Before a frame can be modelled and analysed with a program such as SPACE GASS, it must first be idealised and modelled mathematically. The most popular mathematical model uses the concept of nodes connected by elements of a finite size (finite elements).
SPACE GASS requires that frames are represented by nodes connected by members, cables or plates. Such nodes are generally free to move and rotate in space. Practical structures, however, are connected to a footing in some way, and so node restraints must be applied which limit the movement of selected nodes.
The relative movement between nodes connected by a member, cable or plate is a function of the section and material properties of that element. Loads can be mathematically represented in the model and can be applied elements. Such loads include all of the normal force and moment type loads, in addition to load inducers such as prescribed displacements and temperature differentials. A single analysis can consider numerous load cases, each of which may contain many different load types.
During the analysis phase, all unrestrained node displacements (degrees of freedom) are calculated for each load case. Element forces and moments are then determined from the relative movement of the nodes they are connected to and, finally, reactions are calculated by equating element reactions at each restrained node.
If the analysis selected is non-linear, SPACE GASS does an initial linear analysis and then modifies the stiffness matrix for each member based on the previous analysis node displacements and member axial forces. It then re-analyses the structure for the modified member stiffness and continues iterating the analysis phase in this way until convergence is achieved. Note that because the plate elements are linear elements at this stage, their stiffness is not modified during the non-linear analysis iterations.