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FEA Literature Survey

RRohit Bisht12 Feb 2020

Stress = Ratio of Internal Resisting Force to the cross-sectional area.

Strain = Ratio of Change in dimension to the original dimension.

Longitudinal Strain = change in length on longitudinal by original length in the longitudinal direction.

Lateral/Transverse Strain = Change in length on lateral by orignal in lateral direction

Poisson ratio = Lateral / Longitudnal strain

Poisson Effect

When a material is stretched in one direction, it tends to compress in the direction perpendicular to that of force application and vice versa. The measure of this phenomenon is given in terms of Poisson’s ratio. For example, a rubber band tends to become thinner when stretched.

Poisson’s ratio values for different material

It is the ratio of transverse contraction strain to longitudinal extension strain, in the direction of the stretching force. There can be a stress and strain relation which is generated with the application of force on a body.

For tensile deformation, Poisson’s ratio is positive.
For compressive deformation, it is negative.

Here, the negative Poisson ratio suggests that the material will exhibit a positive strain in the transverse direction, even though the longitudinal strain is positive as well.

For most materials, the value of Poisson’s ratio lies in the range, 0 to 0.5. (-1 to 0.5). (Poisson’s ratio 0.5 means a perfectly incompressible material is deformed elastically at small strains.)

A few examples of Poisson ratio is given below for different materials.

Material	Values
Concrete	0.1 – 0.2
Cast iron	0.21 – 0.26
Steel	0.27 – 0.30
Rubber	0.4999
Gold	0.42 – 0.44
Glass	0.18 – 0.3
Cork	0.0
Copper	0.33
Clay	0.30 – 0.45
Stainless steel	0.30 – 0.31
Foam	0.10 – 0.50

Stiffness is the extent to which an object resists deformation in response to an applied force. The complementary concept is flexibility or pliability: the more flexible an object is, the less stiff it is.

k = F / δ

the spring stiffness is the force required to cause unit deflection

TYPES OF ANALYSIS

1. Linear Static Analysis: In the linear analysis, the FE solver will assume the straight-line path of the stress stain graph where it obeys hooks law.

Example: in terms of linear material Stress=Strain*Youngs Modulus of elasticity.

2. Non-Linear Analysis:

a) Material Non-Linearity

b) Geometrical Non-Linearity

c) Contact Non-Linearity ( where two different bodies are in frictional contact)

3. Dynamic Analysis (Vibration Problem): Where time comes in, where time affects the result.

[M]x'' + [C]x' + [K]x = f(t) (Force is a function of time), For Linear Static Analysis only [K]x=f is used.

where M=Mass

C=Damping coefficient (is a material property that indicates whether a material will bounce back or return energy to a system) (Low Damping Coefficient a Good Bounce Back eg Basketball)

K =Stifness

x''=Accelaration

x'=Velocity

x=Displacement

4. Buckling Analysis: Scenario in which material fail even without seeing the yield stress or tensile stress,

5. Thermal Analysis:

a) Conduction

b) Convection

c) Radiation

6. Fatigue Analysis, (Repeated loading)

a) High Cycle fatigue

b) Low Cycle Fatigue

7. Optimization: To reduce unnecessary material in order to reduce weight and make it cost-effective.

FEA Literature Survey

Poisson Effect

Poisson’s ratio values for different material

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Poisson Effect

Poisson’s ratio values for different material

Ship work like thisin your own course.

Talk to a career counsellor

Ship work like this
in your own course.