Finite Element Analysis
BMCG 4113
MOHD JUZAILA ABD LATIF PhD, CEng, MIMechE
Introduction: Structure
The purpose of structure is to
transfer or to carry applied load. In
the case of building and bridge,
loads are transferred to the
ground.
Structure design
- How to transfer the load on the different component of structure
Structure analysis
- Calculate stress and deformation due to the external loading
Introduction: Structure
Structure design concept
• Elements structure and non-structure
• Integrated structure
✓ Fail safe
✓ Safe life
Introduction: Structure
Structure analysis
• Strength - evaluation of stress level on the design
- how the design could stand to the external load
• Stiffness - evaluation of the deformation on the design
- how the deformation will affect the function or aesthetic of the design
Failure mode
• Fracture mechanic
• Structure instability (buckling)
• Fatigue
• Others: Environmental attack, Wear
Loading
• Static
• Dynamic
• Thermal
• Linear, Non-linear
Introduction: Finite Element Analysis
• A numerical method for solving problems of engineering and mathematical physics.
• Useful for problems with complicated geometries, loadings, and material
properties where analytical solutions can not be obtained.
• Developed by engineer using physical insight, consist of cutting a structure into
several elements (pieces of structure) describing the behavior of each element in a
simple way.
Introduction: Finite Element Analysis
Analytical Solution
• Stress analysis for trusses, beams, and other simple structures
are carried out based on dramatic simplification and idealization:
– mass concentrated at the center of gravity F
– beam simplified as a line segment (same cross-section)
• Design is based on the calculation results of the idealized
structure & a large safety factor (1.5-3) given by experience.
FEA
• Design geometry is a lot more complex and the accuracy
requirement is a lot higher. We need:
– To understand the physical behaviors of a complex object F
(strength, heat transfer capability, fluid flow, etc.)
– To predict the performance and behavior of the design; to
calculate the safety margin; and to identify the weakness of
the design accurately; and
– To identify the optimal design with confidence.
Introduction: Finite Element Analysis
FEA History
• 1950s Aircraft Industry: Wing Structure
• 1960s Civil Structures: Dams, Bridges, Nuclear installations. Complete Aircraft
Structure, Space
• 1970s Ship and Submarine. Heavy Engineering. Offshore Platforms. Machine
tools. Automotive Industry
• 1980s Small Mass-Produced Components. Domestic and Consumer Goods.
Impact and Crash Analysis
• 1990s Airbags. Biomechanics. Pedestrian Impact. Sophisticated Crash Models
Introduction: Finite Element Analysis
FEA Example
Design Criteria
Design of Static Strength
• Static strength
• Failures theory
- Maximum-normal-stress theory
- Maximum shear stress theory
- Distortion energy theory
Design of Fatigue Strength
Failure Mode
Ductile materials
• Ductile material is one which has a relatively large tensile strain before fracture
takes place. Failure is specified by the initiation of yielding.
• Ductile failure can be defined when slipping occurs between the crystals that
compose the material. This slipping is due to the shear stress
Example of ductile material: steels and aluminum
Failure Mode
Brittle materials
• Brittle materials has a relatively small tensile strain before fracture, failure is
specified by fracture
• The fracture of a brittle material is caused only by the maximum tensile stress in the
material, and not to the compressive
Example of brittle material: cast iron
Failure Theories
Ductile materials (yield criteria)
• Maximum shear stress theory
• Distortion energy theory
• Ductile Coulomb-Mohr theory
Brittle materials (fracture criteria)
• Maximum normal stress theory
• Brittle Coulomb-Mohr theory
• Modified Mohr
Failure Theories
• Maximum normal stress theory
Brittle materials fail suddenly through rupture or
fracture in a tensile test. The failure condition is
characterized by the ultimate strength σU.
Maximum normal stress criteria:
Structural component is safe as long as the
maximum normal stress is less than the ultimate
strength of a tensile test specimen.
a U
b U
Failure Theories
• Maximum shear stress theory
Structural component is safe as long as the maximum shearing stress is less than the
maximum shearing stress in a tensile test specimen at yield.
Y
max Y =
2
For a and b with the same sign,
a b Y
max = or
2 2 2
For a and b with opposite signs,
a −b Y
max =
2 2
Failure Theories
• Distortion energy theory (von Mises)
Structural component is safe as long as the distortion energy per unit volume
is less than that occurring in a tensile test specimen at yield.
ud uY
vonMises Y
Where vonMises = a2 − a b + b2
Failure Theories
• Maximum shear stress theory / Distortion energy theory
Comparison between maximum-shear stress and maximum-distortion
energy criteria
Actual torsion test result show
Y/Y range from 0.55 to 0.60.
Thus, the maximum-distortion-
energy theory appears more
accurate
Y
( Y )von _ Mises 3 = 1.15
=
( Y )Tresca Y
2
Y
= 0.577 Y
3
Factor of Safety
yield stress
fS =
working stress
Needed because:
➢ Mathematical models only approximation
➢ Material property vary from batch to batch
➢ Type of loading produce unknown stresses
➢ Residual stresses from manufacturing processes
➢ Effect of environment, heat, ageing, corrosion etc.
