Non-linear analysis procedure

SPACE GASS uses the well-known Newton-Raphson method in its non-linear static analysis solver. The main steps are as follows.

1. An initial linear static analysis is performed.
    

2. For each element in each load case, a modified stiffness matrix is assembled.
   
   For non-cable members, the modified stiffness is based on the deformation of the structure and the member axial forces calculated in the previous analysis iteration. The modifications to the stiffness matrix are in accordance with the theory presented by Ghali and Neville (2) for small displacement theory or the theory presented by Hancock (24) for finite and large displacement theory. They involve changes to the axial and flexural stiffness terms, taking into account P-D and P-d effects (if activated).
   
   For cable members, the modified stiffness is based on the unstrained cable length, the cable lateral loads and the deflected position of the cable ends calculated in the previous analysis iteration.
   
   For "BC" plate elements, the stiffness matrix is unchanged. For "DL" plate elements, the stiffness matrix is adjusted based on the displacements from the previous iteration.
    

3. If P-D effects are turned on with finite or large displacement theory, the non-cable member fixed end actions are adjusted for the deformation of the structure.
    

4. If P-d effects are turned on, the non-cable member fixed end actions are adjusted for the change in flexural stiffness of the member.
    

5. The model is re-analysed with the modified element stiffness matrices. In this and later analysis iterations, each load case must be solved separately because the structure stiffness matrix is now different for each load case. This can take considerably longer than the initial linear analysis, especially if there are numerous load cases.
    

6. The results of the latest analysis are compared with the previous analysis and the level of convergence is displayed on the screen. If the level of convergence has reached the requested convergence accuracy then the results have converged and the analysis terminates. If not, steps 2 and 3 are repeated for the unconverged load cases until a solution is reached. If some load cases have still not converged after the specified number of iterations per load step then the program pauses and asks if further iterations are required. If no further iterations are requested, the analysis terminates and the results for the converged load cases only are saved.