# What does time mean in static structural analysis? – Understanding Time Step, Load Step and Sub-Step

### Introduction

Static analysis is a type of analysis where the input loads do not change with time and the effects of inertia are not considered. In contrast, dynamic analysis considers the effects of time-varying loads and inertia. Although the term “time” is mostly used in dynamic analysis, it can also be used in static analysis. This article will discuss the meaning of time in static analysis.

### Time vs Sequence

In static analysis, time refers to the sequence of events. This is similar to how we associate time with a sequence of events in real life. For instance, when installing a flange on a pressure vessel followed by pressure application, we can set up a static structural simulation in which:

Time Step 1: Apply Preload (Install Flange)

Time Step 2: Apply Pressure

In this case, time step 1 and time step 2 both represent steady-state conditions under different loading situations. Sometimes, time step and load step can be used interchangeably.

We can also think of time in static analysis as it is used in programming languages. When we define t (time) = 1, it only represents an iteration and not physical time.

### Why Apply Loads in Sequence?

One may wonder why loads need to be applied in sequence during a static structural analysis. For instance, in the example given above, why can’t we apply preload and pressure at the same time instead of applying them in two separate steps? Wouldn’t it yield the same end result?

The answer is that applying multiple loads in a single step will give identical results as applying them in separate steps, as long as we analyze a single configuration of the geometry and the analysis is linear (no sources of non-linearity).

By geometric configurations, we mean situations where we model assembly steps, such as the application of preload, introduction of a seal, or removal of weld material.

By linear static analysis, we mean that the dependent variable does not affect the independent variables. A structural analysis is linear as long as the stiffness [K] and force {F} are not functions of the displacements {X}.

The sequence of applied loads can significantly affect the system’s response (stresses and strains) if one or both of the above conditions are not met.

### What is a Substep in ANSYS?

A substep is like a piece of a puzzle. It’s a portion of the time step, meaning that if a force of 1000 N is applied at Time Step 1 (T=1s), it can be applied in smaller increments of loads. For instance, it could be broken down into 5 substeps with 200 N applied in each substep. This means that the force would be F=200N at T=0.2s, F=400N at T=0.4s, and so on.

### Why use Substeps?

There are two main reasons:

• To make it easier to find a solution: Substeps are often used to help the solver apply the load “slowly” and converge to a solution. This is especially important in non-linear analyses.
• To gather more data: Each substep provides specific results, including explicit stress and strain data. This can help analysts determine how a system responds at intermediate loads, which is often valuable information.

In ANSYS, the “Step Controls” menu offers several options for time step control. By default, the Auto Time Stepping is set to “Program Controlled,” meaning that the solver determines how much to increment the load. However, analysts can gain finer control over the time step settings by setting the Auto Time Stepping to “On” and defining by “Time” or “Substeps.”

Good Luck!