the Graphic Window

Before we solve the model, we need to apply boundary conditions. Boundary conditions specify how the beam is supported or fixed at its ends or along its length. In this tutorial, we will apply the boundary condition by fixing the node at the end of the beam.

A related article that is useful for you to know and implement in this section: Boundary Conditions.

• To visualize the model's ports and boundaries in the Graphic Window, enable the Unconnected Ports and Boundary Conditions options in the Configure view settings.

Figure 4.21. Turning on Unconnected Ports and Boundary Conditions options

• Change to the Mesh Elements selection mode → Select the node at the end → Right-click on the Graphic Window →Create Node Port.

Figure 4.22. Creating Node Port

• To constrain the node port, select it → See the Property Tree and select (x. y, z, theta_x, theta_y, theta_z) in Constraint Type. After that, the black point will appear at the port, it performs that the port is constrained successfully.

Figure 4.23. Constraining node port

Figure 4.24. The beam model with the constrained node

In this step, we will apply load on the model. For beams, we can apply four types of loads: Point load, Linear distributed load, Partial distributed load, and Self-weight. For this example, the model only has one uniformly distributed load W = 1000 N/m, therefore we can choose the Linear distributed load type.

Some articles are useful for you to implement in this section: Stored Selection, Create Load Case and Load.

• Stored Selection: Firstly, we need to have a stored selection to apply load on. Change to Subdomains selection mode → Select the beam on the Graphic Window→ Right-click then press Store current selection. The stored selection item will appear under Stored Selection on the left panel.

Figure 4.26. Steps to store model for applying loads

• Load Case: On the left panel, right-click on Load Cases → Add Load Case → Right-click on Load Case 1 → Add load... → The  New Load Case / Load window will appear, select Linear Distributed Load With Moment → Click on the Save button.

Figure 4.27. Creating Load Case and Load

• Click on Linear Distributed Load With Moment 1 → See the Property Tree, select the Stored Selection which is stored above  → input parameters as in the figure below.

Figure 4.28. Creating Linear Distributed Load

Figure 4.29. Load visualization

For the 1D beam element problem, we can only solve it with the FEA solver.

• Set Solver Option:
  • Under Solver Options on the left panel, there is the default - RB-FEA Options. We can use it with some changes. Click on RB-FEA Options → See the Property Tree and change Solver Strategy to FEA. After changing, the name of the default solver will automatically change to FEA Options.

Figure 4.31. The default Solver Option

Figure 4.32. Setting FEA Solver

Figure 4.33. Adding some fields on Solver Option

• Under Scenario on the left panel, there is Default Scenario and we use it. Click on Default Scenario → See the Property Tree and set the coefficients of Load Case 1 to 1.0.

Figure 4.35. Setting Scenario

• Set Solve List: Since there is only one scenario, select the default in Solve List to check that the default scenario is turned on.

Figure 4.36. Setting Solve list

Now you can proceed to solve the model. Firstly, you have to save the aks file to save all settings of the model → Sync the collection to Akselos Dashboard → Run solving.

• Save aks File:
  • Click on the File tab →Save

Figure 4.38. Saving aks file

Figure 4.39. Naming and saving aks file

• Sync Collection:
  • Change to the Collection ribbon → Click on Repository... → Sync

Figure 4.40. Syncing collection

Figure 4.41. Committing for synchronization

• Run Solving:
  • Change to the Solutions ribbon → Click on the Solve button. The solving request will be submitted to Akselos Cloud. You will see the status of this request on the Solution tree. You can see the results once the solving is done, which is usually within seconds with Akselos solver. 

Figure 4.42. Solving model

After a few seconds, you should receive the solution as shown in Figure 4.52. To visualize the solution, you need to change the Solution Field on the Graphic Window.

 Figure 4.43. The Solution returned after solving

There are some solutions of the model after solving:

• Displacement z: maximum = 0.01953 (m)

Figure 5.2. Displacement z

• Shear force: maximum = 2000 (N)

Figure 5.3. Shear force

• Bending moment: maximum = 2000 (Nm)

Figure 5.4. Bending moment

To validate the results obtained from Akselos' solution, we compared Akselos's results with theoretical results, which turned out to match each other as shown in the following table.

The maximum deflection of the beam is given by the formula:

Where I is the moment of inertia. For the beam cross-section considered here, I = 514247 mm⁴.

Table 5.1. Comparison between Akselos's solution and analytical solution

Related Articles & Similar Case Studies:

• Before we start - Overview of Akselos Simulation Procedure
• Cantilever Beam with 2D Shell Elements
• Cantilever Beam with Solid Elements
• Pushover Analysis with 1D Beam Element