## Question

**I want to know why errors are prevented when entering small stiffness inputs to prevent Singular Error**

## Answer

**Let me explain using the basic equations used in linear static analysis in midas Gen.**

During modeling and analysis, there are cases where arbitrary boundary conditions are applied to avoid unstable states that differ from the actual structure. For instance, in the analysis of underground structures, arbitrary horizontal boundary conditions are applied to prevent horizontal Singular Errors that may occur due to asymmetric horizontal displacements.

Furthermore, to prevent unstable structures even when there is no stiffness related to displacement and rotation, small stiffness values are input to the structure while minimizing their impact. Instead of setting the stiffness for displacement and rotation in the Elastic Link as "0", small stiffness values are input.

The reason why a singular error is prevented when small stiffness is entered can be explained simply by the basic equations used in midas Gen's linear static analysis.

The fundamental equation used in linear static analysis in midas Gen is as follows

[K]{U}={P}

Where, [K] : The overall stiffness matrix of the structure

{U} : Displacement vector of all degrees of freedom

{P} : Applied load vector

In structural modeling, when a small load is applied, if there is no stiffness, the structure can become unstable during analysis, leading to infinite displacements

[0]={1}/{∞}

Therefore, by inputting displacement and rotation stiffness values that do not significantly affect the structure, Singular Error can be prevented.