Analysis on a plate with a hole
Aim: To create 3D CAD models and perform a static analysis on two cases of plate with holes.
Finite Element Analysis
The Finite Element Analysis (FEA) method, originally introduced by Turner et al. (1956), is a powerful computational technique for approximate solutions to a variety of “real-world” engineering problems having complex domains subjected to general boundary conditions. FEA has become an essential step in the design or modelling of a physical phenomenon in various engineering disciplines. A physical phenomenon usually occurs in a continuum of matter (solid, liquid, or gas) involving several field variables. The field variables vary from point to point, thus possessing an infinite number of solutions in the domain. Within the scope of this book, a continuum with a known boundary is called a domain. The basis of FEA relies on the decomposition of the domain into a finite number of subdomains (elements) for which the systematic approximate solution is constructed by applying the variational or weighted residual methods. In effect, FEA reduces the problem to that of a finite number of unknowns by dividing the domain into elements and by expressing the unknown field variable in terms of the assumed approximating functions within each element. These functions (also called interpolation functions) are defined in terms of the values of the field variables at specific points, referred to as nodes. Nodes are usually located along the element boundaries, and they connect adjacent elements.
The finite element analysis method requires the following major steps:
- Discretization of the domain into a finite number of subdomains (elements).
- Selection of interpolation functions.
- Development of the element matrix for the subdomain (element).
- Assembly of the element matrices for each subdomain to obtain the global matrix
- for the entire domain.
- Imposition of the boundary conditions.
- Solution of equations.
- Additional computations (if desired).
Stress concentration
Stress concentration is defined as the localization of high stresses due to the irregularities present in the component and abrupt changes of the cross-section.
Figure: Stress concentrations.
In practice, reduction of stress concentration is achieved by the following methods:
- Additional Notches and Holes in Tension Member.
- Fillet Radius, Undercutting and Notch for Member in Bending.
- Drilling Additional Holes for Shaft.
Objective:
- To 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.
- To run the analysis and compare the results for stress, strain and displacement.
Figure: Flow of the project.
Steps Followed:
- 3D CAD Models are created on the basis of the drawings provided by skill Lync.
- Simulation add-in is selected and a new static study is created.
- Material is provided to the model as alloy steel(default).
- Fixed constraint is provided on the side of the beam.
- External force is provided as an uniformly distributed load.
- Discretization is done using the meshing command.
- Study is run and results are saved.
- Results are studied and a factor of safety plot is defined.
Results:
Case 1: Length=300mm
Height=120mm
Thickness=30mm
Circular Hole at the centre: Diameter=60mm
Figure: Plate with one hole.
Figure: Stress plot.
Figure: Strain plot.
Figure: Factor of safety plot.
Figure: Displacement plot.
Case 2: Length=300mm
Height=120mm
Thickness=30mm
Circular Hole at the centre: Diameter=60mm
Two holes of 30 mm diameter which are placed 90mm away from the central hole on both sides.
Figure: Plate with three holes.
Figure: Stress plot.
Figure: Strain plot.
Figure: Factor of safety plot.
Figure: Displacement plot.
Conclusions:
Plate used in Case 2 is better and safer than the plate used in Case 2 because of following reasons:
- Stress in the first plate is more than that of second plate.
- Strain in first plate is more than that of second plate.
- Factor of safety of second plate is more than that of first plate.