# Axial Deformation: Manual Calculations vs SolidWorks Simulation

Axial Deformation manual calculation vs CAD simulation of aluminum tapered strap

1. ### Step 1: Axial Deformation of tapered ends of strap

Equation for Tapered ends:

Def = (P*L/E*t*(d2-d1)*[ln(d2/d1)]; this is for a tapered plate

Using the problem from Hibbeler's Statics & Mechanics of Materials 5th Edition, the axial deformation of the two tapered ends is calculated as shown:

2. ### Step 2: Axial deformation of constant cross-section

Def = PL/AE or Def = N*L/A*E ; this is for Constant Cross Section.

Adding the axial deformation of the tapered ends plus the axial deformation of the 800 mm section gives us 2.371 mm total deformation as shown above.

3. ### Step 3: Create the solid model in SolidWorks

Create the simple shape as a solid model in SolidWorks

If the system you are using has the Simulation Package available, add the menu to the Pull-down menu options. If the system does not have this added package, Simulation Express should be used instead which does not require this step. Simulation Express is very user friendly and can solve this problem with similar results.

5. ### Step 5: Set up Simulation Steps

From the Pull-down menus, select Simulation, Static Analysis, and then select ok (green check).

From the Pull-down menus, select Simulation, Material, Apply Material to All, then from the open dialogue box select a material that matches the Modulus of Elasticity (or Elastic Modulus) of the material in the problem. In this case we can select Aluminum 5052-H36. Note that the Elastic Modulus is 7e+10 N/m^2 which is 70X10^6 Pa.

Alternatively, a new material can be created and added to the user-defined materials if other properties are needed to match a specific material that is not available in the SolidWorks library of materials.

6. ### Step 6: Assign the Restraints on the model

From the Pull-down menus, select Simulation, Load/Fixtures, Fixture, and then Fixed Geometry. Then select or pick one end or the face of the model to place a fixture or a fixed end so that end can not move from it's location due to the load that will be placed next. Select ok.

7. ### Step 7: Place a load on the other end of the strap

From the Pull-down menus, select Simulation, Loads/Fixture, Force. From the Force/Torque dialogue box, make sure the Force option is selected, then pick the face of the other end of the Aluminum strap. Change the force value in the dialogue box to the force given in the problem (30,000 N), and then pick the Reverse Direction if necessary so the force is pulling on the end of the strap, the select ok.

8. ### Step 8: Create the mesh in the solid model

From the Pull-down menus, Select Mesh, Apply Control. When the dialogue box opens, select the name of your model at the upper left corner of the graphics window so that the model name appears in the dialogue box labeled 'Selected Entities.' The Mesh Density may be increased some by sliding the density indicator slider to the right about half way between the mid point and the Fine point. Select ok.

Now, from the Pull-down menus, Select Mesh, Mesh Create. From the open dialogue box, the Mesh Density may again be increased by sliding the indicator slightly to the right. Select ok.

The mesh should now fill in the entire solid model with small prismatic elements, a finite number of elements or a FEM (finite element model).

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9. ### Step 9: Run the Analysis

From the Pull-down menus, Select Run, run. The default view after running the analysis shows the stress in a von Mises stress color chart. The default is also in Metric units of stress of N/m^2 or Pascals. The units can be changed by right clicking on the Stress feature under Results in the Feature Manager Tree, and then selecting Edit Definition.

The dialogue box to change the units or other options are shown.

Now change to displaying the axial deformation results by right clicking on the Displacement also under the Results feature in the Feature Manager Tree. Note that the total displacement or axial deformation is similar to the values that were calculated manually.

From a video tutorial of this process, here is one available in YouTube: