Challenge 2- Comparing the performance of three types of beams under bending load.

                                                                            FEA OF THREE TYPES OF BEAMS UNDER A BENDING LOAD

AIM

To perform a Finite element analysis (FEA) on three types of beams under a bending load using solidworks.

INTRODUCTION

Finite element analysis is the use of calculations, models and simulations to predict and understand how an object might behave under various physical conditions. Engineers use FEA to find problems in their design prototypes. Using finite element analysis can reduce the number of physical prototypes created and experiments performed while also optimizing all components during the design phase. Finite element analysis is based on principles that include boundary conditions, such as forces and pressures.

For finite element analysis to perform its necessary simulations, a mesh containing millions of small elements that together form the shape of a structure must be created. Calculations must be performed on every single element; the combination of each of these individual answers provides the final result for the full structure. FEA is commonly used in mechanical, aerospace, automotive and civil engineering projects as well as biomechanics. Specifically, it is important for designing machines, analysing fatigue for machines and their parts.

Apart from FEA definition here I am going to perform a FEA using solidworks on three different types of beams. In this project the FEA is almost dependent on stress, strain and displacement only. Also, these three parameters are our output as well. So, let’s move on to how FEA works.

THEORY

The finite element method (FEM) is a popular method for numerically solving differential equation arising in engineering and mathematical modelling. Typical problem areas of interest include the traditional fields of structural analysis, heat transfer, fluid flow, mass transport, and electromagnetic potential.  FEA is based on principles that include boundary conditions, such as forces and pressures. Because here we are going to fix the one end and apply a force or pressure on another end that gives you an output result based on our input.

The basic knowledge on stress-strain graph will helps us how to select the input parameters, its results as well. Its important will play a major role on selection of a simulation is linear or non-linear, dynamic or static, etc.

When we study solids and their mechanical properties, information regarding their elastic properties is most important. We can learn about the elastic properties of materials by studying the stress-strain relationships, under different loads, in these materials. The material’s stress-strain curve gives its stress-strain relationship. In a stress-strain curve, the stress and its corresponding strain values are plotted. An example of a stress-strain curve is given below.

Stress:  Stress is defined as force per unit area within materials that arises from externally applied forces, uneven heating, or permanent deformation and that permits an accurate description and prediction of elastic, plastic, and fluid behaviour. Stress is given by the following formula:

σ=F/A

where,

σ  is the stress applied, F  is the force applied and A  is the area of the force applied. The unit of stress is N/m².

Strain: strain is the amount of deformation experienced by the body in the direction of force applied, divided by the initial dimensions of the body. The following equation gives the relation for deformation in terms of the length of a solid:

ϵ=δl/L

where,

ϵ  is the strain due to the stress applied, δl  is the change in length and L is the original length of the material. The strain is a dimensionless quantity as it just defines the relative change in shape.

Displacement: it is defined as the change in position of an object. It is a vector quantity and has a direction and magnitude. It is represented as an arrow that points from the starting position to the final position. For example- If an object moves from A position to B, then the object’s position changes. This change in position of an object is known as Displacement.

Displacement = ΔX= X_f-X₀

X_f = Final Position, X₀ = Initial Position, ΔX = Displacement

PROJECT SET-UP

         Let’s move on to the initial setups for this project like parts design, analysis type, etc. also the part design for this analysis is classified into three cases i) rectangular beam, ii) I-section iii) C-section. Analysis type is taken as static-linear analysis because of the workpiece is going to deform but not permanently. This setup path is given below through pictures.

New study: this is the initial step to start the FEA where we set the simulation type. Because based on this setup our project will keep going on. Here I have used static type from general simulation. This one is common for all three cases.

Material: based on the given material to the components our output result will come. There are many options in solidworks to obtain our expected results. here I was used a “plain carbon steel” linear elastic isotropic for all three parts. This one also common for all three cases.

Fixtures: as I told in the beginning of this project, we need to fix any one of the ends based on design you have. Here I have fixed one of the smaller dimension faces of all three beams. This one also common for all three cases.

External load: this is the input load/force based on this we will get the result. Apply a load of 1500N on the larger dimension as well as smaller face (i.e., 45mm face for case 1, 40mm face for case 2-, and 45-mm face for case 3)

Mesh: Meshing is one of the most important steps in performing an accurate simulation using FEA. A mesh is made up of elements which contain nodes (coordinate locations in space that can vary by element type) that represent the shape of the geometry. Here I have used mesh parameter to keep the common mesh density of 5mm of global size for all three cases.

Case-(i) rectangular section beam

Case-(ii) I-section beam

Case-(iii) C-section beam

RESULTS

If we compare the all three cases C-section is better option. Because its displacement is minimum then others. Rectangular section also similar value but the maximum stress and strain values are higher.

I section is always better choice but here based on its design our output did not match our expectations when compare with others cases.

CONCLSION

         FEA using solidworks is always helps to manufacturers on choosing the best product and its material used, how much load it will withstand before starting its production. Here also same process for three different types of beams but same conditions and inputs.  

https://drive.google.com/file/d/11Zkf0elGMneAT4FIsanVoK8BdL80Z54T/view?usp=sharing