ANALYSIS OF 2D SHELL ELEMENTS USING MESHING PROPERTIES

Aim

1.Using the crash beam file from the previous assignment, change the run time to 55 ms.

2. Change the number of animation steps during simulation to a minimum of 25 and maximum of 60.

3. Run the base simulation without any modification to element properties.

4. At the end of the simulation, do the energy error and mass error checks and determine whether results would be acceptable.

5. If acceptable, Plot rigid wall forces, internal energy, hourglass energy, contact energy, total energy of the simulations.

Solution

We will first discuss the properties and their recommended values so that we get good results :

1.Ishell

Ishell can be categorized into :

a.Q4

b.QBat

c.QEPH

These above ones are used for quad elements and for trias we have C0.

Now  Q4 AND QEPH have reduced integration and have relative cost of 1 and 1.15 respectively.By reduced intergartion we mean that there is basically one integration point on the element ,this master point takes average from the other 4 nodes and calculates the results ,the drawback is that it has compartively lesser accuracy but gives us the benefit of reduced time .Full intergration gives us the more accuracy but takes more time to compute.

Hence we need Ishell element which has more accuracy but takes less time to compute and thats why we select QEPH type because its between the two.

Recommended Ishell :QEPH

Ishell:24

2.Ismstrn

It tells us that if the deformation taking  place is small deformation or large deformation and accordingly it will solve the equations depending on the deformation as the plasticity of the material changes aove the yield point.

Recommended Ismtrn:2

3.Ish3n

This is used for 3 noded elements are created and generate their equations at these nodes ,these should be minimised as possible as they give inaccurate results .

Recommended Ish3n:2

4.N

This is the no of integration points and the number of integration and the recommended value is 5.

5.Iplas

This is a property which helps to calculate the stress beyond the yield point of any material and changes the elasticity accordingly .It helps to calculate the strain and the strain rate .

Recommended value:1

Now we will go with the analysis of the given component as shown below:

Now we will run the simulation without the recommended properties:

As you can see the properties have not been modified and are used as default.

Now we will change the run time to 55 seconds as shown:

Now we have simulated the model for 55 seconds as shown below:

We have loaded the animation file as shown below:

Since the maximum anime step is 60 and minimum step is 25 ,we will select a step of 50 and therefore frequency is given by 

Frequency = run time/anime step

                =  55/50 

                =   1.1

Now we will define energy error as the following:

Energy error =  current energy - reference energy - work done / max(current energy ,reference energy,kinetic energy)

where Reference energy = internal energy + kinetic energy + hourglass energy

current energy = internal energy + kinetic energy + hourglass energy 

work done = work done by constraints + work done by loads + work done by elements

Now whenever there is energy error it means that some amount of energy has been dissiapated into the surrounding because of the above mentioned energies now our aim should be to keep energy error as close to zero that is the enrgy of the sysytem be conserved. The system should not gain energy nor should it remove energy ,it should be constant throughout ideally.

Ideally energy error should be between -15 and -5 ,for QEPH models and fully integrated models the energy can be slightly positive as there is no hourglass energy.

Now we will check for energy error for the given component :

The energy error begins form 0 % and goes upto a maximum value of 10%

The maximum value of -10.4% is shown below :

Hence it is within the recommended  energy error  limits and therefore we can check it for rigid wall forces, internal energy, hourglass energy, contact energy, total energy of the simulations.

Now we will use hypergraph to plot these values as shown below:

The internal energy 

As you can see the internal energy is increasing with time 

Kinetic energy

As you can see the kinetic energy is decreasing while the internal energy is increasing meaning that all the kinetic energy is getting converted into the internal energy.

Rigid Wall force 

As you can see in the beginning the impact is the largest and it decreases with time.

Hourglass energy

Contact energy

Now we will input the recommended values in the properties chart as mentioned above:

Now we will simulate with these settings :

Now we will use hypergraph to see the various energies :

Internal and Kinetic energy:

Rigid Wall force :

Hour glass energy 

Contact Energy 

Total Energy:

Comparison between the two conditions:

1.Comparsion between internal and kinetic energy:

Now if we compare the graphs between the two we can see that the the slope of condition 1 that simulation without any properties is more steep  where as the slope of condition 2 that is the simulation has more smooth slope .

Reason: This is because as we have introduced the properties such QEPH,Ismtrn etc,the calculations have more accuracy at the elemental level and hence we are getting more accurate results.In condition one we did not take the plastic deformation into account but in condition 2 and hence we are getting more accurate results.

2.Comparsion between Rigid Wall Force :

As you can see the the drop of wall force from the maximum to the minimum value is lower in condition 2 compared to condition 2 ,as we have introduced the properties we can see that more amount of force is getting transferred to the wall and hence this increase in wall force .

3.Comparison between hour glass energy :

In condition 1 we can see that the hourglass energy is increasing with time and condition 2 we can see that the hourglass energy is zero

Reason: As we have introduced the QEPH model ,the nodal calculations takes account of the excessive amount of deformation and hence we get no hourglass energy.

4.Comparsion between contact energy:

We can see that the maximum contact energy in condition 1 is approximately 25000 whereas the maximum contact force in condtion 2 is 6000.

Reason: As more amount of energy is getting transfered due to better accuracy the magnitude of contact energy has gone down.

5.Comparison between total energy:

We can see that the total energy has decreased because of better energy transfer