About Static Steps

Time Period

During a static step you assign a time period to the analysis. This is necessary for cross-references to the amplitude options, which can be used to determine the variation of loads and other externally prescribed parameters during a step (see Amplitude Curves). In some cases this time scale is quite real—for example, the response might be caused by temperatures varying with time based on a previous transient heat transfer run; or the material response might be rate dependent (rate-dependent plasticity), so that a natural time scale exists. Other cases do not have such a natural time scale; for example, when a vessel is pressurized up to limit load with rate-independent material response. If you do not specify a time period,Abaqus/Standard defaults to a time period in which “time” varies from 0.0 to 1.0 over the step. The “time” increments are then simply fractions of the total period of the step.

Nonlinear Static Analysis

Nonlinearities can arise from large-displacement effects, material nonlinearity, and/or boundary nonlinearities such as contact and friction (see General and perturbation procedures) and must be accounted for. If geometrically nonlinear behavior is expected in a step, the large-displacement formulation should be used. In most nonlinear analyses the loading variations over the step follow a prescribed history such as a temperature transient or a prescribed displacement.

Local Instabilities

In other unstable analyses, the instabilities are local (e.g., surface wrinkling, material instability, or local buckling), in which case global load control methods are not appropriate. Abaqus/Standard offers the option to stabilize this class of problems by applying damping throughout the model in such a way that the viscous forces introduced are sufficiently large to prevent instantaneous buckling or collapse but small enough not to affect the behavior significantly while the problem is stable.

Incrementation

Abaqus/Standard uses Newton's method to solve the nonlinear equilibrium equations. Many problems involve history-dependent response; therefore, the solution usually is obtained as a series of increments, with iterations to obtain equilibrium within each increment. Increments must sometimes be kept small (in the sense that rotation and strain increments must be small) to ensure correct modeling of history-dependent effects. Most commonly the choice of increment size is a matter of computational efficiency: if the increments are too large, more iterations will be required. Furthermore, Newton's method has a finite radius of convergence; too large an increment can prevent any solution from being obtained because the initial state is too far away from the equilibrium state that is being sought—it is outside the radius of convergence. Thus, there is an algorithmic restriction on the increment size.

In most cases the default automatic incrementation scheme is preferred because it will select increment sizes based on computational efficiency.

Direct user control of the increment size is also provided because if you have considerable experience with a particular problem, you might be able to select a more economical approach.