Analysis of Buckling phenomenon

AIM

To perform a Finite Element Analysis of a Buckling phenomenon.

OBJECTIVES

• To perform Buckling analysis on a Cyclonic Separator Stand
• To create a metallic stiffener on the legs of the stand and run the analysis to find out the change in Buckling factor of safety .
• To run a Design study to find the optimum position of the Stiffener.

INTRODUCTION

Finite element analysis (FEA) is the process of simulating the behaviour of a part or assembly under given conditions so that it can be assessed using the finite element method (FEM).

The simulations used in FEA are created using a mesh of millions of smaller elements that combine to create the shape of the structure that is being assessed. Each of these small elements is subjected to calculations, with these mesh refinements combining to produce the final result of the whole structure.These approximate calculations are usually polynomial, with interpolations occurring across the small elements, meaning that values can be determined at some but not all points. The points where the values can be determined are called nodal points and can usually be found at the boundary of the element.

In engineering, Buckling is the sudden change in 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

THEORY

Buckling occurs as an instability when a structure can no longer support the existing compressive load levels. Many structural components are sufficiently stiff that they will never suffer any form of instability. In Fig. 1 these structures are classically described as “short.” In practice it is the relationship between radius of gyration and length that is the deciding factor and hence long span girders of heavy section could easily be clear of any instability mode. This type of structure would only fail in compression by local yielding if load levels can reach that extreme.

Fig. 1: Classical identification of structural types and buckling response.

At the other extreme, structures that are slender could fail at load levels well below what is required to cause compressive yielding. The failing mode tends to be toward the classic Euler buckling mode. For long thin rods and struts the Euler buckling calculation can be quite accurate. The buckling here is of a bifurcation type — there is a rapid transition from axial loading response to a lateral response, which is usually catastrophic.

A very large number of structures fall into the intermediate category where the Euler buckling calculation is not very accurate and can tend to seriously overestimate the critical buckling load. The transition to instability is more gradual in this category. The structure is able to carry increasing loads, with perhaps changes in deformed shape and plasticity, until a maximum (or limit) load is reached. At this point instability occurs. This may be catastrophic, or the structure may transition to a new mode shape that can carry further load. Examples include the initial buckling of a drink can, initial buckling of a thin wing spar shear web, or the light frame of a screen door.

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.

CASE SETUP

1. First, the cyclone separator file was imported to SOLIDWORKS, then opened as an Assembly file.
2. Then all the parts excluding the Cyclone Separator Stand were suppressed and the stand was saved as a Part(SLDPRT) file.
3. This Part file is opened and the Stiffener was created-
4. The sketch of the Stiffener was made on the Top Plane.
5. Then the sketch was extruded to 75 mm at an offset distance of 1000mm from the Top Plane.
6. Then a new study was created after enabling SOLIDWORKS Simulation from SOLIDWORKS Add-ins.
7. The material was defined as ‘Alloy Steel’.
8. The bottom faces of the legs of the stand was fixed using ‘Fixed Geometry’ from ‘Fixtures’ option.
9. Then using the ‘External Loads’ option a force of 150kN was applied on the Top face of the stand.
10. Then the mesh was created and simulation was done using ‘Mesh and Run’ option.
11. Then the Design Study was carried out -

1. The Variable was chosen as the Offset distance of the Stiffener from the Top Plane.This offset distance was varied from 100mm to 2000mm with a step of 100mm.
2. The Constraint was that the Buckling Factor of Safety should be greater than 25.
3. And the Goal was to maximise the Buckling Factor of Safety.

Cyclone Separator Stand without Stiffener

Cyclone Separator Stand with Stiffener

Cyclone Separator Stand with Stiffener(with Mesh,Fixtures and Load applied)

RESULTS

Component name	Units	Current	Initial	Optimal	Scenario1	Scenario2	Scenario3	Scenario4	Scenario5	Scenario6	Scenario7	Scenario8	Scenario9
Offset	mm	1000	1000	1000	100	200	300	400	500	600	700	800	900
Buckling Factor of Safety1		27.934568	27.934568	27.934568	10.751412	11.588706	12.766006	14.145105	15.797284	17.724083	20.037357	22.767336	25.782118
Buckling Factor of Safety2		27.934568	27.934568	27.934568	10.751412	11.588706	12.766006	14.145105	15.797284	17.724083	20.037357	22.767336	25.782118

Component name	Units	Scenario10	Scenario11	Scenario12	Scenario13	Scenario14	Scenario15	Scenario16	Scenario17	Scenario18	Scenario19	Scenario20
Offset	mm	1000	1100	1200	1300	1400	1500	1600	1700	1800	1900	2000
Buckling Factor of Safety1		27.934568	26.388687	23.379381	20.537903	18.120789	16.112049	14.385419	12.950883	11.733503	10.710385	9.900243
Buckling Factor of Safety2		27.934568	26.388687	23.379381	20.537903	18.120789	16.112049	14.385419	12.950883	11.733503	10.710385	9.900243

EXPLANATION

• From the Buckling Analysis, it is seen that adding a Stiffener will provide support to the Stand and increase its ability to withstand the compressive load and prevent Buckling(all the values of Buckling Factor of Safety in the Design Study are greater than the Buckling Factor of Safety of Stand without Stiffener,i.e. 9.40)

Buckling Factor of Safety(without Stiffener)=9.40

Buckling Factor of Safety(with Stiffener)=27.93

• From the Design Study it is seen that the Buckling Factor of Safety is maximum (27.93) at 1000mm.
• Also,the Buckling Factor of Safety increases as the stiffener comes close to 1000mm.

CONCLUSION

Therefore, the Buckling Analysis was performed and the optimum position of the Stiffener was found out to be at 1000mm below the Top Face of Stand i.e. at the middle of the stand.