5. METHODSTO SOLVEANY ENGINEERINGPROBLEM
Analytical Method Numerical Method Experimental Method
Classical approach Mathematical representation Actual measurement
100 % accurate results Approximate, assumptions made.
Applicable even if physical
prototype not available (initial
design phase)
Time consuming & needs
expensive set up
Applicable only for simple
problems like cantilever, simply
supported beams etc.
Real life complicated problems Applicable only if physical
prototype is available
Results can not be believed blindly
& must be verified by
experimental method or hand
calculation for knowing the range
of results
Results can not be believed
blindly& min. 3 to 5 prototypes
must be tested
Strain Gauge, photoelasticity,
Vibration Measurements,
Fatigue Test
Sensor for temp & Pressure etc
6. Finite Element Method: Linear, Non linear. Buckling, Thermal. Dynamic &
Fatigue analysis
Boundary Element Method: Acoustics/NVH
Finite Volume Method: CFD
(Computational Fluid Dynamics) & Computational
Electromagnetism
Finite Difference Method: Thermal & Fluid flow analysis (in combination with
FVM)
Numerical Methods
7. Is it possible to use all of the methods listed above (FEA, BEA, FVM,
FDM) to solve the same problem (for example, a cantilever problem)?
The answer is YES! But the difference is in the accuracy achieved,
programming ease, and the time required to obtain the solution.
8. What is FEA/FEM ?
Numerical method, Mathematical representation of an actual problem, approximate
method.
The finite element reduces the degree of freedom from infinite to finite with the help
of discretization or meshing(nodes and elements).
9. Modelling of a body by dividing it into a equivalent system of finite elements,
interconnected at a finite number of points on each element called Nodes.
This whole process of dividing continuous objects into discrete parts called
as Discretization.
Discretize the given continuum/domain
10.
11. Nodes
An independent entity in space is called a node. Nodes are similar to the points in geometry and
represent the corner points of an element. The element shape can be changed by moving the
nodes in space. The shape of a node is shown in Figure.
• Node
Elements
Element is an entity into which the system under study is divided. An element shape is specified
by nodes. The shape (area, length, and volume) of an element depends on the nodes with which
it is made. An element (bar element) is shown in Figure.
12.
13. What Is Stiffness And Why Do We Need It In FEA?
Stiffness ‘K’ is defined as Force/length (units N/mm). Physical interpretation –
Stiffness is equal to the force required to produce a unit displacement. The
stiffness depends on the geometry as well as the material properties.
Measure the force required to produce a
1 mm displacement
KCI > KMS > KAl
14. Consider 3 different cross sectional rods of the same material. Again, the force
required to produce a unit deformation will be different.
Stiffness depends on the geometry as well as the material.
15. Importance of the stiffness matrix
For structural analysis, stiffness is a very important property.
The equation for linear static analysis is [F] = [K] [D].
The force is usually known, the displacement is unknown, and the stiffness is a
characteristic property of the element.
16. General Steps
Discretize the given continuum/domain
Divide domain into finite elements using appropriate element
types (1-D, 2-D, 3-D, or Axisymmetric)
Select a Displacement Function
Define a function within each element using the nodal values
Derive the Element Stiffness Matrix and Equations
Assemble the Element Equations to Obtain the Global Stiffness
matrix
17. General Steps
Enforcing the Boundary Conditions
Elimination Method
Penalty Method
Solve for the Unknown Degrees of Freedom (i.e primary
unknowns)
20. FEM Packages
• Commercial Softwares
– Designed to solve many types of problems
– Can be upgraded fairly easily
– Initial Cost is high
– Less efficient
• Special-purpose programs
– Relatively short, low development costs
– Additions/ Modifications can be made quickly
– Efficient in solving their specific types of problems
– Can’t solve different types of problems
22. MERITSOF FEM
Can readily handle very complex geometry
The heart and power of the FEM
Can handle a wide variety of engineering problems
Solid mechanics - Dynamics - Heat problems - Fluids - Electrostatic
problems
Can handle complex restraints
Indeterminate structures can be solved.
Can handle complex loading
Nodal load (point loads) - Element load (pressure, thermal, inertial
forces) - Time or frequency dependent loading
23. MERITSOF FEM
Can handle bodies comprised of nonhomogeneous materials
Every element in the model could be assigned a different set of material
properties.
Can handle bodies comprised of nonisotropic materials
• Orthotropic • Anisotropic
Special material effects are handled
• Temperature dependent properties. • Plasticity • Creep • Swelling
Special geometric effects can be modeled
• Large displacements. • Large rotations. • Contact (gap) condition.
24. DMERITSOF FEM
A specific numerical result is obtained for a specific problem
Experience and judgment are needed in order to construct a
good finite element model.
A powerful computer and reliable FEM software are essential.
Input and output data may be large and tedious to prepare and
interpret.
25. DMERITSOF FEM
Numerical problems:
Computers only carry a finite number of significant digits.
Round off and error accumulation.
Can help the situation by not attaching stiff (small) elements to flexible
(large) elements.
Susceptible to user-introduced modelling errors
Poor choice of element types.
Distorted elements.
Geometry not adequately modelled.
Certain effects not automatically included
Complex Buckling • Hybrid composites. • Nanomaterials modelling . •
Multiple simultaneous causes..
26. APPLICATIONS OF FEM
Stress and thermal analyses of industrial parts such as
electronic chips, electric devices, valves, pipes, pressure
vessels, automotive engines and aircraft.
Seismic analysis of dams, power plants, cities and high-rise
buildings.
Crash analysis of cars, trains and aircraft.
Fluid flow analysis of coolant ponds, pollutants and
contaminants, and air in ventilation systems.
27.
28. APPLICATIONS OF FEM
Electromagnetic analysis of antennas, transistors and aircraft
signatures.
Analysis of surgical procedures such as plastic surgery, jaw
reconstruction, correction of scoliosis and many others.
29. Finite Element Model of floor panel of
Automotive
FEM- model of a 3 cylinder engine
Automotive Applications
