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[Venkata Subramanian M]

I have some doubt regarding the mathematical reason for static structural analysis without assigning the support in the structure. I  know the meaning of static structural analysis in which we need to assign the support in the structure. The formula used is [K] * {u} = {F}, and using the Principle of Virtual work method.

My question is about if I assign the boundary condition the nodal force only in required nodes without assigning the support. The error arries as ' boundary condition is not assigned properly for this analysis'. Sir/ madam kindly explain this error mathematically.

[Sahil Sura]

Hi @Venkata Subramanian M,
So if we see the basic conditions of static analysis, the load should be assumed to be steady such that the load and structure's response varies slowly with respect to time. Or in other words, Loads and Boundary Conditions do not change with time. This doesn't allows rigid body motion to take place.

So let's say you add a load to the tip of a cantilever beam without any support defined, this will lead to unconstrained displacement, which might tend towards infinity (causing rigid body motion) and will make the equation produce an infinite number of solutions.

Mathematically if we say, when there exists a rigid body motion situation in the model, the matrix from the governing equation turns singular.
Thus there won't be a case of expected outcome.

There are certain situations where the model is unconstrained like flying objects, aquatic objects, etc. but in such situations, different methods are used to counter the problem.

For more information please refer to the following video which might tell you more on the need to fully constrain the model.
Understanding the Need to Fully Constrain the Model - Lesson 2 - ANSYS Innovation Courses

Hope this helps!
Thanks,
Sahil
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[Venkata Subramanian M]

Thanks for your reply. I understood the problem.

Can you explain which method is used to extract the solution from this equation [K] * {u} = {F}. Because the stiffness matrix has many rows and columns. 

Another question that If I have increased the time step with displacement. Can I use static structural analysis (the process is like a compression test) ?