Static Analysis on a Plate with Holes using FEA in Solidworks

Aim:- Static Analysis on a Plate with Holes using FEA in Solidworks

Objective:-

1. To perform a static analysis on two models of a plate with holes
2. To run the analysis and compare the results for stress, strain, and displacement

Introduction:-

The finite element method (FEM) is the most widely used method for solving problems of engineering and mathematical models. Typical problem areas of interest include the traditional fields of structural analysis, heat transfer, fluid flow, mass transport, and electromagnetic potential. The FEM is a particular numerical method for solving partial differential equations in two or three space variables (i.e., some boundary value problems). To solve a problem, the FEM subdivides a large system into smaller, simpler parts that are called finite elements. This is achieved by a particular space discretization in the space dimensions, which is implemented by the construction of a mesh of the object: the numerical domain for the solution, which has a finite number of points. The finite element method formulation of a boundary value problem finally results in a system of algebraic equations. The method approximates the unknown function over the domain. The simple equations that model these finite elements are then assembled into a larger system of equations that models the entire problem. The FEM then uses variational methods from the calculus of variations to approximate a solution by minimizing an associated error function.

Stress is the ratio of applied force F to a cross-section area - defined as "force per unit area".

Strain is defined as "deformation of a solid due to stress".

Procedure:-

1. Design the model and create a new static study from the simulation menu.
2. Apply material like alloy steel in this case.
3. For this study, fix one end of the plate and apply 1000 Newton force such that tensile stress occurs in the plate.
4. Define mesh as fine for better results.
5. Run the study and compare the results.

Material and properties for this analysis:-

Name: Alloy steel

Model type: Linear elastic isotropic

Failure criterion set: Max Von Mises stress

Yield strength: 6.20422e+08 N/m²

Tensile strength: 7,23826e+08 N/m²

Mass density: 7700 kg/m³

Elastic modulus: 2.1e+11 N/m²

Poisson’s ratio: 0.28

Study 1- Plate 1 with 1 hole

Sketch model:

Length=300mm
Height=120mm
Thickness=30mm
Circular Hole at the center:
Diameter=60mm

Fixture and Load:

Apply a fixed relation to one of the short sides of the plate and apply a force of 1000N on the other such that the plate is stretched.

Here left face is fixed and the force of 1KN is applied on the right face so that tensile stress occurs.

Mass Properties:

Stress:

Displacement:

Strain:

Study 2- Plate 2 with 3 holes

Sketch model:

Length=300mm
Height=120mm
Thickness=30mm
Circular Hole at the center:
Diameter=60mm

Two holes of 30 mm diameter are placed 90mm away from the central hole on both sides.

Fixture and Load:

Apply a fixed relation to one of the short sides of the plate and apply a force of 1000N on the other such that the plate is stretched.

Here left face is fixed and the force of 1KN is applied on the right face so that tensile stress occurs.

Mass Properties:

Stress:

Displacement:

Strain:

Data Comparison:-

Properties		Plate with 1 hole		Plate with 3 holes
		Max	Min	Max	Min
Stress (N/m^2)		1,189,106.125	42,734.238	1,155,990	6,185.811
Strain (mm)		`4.38*10^-6`	`0.25*10^-6`	`4.19*10^-6`	`0.03*10^-6`
Displacement (mm)		`5.24*10^-4`	0.0	`5.66*10^-4`	0.0
Mass (kg)		7.66		7.34

On comparing the maximum values, we concluded that:

In the plate with 1 hole, the stress and strain are maximum, while the displacement is less than the plate with 3 holes.

In the plate with 3 holes, the stress and strain are less than the plate with 1 hole, while the displacement is more.

The mass of the plate with 1 hole is greater than the plate with 3 holes because the solid material is more in plate 1 than plate 2, while the plate dimensions are the same.

Conclusion:-

1. As per the optimum selection of the plates, we will choose a plate with 3 holes because the stress and strain are less than the plate with only 1 hole. Moreover, it has slightly less mass than the plate 1, which will be economical.
2. The stress is acting vertically around the diameter of the center hole while the force is applied longitudinally along with the plate.
3. The stress and strain values are more on the plate with a single hole.
4. The stress and strain that occurred in the plate with 3 holes are less than the plate with a single hole because they got distributed among all the holes.
5. From this study, we observed that how a model changes its behaviour if certain changes are made to its geometry while keeping the study parameters constant.

Reference:-

https://en.wikipedia.org/wiki/Finite_element_method

https://www.engineeringtoolbox.com/stress-strain-d_950.html#:~:text=Strain%20is%20defined%20as%20%22deformation%20of%20a%20solid,in%20angle%20between%20two%20line%20segments%20originally%20perpendicular