Buckiling Analysis And Optimization Of Cyclone Separator Stand
AIM:
To perform Buckling Analysis for the Cyclone Separator Stand with and without Stiffener and Optimize the model for Rectangular and L shaped Stiffener at different positions with constrained Buckling factor of safety to get optimal Buckling factor of safety (BFOS) and to compare the results.
DESCRIPTION:
In engineering, buckling is the sudden change in the shape of a structural component under load such as the bowing of a column under compression or the wrinkling of a plate under shear. If a structure is subjected to a gradually increasing load, when the load reaches a critical level, a member may suddenly change shape and the structure and component is said to have buckled.
Buckling may occur even though the stresses that develop in the structure are well below those needed to cause failure in the material of which the structure is composed. Further loading may cause significant and somewhat unpredictable deformations, possibly leading to complete loss of the member's load-carrying capacity. However, if the deformations that occur after buckling do not cause the complete collapse of that member, the member will continue to support the load that caused it to buckle. If the buckled member is part of a larger assemblage of components such as a building, any load applied to the buckled part of the structure beyond that which caused the member to buckle will be redistributed within the structure. Some aircraft are designed for thin skin panels to continue carrying load even in the buckled state.
Buckled skin panels on a B-52 aircraft
GOVERNING EQUATIONS:
The two main factors leading to the failure of the mechanical component is ‘material failure’ and ‘structural instability’, which is often known as ‘buckling’.
Material failure can be predicted by the linear finite element analysis, by solving the linear algebraic system for unknown displacements,
`K.δ=F`
The stress and strain obtained from the analysis is compared with the design stress or strain(allowable) everywhere within the component
Buckling failure is primarily characterized by loss of structural stiffness, and is not modelled by usual linear finite element analysis.
What is Buckling Analysis and how it is Calculated?
Buckling is usually independent of the material strength and always occurs within the elastic range of the material.
It can be modelled by finite element eigenvalue – eigenvector solution,
`|K+λ_m K_F | δ_m=0`
Where,
`K_F`= Additional Geometric Stiffness due to stress caused by loading
`λ_m`= Buckling load Factor (BLF) for m-th mode
`δ_m` = Buckling displacement for m-th mode
What is Euler-buckling?
The spatial distribution of the load is important than its magnitude
The long slender member subjected to a compressive force moves laterally to the direction of the force applied, commonly known as ‘Euler-buckling’
The force F, necessary to cause the buckling is sensitive to the component restraints (end restraints)
Note: For very long columns the loss of stiffness occurs at stresses far below the material failure.
BUCKLING TERMINOLOGY:
1) STIFFNESS
2) SLENDER
3) LONG
1) STIFFNESS:
Stiffness is related to either elastic modulus E, or its Shear Modulus G,
G=E/(2+2v)
Where v is Poisson’s ratio
2) SLENDER:
Slender is a geometric concept of a two-dimensional area that is quantified by the radius of gyration, r
The radius of gyration, r, has the units of the length and describes the way in which the area of cross-section is distributed around its centroidal axis.
If the area is concentrated far from the centroidal axis it will have a greater value of r and greater resistance to buckling.
A non-circular cross-section will have two values for its radius of gyration and section tends to buckle around the axis with the smallest value the radius of gyration r, is defined as:
`r=(I/A)^(1/2)`
I – Moment of inertia
A – Cross-section Area
3) LONG
Long is also a geometric concept that is quantified by the non-dimensional ‘slenderness ratio’ L/r, where L denotes the length of the component.
The slenderness ratio is defined to be long when it obeys the inequality
`L/r>(π/K).((2E)/σ_y )^(1/2)`
Where K is a constant that depends on the restraints of the two ends of the column
A long slenderness ratio is typically in the range of > 120
The above equation is the dividing point between long (Euler) columns and Intermediate (empirical) columns.
INFLUENCE OF END RESTRAINTS ON CRITICAL BUCKLING LOAD:
The critical buckling force is
critical Euler buckling stress is
Buckling Load Factor (BSF):
The buckling load factor (BLF) is an indicator of the factor of safety against buckling or the ratio of the buckling loads to the currently applied loads.
Always utilize a high factor of safety (FOS) for buckling loads.
The following table shows the possible BLF Values returned by SOLIDWORKS SIMULATION,
OBJECTIVES:
1) To determine the Buckling factor of safety for Buckling of Cyclone Separator Stand without any Stiffener.
2) To compare the Buckling factor of safety for Cyclone Separator Stand without stiffener and with Rectangular and L shaped Stiffener, both having the same cross-sectional area.
3) To Run a Design study and to Optimize the model for Rectangular and L shaped Stiffener for different positions with constrained Buckling factor of safety to get optimal Buckling factor of safety (BFOS) and compare the results.
PROCEDURE:
The Entire Process of FEA analysis is divided into 3 parts
1) Pre-Processing
Geometry Creation
Generation of Mesh
Assignment of Material properties
Boundary Conditions
2) Processing
Governing Equations are applied to the discretized elements and displacements will be calculated.
[F]=[K]*[X]
F=Loads
K= indicates geometric and material properties
X=Displacement
Run the simulation
3) Post-Processing
After the calculation of the displacements across the nodes the Stress and Strains can be calculated at any point.
Create the required Contours and Plots
Interpret the Results
Modify the geometry to get the optimized results
PRE-PROCESSING:
GEOMETRY AND MATERIAL PROPERTIES:
We will be performing simulations for 3 cases and run an optimization design study
CYCLONIC SEPERATOR STAND
1) WITHOUT STIFFENER
2) WITH RECTANGULAR STIFFENER
3) WITH L SHAPED STIFFENER
For all cases, we have assigned the material as Alloy-steel
Properties: Alloy-steel
Cyclone separator along with stand is modelled and in this, the cyclonic separator is suppressed to perform simulation on its stand.
CASE 1: WITHOUT STIFFENER
CASE 2: WITH RECTANGULAR STIFFENER
CASE 3: WITH L SHAPED STIFFENER
BOUNDARY CONDITIONS:
Here for all the cases the top part of the Stand is are applied by a load of 150KN uniform along the face and is Fixed from the ends of the four legs.
CASE 1: WITHOUT STIFFENER
CASE 2: WITH RECTANGULAR STIFFENER
The stiffener is positioned 800mm from top face
CASE 3: WITH L SHAPED STIFFENER
The stiffener is positioned 800mm from top face
MESH:
CASE 1: WITHOUT STIFFENER
CASE 2: WITH RECTANGULAR STIFFENER
CASE 3: WITH L SHAPED STIFFENER
PROCESSING:
HIT RUN
Governing Equations are applied to the discretized elements and displacements will be calculated.
Buckling is usually independent of the material strength and always occurs within the elastic range of the material.
It can be modelled by finite element eigen value – eigen vector solution,
It can be modelled by finite element eigenvalue – eigenvector solution,
`|K+λ_m K_F | δ_m=0`
Where,
`K_F`= Additional Geometric Stiffness due to stress caused by loading
`λ_m`= Buckling load Factor (BLF) for m-th mode
`δ_m` = Buckling displacement for m-th mode
POST-PROCESSING:
RESULTS AND CONTOURS
STUDY 1: BUCKLING ANALYSIS OF CYCLONE SEPERATOR STAND WITHOUT STIFFENER
AMPLITUDE CONTOUR:
BUCKLING FACTOR OF SAFETY (BSOF):
STUDY 2: BUCKLING ANALYSIS OF CYCLONE SEPERATOR WITH RECTANGULAR STIFFENER
BUCKLING FACTOR OF SAFETY (BSOF)
STUDY 3: BUCKLING ANALYSIS OF CYCLONE SEPERATOR WITH L SHAPED STIFFENER
BUCKLING FACTOR OF SAFETY (BSOF):
STUDY 4: DESIGN STUDY- TO OPTIMIZE THE MODEL WITH RECTANGULAR STIFFENER FOR DIFFERENT POSITION TO GET MAXIMIZE THE BUCKLING FACTOR OF SAFETY (BSOF)
Here the input is taken as the offset distance from the Top-face and the distance is varied from 100mm to 2000mm with an increment of 100mm
Buckling factor of safety is taken as the constraint to have a value greater than 22
And goals are set to Maximise the Buckling factor of safety
RESULTS:
Here we have 20 Scenarios
PLOT:
Form the plot we can see that as we increase the offset distance from 100mm the buckling factor of safety increases up to the point where it is maximum of value 27.616 at Scenario 10 at an offset distance of 1000mm from top face and then decreases as the offset distance increases further.
STUDY 5: DESIGN STUDY- TO OPTIMIZE THE MODEL WITH L SHAPED STIFFENER FOR DIFFERENT POSITION TO GET MAXIMIZE THE BUCKLING FACTOR OF SAFETY (BSOF)
Here the input is taken as the offset distance from the Top-face and the distance is varied from 100mm to 2000mm with an increment of 100mm
Buckling factor of safety is taken as the constraint to have a value greater than 25
And goals are set to Maximise the Buckling factor of safety
RESULTS:
Here we have 20 Scenarios
PLOT:
Form the plot we can see that as we increase the offset distance from 100mm the buckling factor of safety increases up to the point where it is maximum of value 28.3038 at Scenario 9 at an offset distance of 900mm from top face and then decreases as the offset distance increases further.
CONCLUSION:
|
MAXIMUM BUCKLING FACTOR OF SAFETY (BSOF) |
|
|
WITHOUT STIFFENER |
9.3619 |
|
WITH RECTANGULAR STIFFENER |
27.616 |
|
WITH L SHAPED STIFFENER |
28.3038 |
From the Results contours and plots we can observe that the least value of buckling factor of safety (BFOS) is obtained when there is no stiffener used and in the comparison between the case when a rectangular stiffener is used to that when L shaped stiffener is used for the same cross-section, the L-shaped Stiffener gives a higher value of BFOS compared which is 28.3028 at 900mm offset from the top face compared to the Rectangular Stiffener which gives 27.616 at 1000mm offset from the top face. Hence adding stiffener to the stand increases the BFOS and the L-shaped Stiffener is preferred over the Rectangular Stiffener.