Question
The error message indicates a singular error and an abnormal displacement error at specific nodes.
Is this due to the omission of X-direction boundary conditions in the seismic boundary condition group? If so, how should I apply the ground reaction coefficients?
Answer
This error often occurs in underground structure modeling when infinite displacement arises in a specific direction (X-direction).
For instance, if a horizontal force is applied to a beam with rollers at both ends, there will be infinite displacement for any small load since there are no boundary conditions in the horizontal direction.
This state is referred to as 'unstable'.
If the analysis model is in such a condition, it will result in errors like Singular error or Abnormal displacement.
This 'unstable' state of the structure often occurs when designing underground structures and considering ground springs. (Coefficient of subgrade reaction)
If the shear stiffness of the ground is included, there is no need to input separate boundary conditions.
However, if the shear stiffness of the ground is not considered, the boundary conditions of the underground structure become unstable.
In this state, since there are no horizontal boundary conditions, the program may output a Singular Error, and such results can be unreliable.
To prevent the Singular Error, horizontal boundary conditions should be inputted. These boundary conditions, not being real, must be inputted in a way that they do not affect the structure.
The horizontal subgrade reaction coefficient is typically applied at about 1/3 of the vertical ground reaction coefficient. Applying the horizontal subgrade reaction coefficient can ensure structural stability in the horizontal direction.
However, if the horizontal subgrade reaction coefficient is not applied, it may be necessary to apply minor stiffness in the horizontal direction to appropriate nodes, or if the structure is asymmetric, to consider constraints or reinforcement measures due to the difference in horizontal loads.
Many users simply input DX direction Support as a boundary condition to prevent the Singular Error. While not incorrect, it is not the best method.
It is acceptable to input in this way when there are only vertical loads and the structure is symmetrical. However, if horizontal loads are asymmetric and the structure is not symmetrical, the inputted boundary conditions can generate horizontal reactions, leading to a completely different scenario than originally intended.
To minimize impact on the structure while preventing the Singular Error, using Point Spring Supports is advisable. The stiffness should be inputted as low as possible to have minimal impact on the structure. The placement should be at the center of the structure or inputted symmetrically.
For 2D analysis, only the DX direction needs to be added. For 3D analysis, small stiffness boundary conditions should be inputted in both DX and DY directions. These should be arranged around the structure to avoid asymmetry.
Even after inputting these conditions, it is crucial to check the reactions after the analysis. Since these boundary conditions do not actually exist, the reactions should be "0" or close to "0" to ensure they do not impact the structural system.