Sometimes highly ill-conditioned
frames can also be interpreted as being unstable by the program.The most common analysis errors are caused by structures that are not correctly conditioned or stabilised.
Ill-conditioning commonly occurs when frames contain members of widely varying stiffness’s. When a very stiff member is connected to a very flexible member and their stiffness matrices are assembled into the structure stiffness matrix, some of the stiffness terms of the flexible member can be completely lost due to their insignificance in comparison with the stiffness terms of the stiff member. Hence, the flexible member is not completely represented and ill-conditioning occurs.
SPACE GASS contains an algorithm which checks for possible ill-conditioning and displays warning messages if appropriate. Generally, these messages appear well before ill-conditioning actually occurs. They do, however serve to highlight structures which are close to being ill-conditioned. If after the analysis, the sum of the reactions equals the sum of the applied loads then it can be assumed that the frame is well conditioned.
Instabilities occur when one or more nodes are free to translate or rotate without resistance from the frame. Sometimes unstable structures are very easy to detect, such as when restraints have not been applied or when an obvious collapse mechanism is possible.
Instabilities are often very subtle and difficult to isolate. For example, if an unrestrained node has a pinned connection to each of its connecting members then it would be free to rotate and an instability would result. This type of instability can be hard to detect because it only affects one node in the structure. True trusses must therefore have every rotational degree of freedom restrained.
Sometimes highly ill-conditioned
frames can also be interpreted as being unstable by the program.
Another common type of instability occurs when a group of members connected end-to-end in a straight line are free to rotate about their longitudinal axis. The instability occurs because during the analysis the program is unable to determine the amount of rotation of the intermediate nodes.
Some instabilities cannot be detected by a static analysis, and you should therefore be wary of results that contain very large deflections or deflections that occur in the wrong direction. However most instabilities can be detected by a buckling analysis and are identified by very low buckling load factors. If you get buckling load factors that are below the minimum allowable value (eg. shown as "<0.001" when the minimum allowable value is 0.001), this could indicate an instability problem rather than a buckling problem. It is even more likely to be an instability problem if the low buckling load factors occur in every load case.
Note, however, that a buckling analysis using the "Classic Eigensolver" theory will not be as good at finding instabilities as the "Signcount Eigensolver" theory.
If the model contains instabilities, the buckling analysis may, in some cases, give invalid results. In the absence of instability or buckling messages from the static analysis, you should always check the deflections to see if they are excessive or not. Excessive deflections are sometimes the only indicator of instabilities.
Instabilities can also be caused as a result of plate elements having no rotational stiffness about an axis normal to their plane (also known as their "drilling stiffness"). SPACE GASS automatically applies a small drilling stiffness to all plate nodes in order to avoid instabilities, however sometimes you may need to adjust the drilling stiffness if the default value is not suitable. For more information, refer to "drilling stiffness".
There are no hard and fast rules to follow in the detection of conditioning and stability problems, however if the structure is clearly drawn and examined, the problem usually becomes evident to any moderately experienced user.
SPACE GASS is now able to automatically rectify some instabilities caused by nodes that are free to rotate or translate in one or more directions without resistance from interconnecting members, restraints or constraints. For more information, refer to "Stabilize unrestrained nodes" in Running a static analysis.