Assignment 3-2D Element Formulation Challenge

2D Element Formulation

 

Aim-

• To run the simulation for the given component with and without changing the recommended element parameters using a radioss solver.

Objective-

• To change the run time to 55 ms and to change the number of animation steps to 60.
• To run the base simulation with default element parameters.
• To check the energy error and mass error for the base simulation.
• To plot the graphs for kinetic energy, internal energy, hourglass energy, total energy, contact energy, and rigid wall forces.
• To run the new simulation with recommended element parameters and to plot the graphs again.

Theoretical Frame Work-

 

Element Formulations :

• Discretization is the process of dividing a model body into an equivalent system of many smaller bodies (finite elements) interconnected at points (nodes or nodal points) common to two elements. Suppose we need to find the stresses and displacement upon loading an object with an arbitrary shape. So in order to model this, we need elements that have a geometric shape similar to the real structure or region.
• One geometric shape cannot represent all possible engineering structural shapes. The user will model with elements that look like a beam, truss, plane, cylinder, etc. In FEA, by using basic element almost all structures are approximated. The different element formulations (1D, 2D, 3D) require different parameters to be set.
• An understanding of FE elements, their types, and their capabilities is the first step to ensuring that the performance of the model is as close to the performance of empirical study as the numerical model will allow. The basic set of information output from a run includes stress and strain and physical displacement and rotation.
• Radios element library contains elements for one, two or three-dimensional problems and can be classified into the following categories of elements:

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

 

1D Elements-

• 1D Elements are modeled by connecting two nodes together linearly and then assigning constant cross-sectional properties to that element to define the element’s behavior.
• There are three general types of 1D Elements available-Truss Elements, Beam Elements, and Spring Elements. 

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.

 

Figure 1-Automotive Applications of 1D Elements.

 

2D Elements :

• Shell elements are 3 or 4 node 2D planar elements with constant thickness, and have either a triangular or quadrilateral shape, that can be oriented in the space.
• They are typically used to model structures such as pressure vessels, automobile bodies, ship hulls,aircraft fuselage etc.
• Shell elements support all translational degrees of freedom as well as all rotational degrees of freedom, that is shell elements have 6 degrees of freedom. RADIOSS shells are based on Mindlin-Reissner theory that includes transverse shear deformation valid for moderately thick and thin shells.
• RADIOSS provides both reduced and fully integrated 4-noded shell elements.

 

 Reduced and Fully Integration Nodes :

 

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

 

Table-1

 

 

Figure 2-Reduced and Fully Integration Nodes.

 

 Hourglass :

• Hourglass deformation happens to a element due to a applied load.
• It is excessive deformation in finite element mesh.
• Element having zig-zag or hourglass like shapes.
• Hourglass deformation occurs due to an under integrated nodes.I have explained above,what is under integrated node,reduced integrated node and fully integrated node.
• Under intergrated node is nothing but reduced integrated node.
• Hourglass can occur in 2D or 3D element(reduced integration scheme) when subjected to bending load.

 

 

Figure 3-Hourglass Modes in Shells.

 

Figure 4-Hourglass Deformation.

 

Methods to Control Hourglass :

• There are two methods to control hourglass deformation called

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

• The hourglass deformation is detected with the relative motion (velocity) of the nodes.
• When hour glassing is detected, a force is applied on the node to stabilize the deformation.
• This force is defined according the element stiffness (Young modulus, yield stress, plastic tangent).
• This force introduces an artificial energy (named hourglass energy).

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

• Hourglass yield depends on natural yield.
• Hourglass loading stiffness depends on natural tangent modulus.
• The hourglass treatment is done at the material level.
• QEPH is not recommended for orthotropic materials.

[Note: Hourglass should not exceed 5% of internal energy]

 

 2D Element Formulations :

 

 

Figure 5-2D Element Formulation.

 

 

Figure 6-Key Parameters for Shell Elements.

 

 Q4 Element :

Figure 7-Ishell 4.

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

 

 QBAT Element :

 

Figure 8-Ishell 12.

 

• 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 :

Figure 9-Ishell 24.

 

• 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 costs only up to 15% more than a BT element and the results are close to those of QBAT.

CO Element :

Figure 10-Ish3n 2.

 

• 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 :

Figure 11-Number of Integration Points Through the Thickness.

 

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

Shell Strain Formulation Ismstr :

Figure 12-Ismstr Shell Strain Formulation.

 

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 possible in RADIOSS Engine in the event that time step reaches D Tmin due to element deformation.

Shell Stress Computation -

• From the deformation and the strain rate of the previous step, RADIOSS computes the strain to each integration point.
• From this strain, the stress is computed with a elastic stress increment.

 

Figure 13-Computes Stress.

 

• With these computed stress values, the Von Mises stress is computed and compared to the yield stress of the material.

`σ_vm^2=σ_x^2+σ_y^2-σ_x σ_y+3σ_xy^2`.

• If the Von Mises stress is smaller than yield stress, the computed stress is the one used in order to compute the internal force of the elements.

Shell Plane Stress Plasticity Iplas -

Figure 14-Iplas Shell Plane Stress Plasticity Flag.

 

`***` If the Von Mises stress is bigger than 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 -

Figure 15-Ithick Thickness Change.

 

• 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 -

 

 

Figure 16-Shell Elements Recommendations for Crash Applications.

 

Figure 17-Applications of Shell Elements.

 

Procedure -

Phase 1-Import the Starter File into the Solver Deck Radioss

• While opening hypermesh software,A user profile window will pop up,Switch to the radioss user profile as shown in below figure 18 and start importing the model into the solver deck.

 

Figure 18-User Profile Window.

 

• Now after switchin the user profile to radioss,import the model (starter file) into the radioss solver deck.
• To import the model,Go to Standard Panel >> Import >> Import Solver Deck.

 

Figure 19-Importing Model into Radioss Block.

• Import Solver Deck option should be selected to import the radioss starter file.

 

 

Figure 20-Selecting the Starter File to Import.

 

• Here the import browser will appear as shown in above figure 20,Select the appropriate starter file to import into GUI.
• Switch the File Type to Radioss Block and import the model into GUI.

 

Figure 21-Model Imported into GUI.

 

• Here the model is in wireframe mode,Switch to the shaded mode as shown in below figure 22.
• To switch to shaded mode,Go to Visualization Tab >> Shaded Elements and Mesh Lines.

 

Figure 22-Visualization Tab to Switch to the Shaded Elements and Mesh Lines.

 

Figure 23-Shaded Elements and Mesh Lines Mode.

 

Phase 2-Edit ENG_RUN File [Tstop] and ANIM_DT File [Tfrequency] :

• 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.

 

Figure 24-Model Browser.

 

1) Run Time [Tstop] :

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

Where `Delta`t = 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 figure 25.

 

Figure 25-Tstop Value Edited.

 

2) ANIM_DT [Tfrequency] :

• As per our requirement,Engine file have to generate between 25 -60 animation files.
• Here im taking maximum value 60,the solver will create 60 animation files within the termination time.
• Tfrequency =`frac{Run Time}{Number of Animation Steps}`
• Tfrequency =`55/60`
• Trequency = 0.9166.
• Now Go to the Model Browser >> Select Appropriate Control Card >> ANIM_DT >> Enter the Value as 0.9166 as shown in below figure 26.

 

Figure 26-Tfrequency Value Edited.

 

Phase 3 - Run the Base Simulation With and Without Changing the Recommended Shell Parameters

Case 1 -Without Changing the Recommended Shell Parameters.

• Run the base simulation with default shell parameters as shown in below figure 27.Don't assign any recommended shell parameters.

 

Figure 27-Default Shell Parameters.

 

• Now run the simulation,To run simulation,Go to Analysis Panel as shown in figure 28.
• 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,If there are any connectors in the model,The connectors will also be taken into account.
• Type -NT 4 in options tab,This will make the simulation faster.
• Where NT indicates No of threads,4 indicates assigning the task to 4 cores in the system.

 

Figure 28-Analysis Panel.

 

Figure 29-Radioss Sub-Panel.

• Here save the input file in a different folder, and rename it as case-1 which is shown in below figure 30.
• Now run the solver by hitting on radioss.

 

Figure 30-Save the Input (Starter File) in a Separate Folder and Run the Simulation.

 

• After completing the simulation,the radioss will pop up a solver window stating Radioss Job Completed which indicates the simulation has been completed,Which is shown in below figure 31.

 

Figure 31-End of Solver Output.

 

• Now verify the Tstop and Tfrequency values are properly assigned in Engine .rad file [00001.rad] .
• Open Engine .rad file [00001.rad] with notepad as shwon in below figure 32.

 

Figure 32-Tstop and Tfrequancy Values have been Properly Assigned in Engine File[00001.rad]

 

• 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 60.
• Here the number of animation steps obtained are 61 which is shown in below figure 33.

 

Figure 33-61 Animation Files Obtained as Specified in the Beginning.

 

Phase 4-Do Energy Error and Mass Energy Error Checks

• Now Engine Output File [00001.out] has been generated after analysis.
• 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.

• Here 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 has been shown in below figure 35.
• The Acceptable Energy Error Range is -15% to +5%.
• The Acceptable Mass Error Range is 0 to 2%.

 

Figure 34-Engine File [00001.rad]

 

Figure 35-Engine File [00001.out]

 

• Scroll down to see the maximum value obtained for the Energy Error,Kinetic Energy Error,Internal Energy Error and Mass Error as shown in below figure 36.

 

Figure 36-Energy Error and Mass Error.

 

• The Maximum Energy Error is= -10.3%.
• The Maximum Internal Energy Error=`0.1932xx10^8``gm^2/s^2`.
• The Maximum Kinetic Energy Error=`0.3563xx10^8 gm^2/s^2`.
• The Maximum Mass Error=`0.1659xx10^-<a href="undefined" target="_blank">3</a>`g=`1.659xx10^-4`g.

[Note : 1) The Acceptable Energy Error Range is -15% to +5%.

            2) The Acceptable Mass Error Range is 0 to 2%.].

 

• Now these two error values are acceptable,they are not going beyond the standard values.

 

Phase 5 - Postprocessing 

1) Review the Simulation using -HyperView.

2) Plot the graphs using -Hypergraph 2D.

 

1) Review the Simulation using HyperView :

• Hyperview 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 differnt ways to load the input deck and their corresponding results into hyperview.
• First to begin the postprocessing in the Hypermesh,Split the Screen as shown in below figure 38.
•  Import the animation file .h3d into the hyperview.

 

Figure 37-Splitting the Screen.

 

Figure 38-Screen Splitted into Two.

• And then activate the Client HyperView

Figure 39-HyperView Panel.

 

• To access the load model panel
• Select Load Model Button from the HyperView Panel and open .h3d file as shown in below figure 39.

 

Figure 39-Opening .h3d File.

 

Figure 40-Model Loaded.

 

• After loading the model into hyperview,It will be represented as shown in below figure 41.

 

Figure 41-Model Imported into HyperView.

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

 

Figure 42-Contour Panel.

 

• Now switch to the Von Misses Stress in result type and select the component,select the averaging method as simple and then click apply as shown in below figure 43.

 

Figure 43-Selecting the Paremeters in Contour Panel.

 

• After applying ,Run the Simulation,The Simulation animation is shown in below figure 44.

 

Figure 44-Case 1-HyperView Simulation Animation.

 

2) Plot the graphs using -Hypergraph 2D.

• 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 sophisicated 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.

 

Figure 45-Switching to Hypergraph 2D.

 

• Here switch to the Hypergraph 2D to plot the graphs.
• To switch,Go to Client Selector >> Choose the Hypergraph 2D as shown in above figure 45.

 

Figure 46-Screen Splitted into Three.

 

[Note : Before plotting the graphs,Make sure to split the screen into three or four as shown in above figure 46 and then plot the graphs.]

• 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.

 

Figure 47-Select the Appropriate T01 File.

 

Figure 48-Plotting Graph for Rigid Wall Forces.

 

• Here the graph has been plotted for the Rigid Wall Forces as shown in below Figure 50.
• 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.

 

Figure 49-Units Profile.

 

• While plotting the graph,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 :

Figure 50-Rigid Wall Force [Total Resultant Force] Graph.

 

• Total Resultant Force =`sqrt f1^2+f2^2`.
• Rigid wall forces are the forces which are acting on the rigid wall.
• Here the rigid wall forces is at higher value in the beginning.
• In beginning there is no impact in the simulation,But in the graph the rigid wall forces are at the higher value.
• This is because,the solver didn't record in that time,so the rigid wall force is at higher value in the beginning.
• When the rail component hits the rigid wall,The rigid wall forces increases from the beginning.
• And it goes on decreasing,Because the deformation is happening to the rail component when it hits to the rigid wall.

[Note :The solver starts to record when the rail component hits on the rigid wall,This is the reason why in the beginning,the rigid wall forces is in higher value or increases and goes on decreasing.]

 

• Next plot the graphs for the Kinetic Energy,Internal Energy,Total Energy,Contact Energy and Hourglass Energy.Those graphs are plotted and shown in the below Figure 51.

 

Figure 51-Graphs Plotted for Kinetic,Internal,Total,Contact and Hourglass Energy.

 

Kinetic Energy :

• Kinetic Energy is at peak in the starting,Why because,we have huge mass which is shown in below figure 53,So
• To Check Mass,Go to Tools >> Mass Details >> Mass,COG,Inertia.
• To Check Velocity,Go to SOlver Browser >> INIVEL Card >> Initial Velocity.

 

Figure 52-Mass Check.

 

Figure 53-Total Mass of the Rail Component.

 

Figure 54-Initial Velocity.

 

• Kinetic energy is lower and decreases,why because,there is a velocity applied to the component,so its 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=`1/2xx(503881.28179)(-15.6)^2`

• K.E=61312274.37.

 

• The value calculated here is shown in the figure 56.
• With the calculation,We came to know why kinetic energy is increasing in the beginning itself,Why because the initial velocity is given for the component.

 

 

Figure 55-Kinetic Energy Animation.

 

Figure 56-Kinetic Energy.

• 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 -

 

Figure 57-Internal Energy Animation.

 

Figure 58-Internal Energy Graph.

 

• 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 workdone.
• W=FxD
• F=ma
• Here the internal energy is in Zero,Because there is no deformation initially,So the ineternal emrgy is in Zero and starts from Zero and goes on increasing.
• The internal energy increases because the drformation is happening,there is a displacement,So the internal energy increases,when the displacement or deformation occurs.

 

Total Energy :

 

Figure 59-Total Energy Animation.

 

Figure 60-Total Energy Graph.

 

• Total Energy is sum of Kinetic Energy+Contact Energy+Hourglass Energy + Internal Energy.
• Here total energy starts from higher value,In starting itself its increasing,Why because the total energy is sum of  Kinetic Energy+Contact Energy+Hourglass Energy + Internal Energy.
• All enrgies are in initial condition except kinetic energy,So kinetic energy is only there
• Total Energy=Kinetic Energy+0+0+0.
• Kinetic enrgy is directly proprtional 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.

 

Figure 61-Energy Error.

 

• Why it is decreasing,Let's see mathematically
• Energy Error=10.3%
• =`10.3/100xx61314900`
• =`0.103xx61314900`
• =`6315434.7`
• Now Subract this value with Maximum Total Energy Error.
• Total Energy Error Maximum Value=61314900
• =61314900-6315434.7
• =54999465.3
• We got an minimum value which is shown in above figure 58.

Contact Energy :

 

Figure 62-Contact Energy Animation.

 

Figure 63-Contact Energy Graph.

 

• Here the contact energy starts from origin,Cause the rail component is in intial condition.
• Intially there is no contact between the rail component and rigid wall.
• There is also no deformation intially,But when the component goeas and hits on the rigid wall,The contact energy starts increasing.
• When the deformation or displacement happens to the component,the contact energy increases,cause the crash tube or rail component comes within the contact to the rigid wall.So the contact energy goes on increasing.

 

Hourglass Energy :

 

Figure 64-Hourglass Energy Animation.

 

[Note:`Delta`t > t`implies`Hourglass Exsist.

 `Delta`t < t`implies`Hourglass won't Exsist.

Where `Delta`t-Shockwave.

t - Time taken for the information.]

 

Figure 65-Hourglass Energy Graph.

 

• Here the hourglass energy is starting from origin.Because the reccomended parameters has 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's goes on increasing.

 

Figure 66-All Energies Animation.

 

Figure 67-All Energies Graph.

 

Case 2-With Assigning the Recommended Parameters in the Property

 

• Now enter the reccomended parameters in properties called Hat-Section,Close-Out-Section which is given in the question.
• The recommended parameters have been enetered in the properties as shown in below figure 68.

 

Figure 68-Assigned Recommended Parameters.

 

• Simillarly follow the same process and do the same what we have done for the Case 1-Without Assigning the Recommended parameters in the property.
• Now run the simulation for the case 2.

[Note: Save the Case-2 in other location to have animation files and engine output files etc., and rename it as Case-2.]

 

Figure 69-61 Animation Files Obtained.

 

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

 

Figure 70-Energy Values From the Case 1.

 

• Now run the simulation,To run the simulation we need a additional window.In the main page menu,Go and split the windows into 8 as shown in figure 71.
• In any new window switch to the hyperview and then load the .h3d file.The loaded ,h3d file is shown in figure 71.

 

Figure 71-Loaded .h3d File.

• Now run the simulation and in the result type switch to the von misses stress as shown in below figure 72.

 

Figure 72-Simulation Animation.

• Now plot the graphs for the energies.To see the changes in the results with respect to the case-1.Plot the graphs for all the energies.
• Here the graph has been plotted for the rigid wall forces which is shown in below figure 73.
• Simillarly plot the graphs for all the energies.

 

Figure 73-Rigid Wall Force Graph.

 

• Here there is little bit 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 in below figure 74.

 

Figure 74-All the Energies Graph Plotted.

 

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

 

Figure 75-Hourglass Energy Graph.

• Here hourglass energy is constant,Why because the recommended parameter `I_shell`=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.

[Note :Hourglass Energy limit is 5% of Internal Energy].

 

Final Image -

• Here in the case 2 graphs which is shown below in figure 76.There is no much change.

 

Figure 76-Final Image.

 

 

Figure 77-Comparison of Case-1 and Case-2 Simulation.

[Note : Kindly notice the two simulation animation,There will be a hourglass effect in Case 1 and there will be no hourglass effect in Case-2].

 

Comparison of Case-1 and Case-2 :

S.No	Characteristic	Case-1	Case-2
1)	Maximum Energy Error	-10.3%	-0.1%
2)	Maximum Kinetic Energy	0.3563E+08	0.3941E+08
3)	Maximum Internal Energy	0.1932E+08	0.2186E+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.

Table-2

 

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 and Learning Outcome -

• I conclude that Case-2 with assigning recommended shell parameters is effective.
• In this Challenge ,I came to know
• How to run a simulation with and without assigning shell parameters.
• How to do postprocessing (Plotting the graphs for the various parameters).
• How to understand the curves that are increasing and decreasing in the graphs.
• How to compare the obtained values with the various parameters.