Learning Finite Element Analysis (FEA) from The Qur'an

In the Name of Allah (God), the Most Compassionate, the Most Merciful

Learning Finite Element Analysis (FEA) from The

Qur’anDr. Zaid Kasim Mohammad Ghazzawi

E-mail :zaidquran@gmail.comWebsite: www.quran-miracle.com

What is the Finite Element Method (FEM) ?

The answer can be known fully from the Noble Qur’an

In The Name of Allah (God) The Most Compassionate The Most Merciful

The Qur’an (54: 49)

Allah (God) Almighty states that He created everything in a discrete manner

Thus everything in creation is discrete

Allah (God) created everything in a discrete fashion

Allah (God) Almighty encourages people to study their bodies

The human body is the best textbook of optimal design and analysis

Thus the best designs and analysis procedures can be learnt from the human body

The Qur’an (51: 21)

And in your own self will you not then see

In The Name of Allah (God) The Most Compassionate The Most Merciful

The Design of The Human Skeletal System

Bone

Tortora and Grabowski, 1996 جسم في العظمي الهيكلاالنسان

Focus on this region

Focus on this region

http://www.bmb.psu.edu/courses/bisci004a/bone/lacuna.jpg

http://bodymap.ims.u-tokyo.ac.jp/doc/images/fg3.jpg

Muscle force

Bone strain

Cells that can sense the displacement at every location within bone

Displacement, temperature, magnetic field, and every

property can be obtained at every location within the structure

How is it possible?

Internal Design of Human Bone

Osteocytes

Element

Hydroxy apatite crystal (bone element)

Bone ElementsDefining the shape and material

properties for them

Allah Almighty states that He created you in a process of assembly

Thus everything in the creation of Allah Almighty is composed of basic units

In The Name of Allah (God) The Most Compassionate The Most Merciful

The Qur’an (82: 8)

In whatever form Allah (God) willed He assembled you

Since Allah (God) Almighty perfected everything He has created

Then discretization is the optimal method to design and analyze a system

In The Name of Allah (God) The Most Compassionate The Most Merciful

The Qur’an (82: 32)

Who perfected everything He created and started the creation of human from mud

A complex structure is made simple by:

Discretizing it into simple to analyze basic units

The assembly of these basic units compose the

complex structure

Simple geometrical shapeEvery physical property is easy to be calculated for

these basic units

These units have the following fundamental properties:

Clear geometrical associations between

these units

This is the basis of the finite element method (FEM)

The optimal method to analyze any system as derived from the Noble Qur’an and the human body

1. To discretize the system into basic units and to analyze the design and function (Energy transmission) of these units

2. These units (elements) are easy to deal with and it is easy to calculate any required parameter for these elements

3. The elements the system is composed of are connected together with no discontinuities (Element connectivity)

4. The optimal organization of the elements is a hexagonal pattern (covering maximum volume with the least amount of elements)

5. The dimensions of these elements should be small compared to the dimensions of the system

6. Elements should be stable and exhibit no excessive (i.e. large) displacements

The Creation of a Structure Allah Almighty teaches us that the best way

to do that is to assemble the basic structural units together to create the structure.

Advantages of this method:1. Optimal control over the structure2. Ensuring connectivity between the elements3. Knowledge of the internal details of the structure

Bottom – Up Approach

The Finite Element Method (FEM)

A method to analyze systems by discretizing them into finite elements which are easy to

analyze and to obtain results from

Performing FEM using ANSYS software

Steps to perform FEACan be completely derived from the Noble

Qur’an

Since that the human body is built on discretization (Finite Elements)

Then studying the stages of its creation would yield the following:

The best procedure to design structures based on finite element technique

The optimal methodology to understand finite element technique

)وفي أنفسكم أفال تبصرون(

Reflection upon the verse Conclusion

Then Allah (God) Almighty created the Alaqa (object that clings) into a modgha (chewed like

substance)

Modgha is comprised of the basic elements from which the human body is

to be composed of

Thus the first step in designing a structure is to determine the basic

elements

Then Allah (God) Almighty created the modgha (chewed like substance) into bones Bone is the assembled state of the

basic units mentioned earlier

The next step is to determine the assembly of the finite elements

Then Allah (God) Almighty covers the bones with flesh (muscles, ligaments, cartilage, etc.)

Then external forces and fixation are applied to the model

The next step is to apply boundary conditions (BCs) to the structure

Then Allah (God) Almighty brings forth the structure plus the BCs with another

mechanism of creationThen the applied BCs are activated

The next step is to investigate the interaction between the applied

BCs and the structure

Then We made the Nutfah into a clot (a piece of thick coagulated blood), then We made the clot into a little lump of flesh, then We made out of that little lump of flesh bones, then We clothed the bones with flesh, and then We brought it forth as another creation. So blessed be Allâh, the Best of creators

The Noble Qur’an (23: 14)

In the Name of Allah (God) Almighty The Most Gracious The Most Merciful

Step 1

Step 2

Step 3

Step 4

Steps to perform FEA as found in the Noble Qur’an1. Humans are made of clay (water + soil) طين من اإلنسان خلق2. Humans are made into a nutfah (information regarding the creation of components of the human

body)مكين قرار في نطفة3. The creation of Alaqa from Notfah 3. The creation of Modgha (chewed like substance) from Alaqa

- Element creation (defining material properties and shape) 4. The creation of bones from the Modgha - Creation of geometry, direct generation (use of elements and their assembly in building the

geometry)

5. The covering of bones with flesh (muscles, skin, etc.) - Defining the Boundary conditions (BCs) applied to the structure 6. Bringing the created human forth as another creation - Initializing the solution, solving, and seeing the results

Reflection upon the verse Conclusion

Then Allah (God) Almighty created the Alaqa (object that clings) into a modgha (chewed like

substance)

Modgha is comprised of the basic elements from which the human body is

to be composed of

Thus the first step in designing a structure is to determine the basic

elements

Then Allah (God) Almighty created the modgha (chewed like substance) into bones Bone is the assembled state of the

basic units mentioned earlier

The next step is to determine the assembly of the finite elements

Then Allah (God) Almighty covers the bones with flesh (muscles, ligaments, cartilage, etc.)

Then external forces and fixation are applied to the model

The next step is to apply boundary conditions (BCs) to the structure

Then Allah (God) Almighty brings forth the structure plus the BCs with another

mechanism of creationThen the applied BCs are activated

The next step is to investigate the interaction between the applied

BCs and the structure

Then We made the Nutfah into a clot (a piece of thick coagulated blood), then We made the clot into a little lump of flesh, then We made out of that little lump of flesh bones, then We clothed the bones with flesh, and then We brought it forth as another creation. So blessed be Allâh, the Best of creators

The Noble Qur’an (23: 14)

In the Name of Allah (God) Almighty The Most Gracious The Most Merciful

Step 1

The Modgha Stage in the Creation of the Human Body

Creation of the elements comprising the human body

Defining the shape and material properties for the elements

Element

Hydroxy apatite crystal (bone element)

Bone ElementsDefining the shape and material

properties for them

Step (1) In Finite Element Analysis

Preprocessor StageDefining element shape and material properties

In finite element method (FEM) Nodes describe the geometrical shape of the element The domain is composed of elements and the

elements have nodes Elements are described by their shape. For example:

Brick elements Triangular elements Shell elements

Steps to perform FEA using ANSYS

1. Preprocessing stage1. Select the desired element (ANSYS element library) 2. Define real constants (if needed)3. Define material properties

1. Isentropic material (similar properties is all dimensions)2. Orthotropic material (similar properties in two dimensions

and different in the third)3. Anisotropic material (different properties in all dimensions)

Elements in the finite element method 1D elements

2D elements

Bar element )1D(2 nodes 1 DOF )UX(

Rectangular element )2D(4 nodes 2 DOF )UX, UY(

Triangular element )2D(3 nodes 2 DOF )UX, UY(

Elements in finite element method

3D elements Brick element )3D(8 nodes 3 DOF )UX, UY, UZ(

Pyramidal element )3D(6 nodes 3 DOF )UX, UY, UZ(

Reflection upon the verse Conclusion

Then Allah (God) Almighty created the Alaqa (object that clings) into a modgha (chewed like

substance)

Modgha is comprised of the basic elements from which the human body is

to be composed of

Thus the first step in designing a structure is to determine the basic

elements

Then Allah (God) Almighty created the modgha (chewed like substance) into bones Bone is the assembled state of the

basic units mentioned earlier

The next step is to determine the assembly of the finite elements

Then Allah (God) Almighty covers the bones with flesh (muscles, ligaments, cartilage, etc.)

Then external forces and fixation are applied to the model

The next step is to apply boundary conditions (BCs) to the structure

Then Allah (God) Almighty brings forth the structure plus the BCs with another

mechanism of creationThen the applied BCs are activated

The next step is to investigate the interaction between the applied

BCs and the structure

Then We made the Nutfah into a clot (a piece of thick coagulated blood), then We made the clot into a little lump of flesh, then We made out of that little lump of flesh bones, then We clothed the bones with flesh, and then We brought it forth as another creation. So blessed be Allâh, the Best of creators

The Noble Qur’an (23: 14)

In the Name of Allah (God) Almighty The Most Gracious The Most Merciful

Step 2

The Bone Stage in the Creation of the Human Body

Creation of the geometry Direct assembly of elements to create the

structureBottom – Up approach

Step (2) In Finite Element Analysis

Preprocessor StageCreation of geometry:

-direct generation (use of elements and their assembly in building the geometry)

-Creating the geometry and then discretizing it (meshing)

1st Example using ANSYS

Model the object shown on the right with the applied load

Material: Bone Mechanical properties

Isentropic material Young’s modulus (E) = 17 GPa Poisson’s ratio () = 0.3 Density () = 1750 kg/m3

Fixed at this end

Depth = 2 cm

Width = 1 cm

Height = 1 cm

How to model irregular geometries in ANSYS ?

Keypoints and splines method

MeshingDividing the structure into elements (creating a

mesh of elements)

Steps to perform FEA using ANSYS1. Preprocessing stage

1. Select the desired element (ANSYS element library) 2. Define real constants (if needed)3. Define material properties

1. Isentropic material (similar properties is all dimensions)2. Orthotropic material (similar properties in two dimensions and different in the

third)3. Anisotropic material (different properties in all dimensions)

4. Create the geometry 1. Direct method (defining keypoints which are the nodes of the elements)2. Indirect method (using shapes such as rectangle, triangle, cylinder, sphere or

defining key points and creating lines, areas, and volumes from them)5. Meshing stage

1. Smart meshing (variable element size) 2. Manual meshing (fixed element size)

Manual meshing

Smart meshing (setting 5)

2nd Example using ANSYS

Mesh the structure using Manual meshing Automatic meshing (smart

meshing)

Fixed at this end

Depth = 2 cm

Width = 1 cm

Height = 1 cm

Steps to perform FEA as found in the Noble Qur’an1. Humans are made of clay (water + soil) طين من اإلنسان خلق2. Humans are made into a nutfah (information regarding the creation of components of the human

body)مكين قرار في نطفة3. The creation of Alaqa from Notfah 3. The creation of Modgha (chewed like substance) from Alaqa

- Element creation (defining material properties and shape) 4. The creation of bones from the Modgha - Creation of geometry, direct generation (use of elements and their assembly in building the

geometry)

5. The covering of bones with flesh (muscles, skin, etc.) - Defining the Boundary conditions (BCs) applied to the structure 6. Bringing the created human forth as another creation - Initializing the solution, solving, and seeing the results

Tortora and Grabowski, 1996 جسم في العظمي الهيكلاالنسان

Reflection upon the verse Conclusion

Then Allah (God) Almighty created the Alaqa (object that clings) into a modgha (chewed like

substance)

Modgha is comprised of the basic elements from which the human body is

to be composed of

Thus the first step in designing a structure is to determine the basic

elements

Then Allah (God) Almighty created the modgha (chewed like substance) into bones Bone is the assembled state of the

basic units mentioned earlier

The next step is to determine the assembly of the finite elements

Then Allah (God) Almighty covers the bones with flesh (muscles, ligaments, cartilage, etc.)

Then external forces and fixation are applied to the model

The next step is to apply boundary conditions (BCs) to the structure

Then Allah (God) Almighty brings forth the structure plus the BCs with another

mechanism of creationThen the applied BCs are activated

The next step is to investigate the interaction between the applied

BCs and the structure

Then We made the Nutfah into a clot (a piece of thick coagulated blood), then We made the clot into a little lump of flesh, then We made out of that little lump of flesh bones, then We clothed the bones with flesh, and then We brought it forth as another creation. So blessed be Allâh, the Best of creators

The Noble Qur’an (23: 14)

In the Name of Allah (God) Almighty The Most Gracious The Most Merciful

Step 3

Covering the bones with flesh (muscles, tendon, skin, etc.)

Applying the boundary conditions on the discretized structure

Step (3) In Finite Element Analysis

Solution StageApplying the boundary conditions on the meshed structure

Steps to perform FEA using ANSYS2. Solution phase

1. Select analysis (structural (linear, non-linear), magnetic, electrical, etc.)

2. Apply loads: 1. Displacements 2. Forces and moments

3. Temperature 4. Voltages 5. Magnetic field flux 3. Initialize the solution (Solve current load step (LS))

3rd Example using ANSYS

Apply the shown loads on the meshed structure

Fixed at this end

Depth = 2 cm

Width = 1 cm

Height = 1 cm

1000 N

Steps to perform FEA as found in the Noble Qur’an1. Humans are made of clay (water + soil) طين من اإلنسان خلق2. Humans are made into a nutfah (information regarding the creation of components of the human

body)مكين قرار في نطفة3. The creation of Alaqa from Notfah 3. The creation of Modgha (chewed like substance) from Alaqa

- Element creation (defining material properties and shape) 4. The creation of bones from the Modgha - Creation of geometry, direct generation (use of elements and their assembly in building the

geometry)

5. The covering of bones with flesh (muscles, skin, etc.) - Defining the Boundary conditions (BCs) applied to the structure 6. Bringing the created human forth as another creation - Initializing the solution, solving, and seeing the results

Reflection upon the verse Conclusion

Then Allah (God) Almighty created the Alaqa (object that clings) into a modgha (chewed like

substance)

Modgha is comprised of the basic elements from which the human body is

to be composed of

Thus the first step in designing a structure is to determine the basic

elements

Then Allah (God) Almighty created the modgha (chewed like substance) into bones Bone is the assembled state of the

basic units mentioned earlier

The next step is to determine the assembly of the finite elements

Then Allah (God) Almighty covers the bones with flesh (muscles, ligaments, cartilage, etc.)

Then external forces and fixation are applied to the model

The next step is to apply boundary conditions (BCs) to the structure

Then Allah (God) Almighty brings forth the structure plus the BCs with another

mechanism of creationThen the applied BCs are activated

The next step is to investigate the interaction between the applied

BCs and the structure

Then We made the Nutfah into a clot (a piece of thick coagulated blood), then We made the clot into a little lump of flesh, then We made out of that little lump of flesh bones, then We clothed the bones with flesh, and then We brought it forth as another creation. So blessed be Allâh, the Best of creators

The Noble Qur’an (23: 14)

In the Name of Allah (God) Almighty The Most Gracious The Most Merciful

Step 4

Bringing the Human Body forth as another creation

Seeing the functionality of the system (i.e. The interaction between the boundary

conditions and the structure)

Steps to perform FEA using ANSYS3. Post-processing stage

1. Plot results:1. Displacements2. Stress (1st, 2nd, and 3rd principal stresses, von Mises)3. Strain4. Vector plot 5. Path plot

2. Animation: ramping the load from 0 to max value and seeing in real time the effect on the structure.

1. Displacement, stress, strain, etc.

4th Example using ANSYS

Examine the following results from the model: Displacements Von Mises Stress and Strain Vector plots

Fixed at this end

Depth = 2 cm

Width = 1 cm

Height = 1 cm

1000 N

Errors in Finite Element Analysis1. Modeling error: Error resulting from assumptions

done when trying to represent the physical system in the computer.

2. Discretization error: error resulting from the difference in the degrees of freedom between the meshed object and the real one.

3. Numerical error: error resulting from rounding off numbers when solving the equations representing the model of the physical system.

4. Software error: error resulting from errors in the code listing of the program.

1st Example using ANSYS

Model the object shown on the right with the applied load

Material: Steel Mechanical properties

Isentropic material Young’s modulus (E) = 207 GPa Poisson’s ratio () = 0.3 Density () = 7500 kg/m3

Fixed at this end

Depth = 2 cm

Width = 1 cm

Height = 1 cm

2nd Example using ANSYS

Mesh the structure using Manual meshing Automatic meshing (smart

meshing)

Fixed at this end

Depth = 2 cm

Width = 1 cm

Height = 1 cm

3rd Example using ANSYS

Apply the shown loads on the meshed structure

Fixed at this end

Depth = 2 cm

Width = 1 cm

Height = 1 cm

1000 N

4th Example using ANSYS

Examine the following results from the model: Displacements Von Mises Stress and Strain Vector plots

Fixed at this end

Depth = 2 cm

Width = 1 cm

Height = 1 cm

1000 N

Reflection upon the verse Conclusion

Then Allah (God) Almighty created the Alaqa (object that clings) into a modgha (chewed like

substance)

Modgha is comprised of the basic elements from which the human body is

to be composed of

Thus the first step in designing a structure is to determine the basic

elements

Then Allah (God) Almighty created the modgha (chewed like substance) into bones Bone is the assembled state of the

basic units mentioned earlier

The next step is to determine the assembly of the finite elements

Then Allah (God) Almighty covers the bones with flesh (muscles, ligaments, cartilage, etc.)

Then external forces and fixation are applied to the model

The next step is to apply boundary conditions (BCs) to the structure

Then Allah (God) Almighty brings forth the structure plus the BCs with another

mechanism of creationThen the applied BCs are activated

The next step is to investigate the interaction between the applied

BCs and the structure

Then We made the Nutfah into a clot (a piece of thick coagulated blood), then We made the clot into a little lump of flesh, then We made out of that little lump of flesh bones, then We clothed the bones with flesh, and then We brought it forth as another creation. So blessed be Allâh, the Best of creators

The Noble Qur’an (23: 14)

In the Name of Allah (God) Almighty The Most Gracious The Most Merciful

Dr. Zaid Kasim Ghazzawi

E-mail : zaidquran@gmail.com

Website: www.quran-miracle.com