# Finite Element Analysis: Basic Ideas That Every Engineer Should Know

Finite element analysis is a numerical analysis method, simulation.

As the name suggests, simulation simulates the real scene through the computer, so as to master the working conditions to be analyzed in advance, so as to guide the actual engineering application.

To put it more simply, designers can not accurately know how the equipment or a part works under the actual working conditions, so they can “manufacture” the possible working conditions of the equipment on the computer, and place the equipment or parts under the simulated working conditions to see what changes will happen to the equipment or parts;

Is it in line with the situation expected by the designer?

Does it meet the design requirements? Can the design be further optimized?

Moreover, the working condition of computer “manufacturing” can be adjusted arbitrarily, or when it is impossible to verify with experimental methods, the advantages of simulation will appear.

So, what is the basic idea of finite element analysis?

According to the above introduction, there are three main contents, which I simply call the three-stage finite element method “one construction, two analysis and three calculation”:

1. Establish the model.

Establish the computer model of the specific object to be analyzed;

2. Analyze working conditions.

List all the actual and possible working conditions, and calculate the safety factor according to the worst working conditions;

3. Calculation

The calculated results of working conditions are introduced into the calculation model as boundary conditions, and the model is calculated and analyzed to draw a conclusion.

Here is a detailed explanation of the “three-stage method”.

### 1. Establish model

From the perspective of mechanical design, the model is the model of specific parts, components or components.

The current finite element analysis software is based on three-dimensional, and so is mechanical design;

The current mechanical design is not like the previous two-dimensional drawings.

The current design is three-dimensional design.

People can clearly see the 1:1 real situation of the equipment or parts, as shown in the figure below.

It is a three-dimensional model of a chain hoist, and you can clearly see every detail of the equipment.

Of course, the simplest way is to use the existing models you have in hand to calculate directly. However, some models can be calculated directly, while others can’t.

It needs to be analyzed according to specific conditions. Then I use one of the parts of this chain hoist to analyze it.

The following figure shows a chain axle (blue part) on the chain hoist. The sprocket is installed on the shaft, which is a unpowered shaft.

It can be seen that this axis is a circular axis.

According to the common sense of machinery, we know that without considering the deformation of the object, the contact position between the cylinder and other objects is a point or a line, but in fact, there will be deformation in the contact of our parts, and both the cylindrical surface and the surface in contact with the cylindrical surface will deform under the action of force.

Then the actual contact becomes a surface, which is also a point of attention in our modeling. When we apply boundary conditions, the applied force has size, direction and action point, so the selection of action point is very particular;

If a point or a straight line is selected according to the theory, no appropriate result can be obtained.

For stress calculation, the stress is equal to the stress divided by the area.

The area of a straight line is 0 in the computer, then the stress will tend to infinity.

The point with infinite stress is called the stress singularity, and the value of the stress singularity has no reference value.

Therefore, we should avoid stress singularity in calculation. What if there is a stress singularity? Don’t worry too much about that.

Some that can be obviously found to be stress singularities and do not affect the overall calculation can be ignored;

If there are too many stress singularities, or in some key parts, it indicates that the model treatment is not perfect enough, and further treatment is needed to reduce the stress singularities.

What should I do with the axis model shown in the figure above?

Now let’s analyze it.

First, check whether there are places on the shaft that are easy to cause stress singularities, such as whether the shoulder of the shaft is transitional and smooth.

If not, it needs to be transitional and smooth, such as fillet.

Secondly, whether the action position of the force needs to be treated separately.

We know that the outer surface of the cylinder on the model is a whole cylindrical surface, but the actual contact force surface is a small plane.

How to deal with it?

It is very simple. Just cut a small plane as the stress surface according to the actual stress position, such as the position of the sprocket in this example.

The length of this contact surface can be based on the length of the bearing or sprocket.

As for the width, it is selected according to the size of the shaft diameter.

The width of the shaft of φ30mm here is 2mm, accounting for about 5% ~ 10% of the diameter.

In this way, the model is basically established, and then the material and other physical properties are given.

### 2. Analysis of working conditions

In this example, we know that the load of the chain is transmitted from the dead weight of the bearing to the dead weight of the shaft.

In this example, the load of the chain is transmitted from the dead weight of the shaft to the dead weight of the shaft;

The unbalanced dynamic load caused by the change of chain tension, the impact load when the weight is placed, and some other accidental loads.

It can be seen that the force on this axis is still complex, so is it necessary for us to simulate all the loads?

The answer must be no, there is no need. Because my premise is auxiliary design, not academic research.

It mainly focuses on engineering practical application. In the actual conversion, we give priority to the calculation of static load.

If the dynamic load is small or the fluctuation of dynamic load is relatively stable, it will be converted into static load.

Because the amount of calculation is too large and the modeling is cumbersome, in the use of these equipment, the static stress and stiffness can meet the requirements of life.

It is much easier to add boundary conditions corresponding to the static load condition:

If it is a fixed support, give a fixed constraint;

If it is a simply supported support, give a simply supported support;

The force is at the action position of the force, and the size of the force is given according to the actual force direction.

If the torque is received, the size, position and direction of the torque are given.

### 3. Calculation

Calculation is to import the analysis model into the calculation software for calculation after preparing the model and boundary conditions.

There are many kinds of software. Many 3D design software comes with simulation software, such as the simulation module of SW.

The use of the software will be introduced later. Its essence is to convert the actual parts and working conditions into mathematical models and boundary conditions for calculation and analysis.

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