## Question

**I would like to know why singular error is avoided when inputting small stiffness values.**

## Answer

**This shall be explained using the basic equation used in linear static analysis of CIVIL. **

While modeling and analysing, there are cases where arbitrary boundary conditions are defined to avoid unstable states that are different from the real structure. For example, while modeling underground structures, when asymmetric horizontal displacement occurs, horizontal boundary conditions are defined that singular errors in horizontal directions are prevented.

Additionally, in the case of bridges, small values are inputted instead of '0' for stiffness of displacement and rotation in Elastic Link even though there is no stiffness for displacement and rotation at the supports in order to prevent unstable structures. As a result, the structure is affected as minimally as possible, while singular errors are avoided.

The reason why singular errors are avoided when entering small stiffness values can be easily be explained using the basic equation of linear static analysis used in CIVIL.

The basic equation used in CIVIL's linear static analysis is as follows:

**[K]{U}={P}**

[K] : Stiffness matrix of the structure

{U} : Displacement vector of all degrees of freedom

{P} : Applied load vector

If a small load is applied to the structure and there is no stiffness, the structure becomes unstable, and infinite displacement may occur.

**[0]={1}/{∞}**

Thus, by defining the displacement and rotation stiffness that affect minimally on the structure, a singular error can be avoided.