Methods of solving the singularity using the method of final elements

Let’s discuss the term of singularity. The most common example of singularity used in internet is when we inject the channel with an idle, in the place of the contact will appear huge pressure, but the destruction will not appear. The power F is contact, the square is striving to 0, that’s why the pressure is striving to infinity. Mathematical singularity is the point where the function is striving to the infinity.

Now let’s see the practice analysis. The first and most important what we should do it to find out if it is the singularity or real behavior of the model. If it is the singularity, the pressure in the field and point will grow till the eternity. In the case if it is not the singularity we will have the final value. We will deal with the singularity in the next cases: when we will have sharp edges, when the construction will be fixed hard, especially in the points and edges, and in tasks of mechanic of destruction. (In this case we will often consider the tops of cracks and we will speak about the coefficient of stress intensity factor.

Now let’s see what can we do with singularity. Most of all the singularity appears in sharp edges. But, it’s better to avoid them, because everywhere exists the radius which striving to zero. In the result the completely sharp edge doesn’t exist. But when we have huge size models it is impossible to make the edges round. So0metimes there is no reason to do it and in this case we calculate the full modes and then find partial solution for the specific part (this part is easier and faster to adopt to the necessary coincidence). And as it was mentioned before here we have the hard fixing and it’s better to avoid them and take into consideration the ability to minimize their influence.

Now let’s have a look at these two cases:

  1. If we are sure that the singularity will not influence on the result, in this case we can ignore it.
  2. The second case is when we take 2 points close to our place, then the value of pressure condition will influence these points.

If we have to consider the singularity, we will take the integral with the resilient-plastic deformation.