Analysis

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MainMenuAndMainIconsANALYZE

 

The analysis is performed using the Finite Element Method (FEM) for plane frames. During the analysis process, the program forms the model Global Stiffness Matrix [K] as well as the vector of the External Forces {F}. Then, the linear equations system {F}=[K]{D} is solved in order for the Displacement Vector {D} to be calculated:

{D}=[K]-1·{F}

If the model is statically well-defined then the Stiffness Matrix [K] is reversible (Matrix Determinant greater than zero) and no problems will occur during the analysis process.

 

Errors during the analysis process

Computational errors may occur during the analysis process. In that case, the program warns the user with the following messages:

 

1. 'Finite Element Analysis failed. Please check the Model.'

This error occurs due to the model stiffness matrix being non-reversible. There is a zero-element appearing at the matrix diagonal, the determinant of the model stiffness matrix equals to zero, the matrix is non-reversible thus the linear equations system cannot be solved for displacements.

 

Example: Under-constrained model, such as a Cantilever beam where instead of a fixed support, there is a Pinned support as shown below. The model can freely rotate and Equilibrium cannot be reached, by no means. The model cannot be analyzed and the programs gives us an error message, as shown below.

 

ErrorAnalysisFailed

 

 

2. 'The analysis has been carried out successfully, yet some of the resultant displacements have excessive values (>107). Please check the Model, it is most probably a mechanism.'

This case does not have to do with a computational error occurring during the analysis process. The analysis has been carried out successfully yet some of the resultant displacements have excessive values (greater than 107) which means that probably the structure is a mechanism. In this case the model stiffness matrix is in fact non-reversible but during the analysis process instead of the right zero value, a very small non-zero value appears at the matrix diagonal due to computational approximation errors. As a result, the solver finds a solution (with no practical interest) to the linear equations system yet the resultant displacements have excessive values.

 

ErrorExcessiveDeformation

 

This for example can happen in the Model shown below.

 

ErrorExcessiveDeformation2

 

 

Possible reasons for such error messages:

There are nodes that are not connected to the model via elements.

The constraints are inadequate (under-constrained Model), for example the first model shown above.

Some parts of the structure are not connected to each other and as a result the forces cannot be transferred from one part of the structure to another.

The forces cannot be transferred from one part of a structure to another due to the type of the connecting elements (Hinges).

Due to some other reason, the structure is a mechanism.