SUMMARY OF CAE

What is CAE?

         Computer Aided Engineering is the computer method simulation in engineering which can be perform to evaluating the fatigue life and structural behaviour of the testing components with the help of finite element method(FEM) or finite element analysis(FEA).

   It is very important chapter of an engineering,I  request to all students you should contribute much more to learn finite element method through this you would get more practical exposure of an engineering.

What is FEM or FEA?

          It is nothing but finite element method is based on idea of building the complicated objects into simple pieces or dividing a complex body into small or managable pieces or elements in engineering.

It is closely integrated with CAD/CAM application.

3-D Truss

Threaded bolt and nut

Cover of pressure cylinder

Translational joints

High speed impact

Drop test

Application of FEM  in Engineering

1. Aerosapce,Mechnical,Civil,Automobiles
2. Structural analysis(linear/non-linear and static/dynamics)
3. Thermal/fluid flows
4. Electromagnetics
5. Biomechanics
6. Geomechanics ..etc.                          

 

Procedures to implement FEM analysis

1. Divide structure into pieces(Element with nodes)
2. Describe the behaviour of physical quantities on each elements
3. Assemble the elements at the nodes to form an  approximate equation for the entire structure
4. Solve the system of equation involving unknown quantities at the nodes....(eg: displacements)
5. Calculate the desired quantities  such as stress,strains..etc.. at the elements.

Computer Implementations

1.Preprocessor
       To built the FEM model,constraints and loading conditions
2.FEM Solver
       To assemble the whole model and solve the system of equations by using mathematical forms
3.Postprocessor
       To order and displays the results which means...stress,strain,shear,displacement on each elements

We might know how many commercial FEM Softwares

1. ANSYS (General purposes)
2. SDRC/I-DEAS (Complete CAD/CAM/CAE packages)
3. NASTRAN (General purpose FEM on mainframes)
4. ABAQUS (Non-linear and dynamic analysis)
5. COSMOS (General purpose FEM)
6. ALGOR (PC and workstation)
7. PATRAN (Pre and Postprocessor)
8. HYPERMESH (Pre and Postprocessor)
9. DYNA-3D (Crash and Impact analysis)...etc.

A Link to CAE softwares and company

FEA of an unloader trolley(click for more info)

For more examples: FEA actions


Types of Finite Elements
1. 1-D Elements(Line)
      a.Beam
      b.Spring
      c.Truss
      d.Bar
      e.Pipe..etc.

2. 2-D Elements(Plane)
     a.Membarane
     b.Shell
     c.Plate..etc.

3. 3-D Elements(Solids)
           3-D fields- temperature,displacement,stress and flow velocity).

Linear Static Analysis
                Most of the structural problems can be treated as linear static problems based on the following assumptions are,

1. Small deformation( loading patterns are not changed due to the deformed shape)
2. Elastic materials (which means no plasticity or failure)
3. Stati loads ( the load applied to the structure at slow and steady)

1-D problems
    Spring Elements
Do's and Dont's in the spring elements

1. It is only for stiffness analysis,not for stress analysis of spring elements
2. can have the spring element with stiffness in lateral direction and torsion.etc.

    Spring Force-Displacement relationship
                             
                     F = KU                        U = (u2 - u1 )
                             
F-  Element Nodal force (lb,N)   U- Element Nodal displacement (in,m,mm)   K- Element Spring stiffness (lb/in,N/m).

Checking the results

1. Deformed shape of the body
2. Balance of the external forces
3. Order of magnitude of the number

Bar and Beam Elements
It is based on the follwing realation,

1. Strain-Displacement relationship
2. Stress-Strain relationship

Procedure for Theoretical Calculation

1. We consider the parameters of 1-D bar elements are length(L),cross-sectional area(A),Elastic modulus(E),Displacement(u),stress and strain.
2. To calculate the stiffness by using direct method or formal approach.
3. Direct method means assuming the displacement varying linearly along with the axis of bar.
4. Formal approach means by using the galarkein method to calculate stiffness matrix through the principal potential energy.

For example:A simple plane truss is made up of two identical bars with loaded condition
Steps:

1. We need to convert them to global co-ordinate
2. Calculate the stiffness matrix for the element of the co-ordinate system.
3. Assemble the system of finite element equation
4. Apply the load and boundary condition
5. Rearrange the finite element equation
6. Solve the unknown value of the displacements
7. Finally we calculate the stresses in each bars

But in 3D case the element stiffness matrices are calculated in the local cordinate and the transformed into the global co-ordinate system.

Cheking the results

1. Calculated stresses in the elements are exacts within the linear theory of 1-D bar elements.
2. For tapered bars averaged value of the cross-sectional areas should be used for the elements.
3. We need to find the displacement at first inorder to stresses under the displacement based FEM.

Degrees of freedom(DOF)
Number of components of the displacement vector at a node
In 1-D element,each node has a DOF.

Beam element
The Parameters of the  simple plane beam are  given below,

1. Length(L),
2. Moment of inertia of the cross-sectional area,
3. Elastic modulus(E),
4. Deflection (Lateral displacement) of the  neutral axis,Rotation about Z-axis(teta),
5. Moment about Z-axis(M),
6. Shear force(F)

 Generally two methods are used to calculate the element stiffness either direct method or formal approach

In direct method using the result from Element Beam Theory  to cumpute each element of the stiffness matrix 

 

In Formal approach using strain energy equation with derivation of the shape function.

In 3D cases the element stiffness matrix are formed in local co-ordinate system(2D)  then transformed into Global co-ordinate system to be assembled.

 

Procedure to Calculate the simple plane beam element

1. To form the element stiffness matrices by given lenth and displacement values.
2. Assemble the global finite element equation
3. Apply loads and constraints(BCs)
4. Do find rection forces and moments from the global FE equations

But in 3D case element the stiffeness matrix is formed in the local coordinate system first then it is transformed into global coordinate system to be assembled.

FE Analysis of frame structures
                 Members in a frames are consider to be a rigid connected and forces and moments can be transmitted to their joints so we need
                 Frames= bar+simple beam elements