Structural analysis of plate with holes using SolidWorks
AIM
To perform static analysis on 2 models of plate with holes and compare the results for stress, strain and displacement.
THEORY
Plate structure with holes is widely applied in engineering practices. The reason making holes on the plate could vary, some for installing bolts and other connectors, and others for reducing weight without mainly affecting mechanical properties.
The plates with discontinuities like circular or elliptic holes exist in all metal structures. Those areas represent dangerous zones because of the multiplication of the stresses values under the effect of the stress concentration phenomenon. These stress concentration zones are often areas of crack initiation. They can be dangerous if the loading conditions allow the brutal propagation of the cracks and then promote the rupture. The stresses concentration phenomenon is measured by a parameter called stress concentration factor (SCF), noted Kt. This factor is the ratio of the maximum elastic stress value by the nominal stress calculated in the discontinuity area.
Stress concentration factor
A stress concentration (also called a stress raiser or a stress riser) is a location in an object where the stress is significantly greater than the surrounding region. Stress concentrations occur when there are irregularities in the geometry or material of a structural component that cause an interruption to the flow of stress. This arises from such details as holes, grooves, notches and fillets. Stress concentrations may also occur from accidental damage such as nicks and scratches.
The degree of concentration of a discontinuity under typically tensile loads can be expressed as a non-dimensional stress concentration factor `K_t`, which is the ratio of the highest stress to the nominal far field stress.
`K_t` = `sigma_(max)/sigma_(nomi nal)`
The maximum stress felt near a hole or notch occurs in the area of lowest radius of curvature. In an elliptical hole of length 2a and width 2b, under a nominal or far-field stress `sigma_(nom)`, the stress at the ends of the major axes is given by Inglis' equation:
`sigma_(max) = sigma_(nom)*(1 + 2*a/b) = sigma*(1 + 2*sqrt(a/rho))`
For a circular hole, a=b. Therefore,
`sigma_(max) = 3*sigma_(nom)` or,
`K_t = 3`
OBJECTIVE
The objective of this project is to perform static analysis of 2 models of plate with hole; one having a single hole of diameter 60mm at the center and the other having 3 holes, one of dia 60mm at the center and 2 collinear holes of dia 30mm each, at a distance of 90mm from the center hole. Then, we would compare the effect of the additional holes on the stress, strain and the displacement of the plate under the effect of a tensile load of 1kN.
Case 1: Plate with single hole of diameter 60mm at the center
i) Create the plate as per the given dimensions (300mm x 120mm) and extrude it to a thickness of 30mm. Create a hole of diameter 60mm at the center of the plate.
ii) From simulation tab, select new study and start a new static study.
iii) Apply suitable material to the plate (alloy steel in this case) and fix the smaller face. On the opposite face, apply a tensile load of 1kN.
iv) Create the standard mesh and run the simulation. Right click on results and select compare results and continue.
Case 2: Plate with 3 holes
i) Create the plate same as in case 1. Along with a hole at the center, create 2 more holes, each of diameter 30mm and at a distance of 90mm from the center hole, at either side of it. Make sure all the holes are collinear.
ii) Repeat steps ii), iii), iv) from the case 1.
RESULT
Case 1
Case 2
OBSERVATION AND CONCLUSION
Comparing the results of both the cases, we can see that both the stress as well as the strain in the plate decreases for the plate with 3 holes. The deformation is slightly higher in case 2 than in case 1. It is because with additional holes, the stress gets distributed and is no more concentrated only at the center hole as in case 1. This reduces the chances of failure due to applied loads and thus increases the life of the component.
Not only that, creating additional hole also helps in reducing the weight of the plate while maintaining its functionality and increasing its life, thus making it more suitable to be used. However, drilling extra holes requires more machining time and also increases the manufacturing cost. Therefore, the design must be selected based on the requirements and not just by which one is better.
We can conclude that additional holes in this case act as stress relievers. The small changes in the geometry of the component could greatly affect the stress concentration at a point and lead to increased life. However, it has economic disadvantage as it would require more time as well as effort. Therefore, it is preferred only where it is feasible.