Assignment 3-2D Element Formulation Challenge

AIM:

To compare the results of simulating a model with base simulation properties and improved shell element properties in the Radioss solver deck.

OBJECTIVE:

• To change the run time to 55 ms and to change the number of animation steps to 30.
• To run the simulation under base simulation properties.
• To do the energy error and mass error checks at the end of the simulation and determine whether results would be acceptable.
• To plot the graphs for kinetic energy, internal energy, hourglass energy, total energy, contact energy, and rigid wall forces.
• To run the simulation under the improved shell element properties and plot the corresponding graphs.

THEORETICAL CONTENT:

• Discretization is the process of breaking down a model body into a system of many smaller bodies (finite elements) that are connected at points (nodes or nodal points) that are shared by two elements. Assume we need to determine the stresses and displacements caused by loading an item of any shape. To model this, we'll need elements with geometric shapes that are identical to the real structure or region.
• All potential engineering structural shapes cannot be represented by a single geometric geometry. The user will create a model using elements such as a beam, truss, plane, cylinder, and so on. Almost all structures may be modelled in FEA using simple elements. Different parameters must be adjusted for different element formulations (1D, 2D, and 3D).
• The first stage in ensuring that the model's performance is as similar to that of the empirical study as the numerical model will allow is to comprehend FE elements, their types, and their capabilities. A run's basic collection of data comprises stress and strain, as well as physical displacement and rotation.
• The Radios element library provides elements for one, two, and three-dimensional issues, and they are divided into the following categories:

1. 3D Elements-Tetra,Penta,Pyramid,Hexa.
2. 2D Elements-Trias, Quads.
3. 1D Elements-Springs,Beams,Trusses.

1D ELEMENTS:

• Modeling 1D elements involves connecting two nodes linearly and then applying constant cross-sectional attributes to that element to characterise its behaviour.
• There are three general types of 1D Elements available,

Truss Elements :

• Truss is a 2 noded element.
• Tensile/compression behavior only (no bending stiffness).
• Compatible with elastic and elastoplastic materials (Law 1 and 2).
• Property defined by cross-sectional area.
• Force output in truss orientation.
• Truss is used for modeling cables, ropes, chains.

Beam Elements :

• Its Property is defined by cross-sectional area and inertias.
• The 1-2 node defines element geometry, the 3 node defines the cross-sectional orientation.
• 6 DOFs per node (bending and torsional stiffness).
• ωDOF: flags for release of rotational stiffness at end nodes.
• Based on the Timoshenko formulation, can degenerate into the standard Euler-Bernoulli formulation.
• The existence of bending stiffness is the primary difference between beam and truss elements.

Spring Elements :

• Spring elements are also 1D elements that are modeled using 2 nodes. These elements are commonly used to model connectors in the model.
• Simple physical spring with a dashpot.
• DOF per node undergoes tension and compression behavior.
• Linear elastic.
• Nonlinear elastoplastic.

2D Elements :

• Shell elements are 3 or 4 node 2D planar elements with constant thickness that can be oriented in space and have either a triangular or quadrilateral shape.
• They're commonly used to represent pressure vessels, automotive bodywork, ship hulls, and aeroplane fuselages, among other things. Shell elements support all translational and rotational degrees of freedom, giving them a total of six degrees of freedom.
• RADIOSS shells are based on Mindlin-hypothesis Reissner's for moderately thick and thin shells, which incorporates transverse shear deformation. Both reduced and fully integrated 4-noded shell elements are available from RADIOSS.

Reduced and Fully Integration Nodes :

S.No	Reduced Integration Nodes	Fully Integration Nodes
1.	It will have only one Integration point on the surface	It will have four different integration points on the surface
2.	Less calculation and save a lot of time.	The solving time is high and will take a lot of time.
3.	The results will be less accurate.	The results will be accurate when compared to reduced integration.
4.	The hourglass cannot be controlled due to under integrated node.	The hourglass can be controlled due to the fully integrated node.

Hourglass :

• An element experiences hourglass deformation as a result of a load applied to it.
• Excessive distortion in the finite element mesh is the cause.
• The form of the element is zig-zag or hourglass-like.
• Under integrated nodes cause hourglass distortion.
• Reduced integrated node is the same as integrated node. When bending loads are applied, the hourglass might appear in 2D or 3D elements (reduced integration technique).

Methods to Control Hourglass :

1) Perturbation Method Ishell=1,2,3 or 4 (Q4) [Viscous Method]

• The relative motion (velocity) of the nodes is used to detect the hourglass distortion.
• A force is provided to the node to stabilise the deformation when hour glassing is observed.
• This force is determined by the stiffness of the element (Young modulus, yield stress, plastic tangent).
• This force introduces a synthesized energy source (named hourglass energy).

2) Perturbation Method Ishell= 24 (QEPH) [Stiffness Method]

• The hourglass yield is determined by the natural yield.
• The natural tangent modulus determines the stiffness of hourglass loading.
• At the material level, the hourglass treatment is applied.
• For orthotropic materials, QEPH is not advised.

2D Element Formulations :

Q4 Element :

• Integration point on the surface.
• Relatively inexpensive.
• The default shell formulation is Ishell = 1.
• Q4 is an under-integrated 4 node element (BT).
• Hourglass stabilization with perturbation method.

QBAT Element :

• QBAT is a fully integrated 4 node element (Batoz).
• 4 Gauss integration points on the surface.
• No hourglass deformation.
• 5 local degrees-of-freedoms per node—drilling (rotation around local z) can be activated with Idrill.
• No shear locking due to in-plane reduced integration for shear.
• Transverse shear deformation is taken into account.
• Most accurate element, but higher CPU cost (2 to 3 times that of a Q4).

QEPH Element :

• QEPH is an improved under-integrated 4 node element with 1 integration point on the surface.
• Physical hourglass stabilization.
• Best compromise between cost and quality.
• Generally, QEPH elements cost only up to 15% more than a BT element and the results are close to those of QBAT.

C0 Element :

• C0 is a standard triangle (C0) with modification for large rotation.
• 1 integration point on the surface.
• No hourglass deformation.
• Low CPU Cost.

N-No of Integration Points through the Thickness :

• Up to 10 points through the thickness.
• 1 integration point through the thickness gives membrane behavior.
• N = 5 integration points recommended.

Shell Strain Formulation (Ismstr):

Small Strain:

• Usually for problems with small deformations.
• Strain computed based on the initial element shape.

Large Strain:

• For problems with large displacements and strains.
• Strain computed based on the current element shape with the derivate of the shape function.
• Small strain activation is possible in RADIOSS Engine in the event that the time step reaches D Tmin due to element deformation.

Shell Plane Stress Plasticity (Iplas):

> If the Von Mises stress is bigger than the yield stress, RADIOSS will,

• Update the strain through the thickness.
• Compute the new thickness of the shell element

> Compute the stresses using the material law plasticity surface, the strain, and the strain rate. The projection of the stress on the plastic surface is done with,

• Radial return (faster)
• Iterative.
• Projection with Newton’s method.
• More accurate.

Thickness Change (Ithick):

• Initial thickness is used to compute strains and to integrate stresses, but the thickness variation is still computed for post-processing reasons.
• If a variable thickness is used, true thickness is computed not only for postprocessing but also for strain computation and stresses integration.
• For accurate results, especially when necking or spring back, it is strongly recommended to use iterative plastic projection and thickness variation.

Shell Elements Recommendations for Crash Applications:

PROCEDURE:

• A user profile window will appear when you open hypermesh software. Start importing the model into the solver deck by switching to the radioss user profile.
• Import the model (starter file) into the radioss solver deck after switching the user profile to radioss. Go to Standard Panel → Import → Import Solver Deck to import the model.

• Soon after importing the model is visible in the GUI as shown below,

• Here the model is in wireframe mode, Switch to the shaded elements mode as shown below.To switch to shaded mode,Go to Visualization Tab → Shaded Elements and Mesh Lines.

• As per our requirement,we need to change the Tstop Value and Tfrequency Value. To change the values, Go to Model Browser → Control Cards → Edit the values by selecting the appropriate Control Card.

• Run Time (Tstop):

• Run Time is the total time taken for the sound wave to travel through the entire length of the model.
• Time for sound to travel the length of rail formula is Δt = L/C

Where Δt = Time Step

L=Length of the Rail

C=Speed of the Sound

• Here the Tstop = 55 ms value has been already given in the question, So need to calculate.
• Enter the value 55 in ENG_RUN File which is shown in the below.

• ANIM_DT [Tfrequency] :

• As per our requirement, the Engine file has to generate between 25 -60 animation files.
• Here I'm taking a maximum value of 60, the solver will create 60 animation files within the termination time.
• Tfrequency = Run Time / Number of Animation Steps
• Tfrequency = 55/30
• Trequency = 1.8333
• Now go to the Model Browser → Select appropriate Control Card → ANIM_DT → Enter the Value as 1.833 as shown below

• Run the base simulation with default shell parameters and to run the simulation, Go to Analysis Panel as shown below.

• Go to Analysis Panel → Radioss → Select the Input File → Save it in Different Folder and Rename it as Case-1 → Run.

• Check the Include Connectors option if there are any connectors in the model. Thus the connectors will also be taken into account for simulation.
• Type -NT 4 in options tab, this will result in processing/simulating faster.
• Where NT indicates No of threads,4 indicates assigning of task to 4 cores in the system.

• Here save the input file in a different folder, and rename it as Case - 1 which is shown below and now run the solver by hitting on radioss.

• After completing the simulation, the radioss will pop up a solver window stating Radioss Job Completed which indicates the simulation has been completed.

• Now verify the Tstop and Tfrequency values are properly assigned in the Engine .rad file [00001. rad]. Open Engine .rad file [00001. rad] with notepad as shown below.

• Next, verify the required number of animation steps obtained in the file location or not.
• In the beginning, the specified number of animation steps was assigned as 30.
• Here the number of animation steps obtained is 31 which is shown below.

• The Engine Output File [00001.out] contains the data like

1. Time Step.
2. Energy Error.
3. Mass Error.
4. Internal Energy Error.
5. Kinetic Energy Error.
6. Contact Energy Error.

• Now check for the Mass Error and Energy Error. The obtained values for Energy Error, Mass Error, Internal Energy Error, Kinetic Energy Error, and Contact Energy Error have been shown below.
• The Acceptable Energy Error Range is -15% to +5% and the Acceptable Mass Error Range is 0 to 2%.

• Maximum Energy Error is= -10.3%.
• Maximum Internal Energy Error = 0.1932 x 10^8 gm^2/s^2.
• Maximum Kinetic Energy Error = 0.3563 x10^8 gm^2/s^2.
• Maximum Mass Error= 0.1659 x 10^-3 g = 1.659 x 10^-4 g.

• Now, these two error values are acceptable, they are not going beyond the standard values.
• Now for Postprocessing, Hperview allows for loading and viewing result files obtained from several sources. Based on the solver type of the files and the results you would like to visualize and analyze, there are different ways to load the input deck and their corresponding results into hyperview.
• To access the load model panel select Load Model Button from the HyperView Panel and open the .h3d file as shown below.

• After importing the .h3d file into the GUI, Enable the contour. The contour tool creates contour plots of a model graphically visualize the analysis results.
• To enable contour, Go to Results Toolbar → Contour.

• Now switch to the Von Mises Stress in result type and select the component, select the averaging method as simple and then click apply as shown below.

• After applying, Run the Simulation and the Simulation animation is as shown below

• Now plot the graphs using Hypergraph 2D, We are plotting the graphs to see what is happening in the rail component.
• Hypergraph 2D is a powerful data analysis and plotting tool with interfaces to many popular file formats. It is a sophisticated math engine capable of processing even the most complex mathematical expressions.
• Hypergraph 2D combines these features with high-quality presentation output and customization capabilities to create a complete data analysis system for any organization.
• Here switch to the Hypergraph 2D to plot the graphs. To switch, Go to Client Selector → Choose the Hypergraph 2D as shown below.

• The first graph is plotted for the Rigid Wall Forces. To plot the graph, Go to Hypergraph 2D → Data File → Element_Formulation - Shell-3_assignmentT01 → Apply.

• Here the graph has been plotted for the Rigid Wall Forces as shown. There are various parameters in Rigid Wall like Normal Force, Tangent Force, FX-X Total Force, FY-Y Total Force, FZ-Z Total Force, Total Resultant Force.
• We are selecting only Total Resultant Force, Because we don't know the exact axis of the component placed, So that's why we are selecting Total Resultant Force and then plotting the graph.

• While plotting the graph, the Units profile window will pop up, There select solver units and then plot the graph, Because the graphs will be plotted according to the solver units.

Case 1 - Without Assigning the Recommended Parameters in the Property:

Rigid Wall Forces:

• Total Resultant Force = √f1^2+f2^2.
• Rigid wall forces are the forces that are acting on the rigid wall.
• Here the rigid wall forces are at a higher value in the beginning.
• In beginning, there is no impact in the simulation, But in the graph, the rigid wall forces are at a higher value.
• This is because, the solver didn't record at that time, so the rigid wall force is at a higher value in the beginning.
• When the rail component hits the rigid wall, The rigid wall forces increase from the beginning.
• And it goes on decreasing Because the deformation is happening to the rail component when it hits the rigid wall. Next plot the graphs for the Kinetic Energy, Internal Energy, Total Energy, Contact Energy, and Hourglass Energy. Those graphs are plotted as shown below.

Kinetic Energy:

• Kinetic Energy is at peak in the starting, Why because, we have a huge mass which is shown below.
• To Check Mass, Go to Tools → Mass Details → Mass, COG, Inertia.

• To Check Velocity, Go to Solver Browser → INIVEL Card → Initial Velocity.

• Kinetic energy is lower and decreases, why because, there is a velocity applied to the component, so it is getting deformed and the kinetic energy decreases.
• The formula for Kinetic Energy=`1/2MV^2`.

• Given Data
• Mass=503881.28179 g
• Velocity = -15.6 ms
• K.E = 1/2 x (503881.28179)(-15.6)^2
• K.E = 61312274.37.

• With the calculation, We came to know why kinetic energy is increasing at the beginning itself, Why because the initial velocity is given for the component.

• The kinetic energy decreases, why because the velocity decreases (The rail component starts to deform, after complete deformation, it will be in rest) when the component comes to a rest, So velocity becomes zero and the kinetic energy decreases.

Internal Energy:

• The formula for Internal Energy is I.E = Q`pm`W.
• Here the heat is neglected, Cause there is no heat transfer, We will be having only work done.

• W = F x D
• F = ma
• Here the internal energy is at Zero because there is no deformation initially, So the internal energy is at Zero and starts from Zero and goes on increasing.
• The internal energy increases because the deformation is happening, there is a displacement, So the internal energy increases, when the displacement or deformation occurs.

Total Energy:

• Total Energy is the sum of Kinetic Energy+Contact Energy+Hourglass Energy + Internal Energy.
• Here total energy starts from higher value, In starting itself it is increasing, Why because the total energy is the sum of Kinetic Energy+Contact Energy+Hourglass Energy + Internal Energy.
• All energies are in initial condition except kinetic energy, So kinetic energy is only there
• Total Energy=Kinetic Energy+0+0+0.
• Kinetic energy is directly proportional to the total energy.
• So the total energy is increasing in the beginning.
• Due to 10.3% of energy error, the total energy is decreasing.

• Why it is decreasing, Let's see mathematically
• Energy Error = 10.3%

= 10.3/100 x 61314900

= 0.103 x 61314900

= 6315434.7

• Now Subtract this value with Maximum Total Energy Error.
• Total Energy Error Maximum Value = 61314900

= 61314900 - 6315434.7

= 54999465.3

• We got a minimum value which is shown in above.

Contact Energy:

• Here the contact energy starts from origin, Cause the rail component is in the initial condition.
• Initially, there is no contact between the rail component and rigid wall.
• There is also no deformation initially, But when the component goes and hits on the rigid wall, The contact energy starts increasing.
• When the deformation or displacement happens to the component, the contact energy increases, causing the crash tube or rail component to come within contact with the rigid wall. So the contact energy goes on increasing.

Hourglass Energy:

• Here the hourglass energy is starting from the origin. Because the recommended parameters have not been specified.
• The hourglass energy goes on increasing, Because to balance the rest of energies, An artificial energy is required, that is called hourglass energy and that's the reason why hourglass energy goes on increasing from origin. A lot of hourglass energy is needed, So it goes on increasing.
• All energies plotted in a single plot is as shown below.

Case 2 - With Assigning the Recommended Parameters in the Property

• Now enter the recommended parameters in properties called Hat-Section, Close-Out-Section which is given in the question.
• The recommended parameters have been entered in the properties as shown below.

• Similarly, follow the same process and do the same as what we have done for Case 1-Without Assigning the Recommended parameters in the property.
• Now run the simulation for Case 2.
• Save the Case-2 in another location to have animation files and engine output files etc., and rename it as Case-2.

• Now go and open the Engine Output file to check whether there is an improvement or not.
• There is an improvement when compared to the values obtained from Case 1.
• Here the Energy and Mass Error-values are acceptable and start to run the simulation.

• In any new window switch to the hyperview and then load the .h3d file. Now run the simulation and in the result type switch to the Von misses stress as shown in below.

• Now plot the graphs for the energies. To see the changes in the results with respect to case-1. Plot the graphs for all the energies.
• Here the graph has been plotted for the rigid wall forces which are shown below. Similarly, plot the graphs for all the energies.

• Here there is a little bit of improvement after assigning the recommended shell parameters when compared to case-1.
• Here, there is no hourglass effect due to recommended parameters, So the rigid wall forces curve is again increasing, If you compare the case-1 and case-2 simulation animation properly, you will get an idea.
• The graph has been plotted for all the energies like Kinetic Energy, Internal Energy, Contact Energy, Total Energy, and Hourglass Energy which is shown below.

• Here there is a little bit of improvement in all the energies when compared to case-1.
• Now plot the graph for the hourglass energy to see the result, whether there is any improvement in hourglass energy or not.

• Here hourglass energy is constant,Why because the recommended parameter Ishell">IshellIshell=24 [QEPH 4 noded shell].
• It will be having 4 nodes in the element,So hourglass won't happen,It will be constant.
• In previous case,It was under integrated node,So there was hourglass deformation.
• The graphs plotted for Case 2 is as shown below. Here in the case 2 graphs there is no great changes except in the hourglass energy.

• On observing the above two animated simulations in the report, it can be noticed that there is hourglass effect in Case - 1 wheras in Case - 2 there is no hourglass effect.

Comparison of Case 1 & Case 2:

S.No	Characteristic	Case-1	Case-2
1.	Maximum Energy Error	-10.3%	-0.1%
2.	Maximum Kinetic Energy	0.3563E+08	0.4377E+08
3.	Maximum Internal Energy	0.1932E+08	0.1749E+08
4.	Total Energy	Total Energy Increases and Slightly Decreases due to Energy Error	Total Energy Remains Constant.
5.	Hourglass Energy	Hourglass Energy Increases due to balance all the energies.	Hourglass Energy Remains Constant due to Recommended Shell Parameter.

RESULT:

• Hence the simulation has been runned without assigning recommended shell parameters.
• Hence the simulation has been runned with assigning recommended shell parameters.
• The graphs have been plotted for case-1 and case-2 successfully.
• While comparing Case-1 and Case-2,Case-2 is effective,Cause there is no hourglass deformation.

CONCLUSION:

• I conclude that Case-2 with assigning recommended shell parameters is effective.
• In this Challenge the learning outcomes are the procedures of how

1. to run a simulation with and without assigning shell parameters.
2. to do postprocessing (Plotting the graphs for the various parameters).
3. to understand the curves that are increasing and decreasing in the graphs.
4. to compare the obtained values with the various parameters.