GGU-SLAB: General analysis methods
An analytical solution is only possible for simple systems. We must rely on numerical solution methods when modelling complex systems. These primarily include the:
finite-difference (FDM) and
finite-element (FEM)
methods. When using finite methods, the total area is subdivided into many small (finite) sub-areas (elements). FEM generally employs triangles for these small areas. Simple, generally quadratic approximation functions are used within these triangles. The real, complex, mosaic-like overall solution is composed of the numerous simple partial solutions. This gives rise to equation systems comprised of a number of unknowns corresponding to the number of system nodes. Normally, using the finite difference method, the only option for discretising the total area is by means of rectangular sub-areas. In contrast to FEM, then, FDM is considerably more flexible with regard to adaptation to complicated boundary structures. In addition, mesh refinement is not as easy to perform in some areas. The resulting equation systems are also numerically more stable for FEM. The main advantage of FDM consists only of the theoretically less complex basic mathematical relationships. These will generally be of little interest to the program user. The GGU-SLAB program uses the finite-element method.
When using this program, please remember that all finite element or finite difference methods are approximation methods. The quality of the approximation in terms of the actual solution increases as the mesh refinement increases. Take care to ensure that the mesh is denser in those areas where the principal forces act (e.g. support points, point loads). The shape of the triangles also exercises a certain influence. Optimum conditions are achieved with equilateral triangles. You can get an idea of the quality of the solution by modelling the same system again, but using a either a finer or a coarser mesh and then comparing the results of the two models.
The following general comments on the GGU-SLAB program are also important:
triangle elements are used,
Hooke's Law applies.