ABSTRACT

In this study, the stress distribution of rectangular plate having a circular hole is analyzed. The two different rectangular plates having different geometric parameters are used for this analysis and results compared with one another to get an idea about stress distribution and deformation for the designing of the plate. From the present investigation, it can be concluded that the maximum stress occurs at corners of holes in both the cases. Thus, from the present study, it can be said that finite element analysis is a very effective tool to determine stresses induced in various materials.

INTRODUCTION

The elements, which are used for machining purposes offered with geometrical irregularities, which disturb the stress distribution and therefore, the state of stress in stress concentrated regions cannot be described in machine elements. Thus, the finite element method (FEM) is an important tool used to analyze the stress. The finite element method (FEM) is a numerical method of analysis for stresses and deformations in structures of any given geometry. The structure is discretized into the so-called ‘finite elements’ connected through nodes. The type, arrangement and a total number of elements affect the accuracy of the results.

It is frequently used to solve the difficult engineering problems, mostly in the fields of mechanical, civil, and aeronautical engineering. Also, it is a solution of several other types of engineering problems like heat conduction, fluid dynamics, electric and magnetic fields, structure analysis, solid mechanics, dynamics, thermal analysis, electrical analysis, biomaterials.

1. Material Used:

For our Analysis, we are using 1060 Aluminum alloys, which are the most widely used non-ferrous metals in engineering owing to their attractive properties, such as high strength-to-weight ratio, good ductility, good corrosion resistance, availability and low cost.

1060 aluminum alloy is an aluminum-based alloy in the "commercially pure" wrought family (1000 series). It is fundamentally very similar to 1050 aluminum alloy, with the difference coming down to 0.1% aluminum by weight. However, while both 1050 and 1060 are covered by the same ISO standard, they are covered by different ASTM standards.

As a wrought alloy, it is typically formed by extrusion or rolling. It is commonly used in the electrical and chemical industries, on account of having high electrical conductivity, corrosion resistance, and workability. It has low mechanical strength compared to more significantly alloyed metals. It can be strengthened by cold working, but not by heat treatment.

The material is selected under the ‘Material Section’ of the Feature Tree from the SolidWorks.

Figure 1: Material Properties of 1060 Aluminum Alloy

Thus, nowadays, there is a requirement of information about the stress concentration in designing the structure component. Although, the majorities of service cracks occurred in the area of stress concentration at the edge of a hole. In this investigation, the stress distribution of circular holes plate having two different geometric specifications is carried out and results compared one another to get an idea about stress distribution and deformation for the designing of the plate.

1. Problem Definition:

A rectangular plate of material 1060 Aluminum Alloy has been taken for calculating stresses induced and deformations produced due to the applied load.

So, we perform a static analysis on two models of plate with the holes.

1.1. CASE1:

The dimensions are as follows:

Length: 300mm

Height: 120mm

Thickness: 30mm

Hole Diameter: 60mm.

Figure 2: Rectangular Plate with a single hole

1.2. CASE2:

The Dimensions are as follows:

Length: 300mm

Height: 120mm

Thickness: 30mm

Hole Diameter: 60mm

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

Figure 3: Rectangular Plate with 3 circular hole

We apply a fixed relation to one of the short side of the plate and apply a Force of 1000N on the other, such that the plate is stretched. We perform the simulation study and compare the results for stress, strain and displacement.

2. Boundary Conditions of Rectangular Plate with Circular Hole:

The short side of the rectangular plate is held fixed and a Tensile Force of 1000N is applied on the other side of the plate, so that the plate is in the stretched position.

1. First, click on the Fixtures Tab on the SolidWorks Feature Tree – Under the fixtures tab, we choose the fixed geometry for constraining one end of the rectangular plate.
2. Under the External Loads Tab on the Features Tree we choose the external force of magnitude of 1000N, in the opposite direction i.e. away from the plate.

Figure 4: Boundary Conditions of a Rectangular Plate with Circular Hole

3. Finite Element Method:

The finite element method analysis is executed in popular FEA package in SolidWorks. The model of the geometry is produced and analyzed in SolidWorks. The force is applied on one side of the plate, keeping the other end fixed.

3.1. Meshing:

Meshes are the base of Finite Element Analysis. When possible, symmetries should always be considered in the model in order to reduce the number of elements in the analysis. Moreover, these symmetry conditions will play the role of boundary conditions in this analysis.

In FEA analysis, the number of mesh elements and the element size is very important because accuracy of the results depend on it. One can observe that the Von Mises Stress results are strongly correlated with the mesh size, but this is not the only factor.

Simple triangular elements with 3 nodes TRI3, will almost always give inaccurate results, at least when the mesh size is very coarse.

High level triangular elements with 6 nodes TRI6 will give much better results than TRI3, because they have a middle node on each edge. The only disadvantage is that the number of nodes in the model is much higher and solver will take more time and memory space for the calculation.

Simple quad elements are better than simple triangular elements because they have 4 nodes instead of 3, but meshing with quad element may not be appropriate for all types of geometries.

To get more accurate results, we keep the triangular mesh size as fine as possible.

Figure 4: Triangular Mesh on a Rectangular Mesh

In figure 2, (Case1) the triangle mesh size is 4mm. The model is meshed with solid 95048 elements and having 138523 total nodes. This element has the capabilities like plasticity, creep, stress stiffening, large deflections etc.

Figure 5: Number of Nodes and Elements for Case 1

For Case 2:

Figure 6: Triangular Mesh on a Rectangular Plate

In figure 2, (Case1) the triangle mesh size is 4mm. The model is meshed with solid 95048 elements and having 138523 total nodes. This element has the capabilities like plasticity, creep, stress stiffening, large deflections etc.

Figure 7: Number of Nodes and Elements for Case 2

Results:

For Case1:

Figure 4 – Equivalent Von-Mises Stress, Displacement, Strain & Factor of Safety for a Rectangular Plate with a circular hole.

For Case 2:

Figure 5 – Equivalent Von-Mises Stress, Displacement, Strain & Factor of Safety for a Rectangular Plate with 3 circular holes.

Table 1: Parameters obtained from Finite Element Analysis:

Model	Material	Maximum Von-Mises Stress (N/mm^2)	Maximum Displacement (mm)	Maximum Strain	Minimum Factor of Safety
Rectangular plate with a single hole	1060 Aluminum	1.214	0.002	1.45e-5	22.71
Rectangular plate with 3 circular hole	1060 Aluminum	1.166	0.002	1.45e-5	23.655

The stress holding capacity for the Rectangular plate with 3 circular holes is more than the rectangular plate with a single hole and also has higher maximum stress holding capacity as compared to the other.

Conclusion:

From the present investigation, it can be concluded that the maximum stress occurs at corners of holes in both the cases. The rectangular plate with 3 holes can be used for other applications in comparison with the rectangular plate with a single hole since it is having higher factor of safety and is also having higher stress taking capacity.