Nonlinear Loading Procedures

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Nonlinear Loading Procedures

The type of loading is of importance when determining whether a load level from one increment is "remembered" or " forgotten" in subsequent increments when using manual or automatic load incrementation. Some loading types are total in nature whilst other are incremental. At present all of the loading types in LUSAS are total with the exception of the Incremental Prescribed Displacement loading type (PDSP).

Total load types (Note that most load types are total): These apply only the specified loading magnitude to the structure. This means that any previously specified loading at a node or element is overwritten by the current specification of load. Consider an automatic, fixed load increment, for example, in which a concentrated load magnitude of 5.0 is to be incremented from a reference load factor of 0.2 over 3 increments. The initial load applied would be calculated according to 0.2*5.0. The subsequent two load increments would be calculated as 0.4*5.0 and 0.6*5.0
Incremental prescribed displacement apply the specified loading magnitude in addition to the load already applied to the structure. Considering the previous example, but with incremental prescribed displacement loading, the initial load applied would be calculated according to 0.2*5.0. The subsequent two load increments would be calculated incrementally as (previous load + next increment of load), i.e.

2nd Increment: 0.2*5.0 + (0.4 - 0.2)*5.0

3rd Increment: 0.4*5.0 + (0.6 - 0.4)*5.0

General Loading Rules:

In switching from manual to automatic control, any loading input under the manual control is remembered and held constant while the automatic procedure is operating
In switching from automatic back to manual control, any loading accumulated under automatic control is forgotten and only the manual load is applied. To include the final load level from the automatic load increments, the load datasets from which it comprises must be assigned to this manual load case
In switching from manual to manual control, any loading accumulated under previous manual controls is forgotten and only the current manual load is applied.
In switching from automatic to automatic control, any loading accumulated under the previous automatic control is forgotten and only the current automatic load is applied. To include the final load level from the previous automatic load increment, an additional loadcase must be inserted prior to the next automatic increment and the load datasets from the previous automatic increment assigned to this manual load case.
If incremental prescribed displacements are being used then, in any switching from one type of control to another, the effect of prescribed displacements will be remembered and will not need to be input again. This is not the case for total prescribed displacements which are total loads
The stress and strain state will always be remembered whatever loading is applied on iteration zero after the change of control. For example, the stresses will drop to zero if the load is removed but any plastic strains will remain. Additionally, if the same load magnitude is maintained across a change of control, convergence will be achieved in one iteration because the stress state and the equilibrium internal forces do not change.

I) Examples for Total Loading Types

Note: This is the case for all load types expect for Incremental Prescribed Displacements

The following examples illustrate common loading requirements for total loading types:

Automatic followed by Automatic

Model data
1:loadcase 1 (automatic incrementation – load of 15 applied gradually and evenly over 3 increments)
2:loadcase 2 (automatic incrementation – load of 30 applied gradually and evenly over 3 increments)

Results file:1
1:Loadcase 1 (automatic incrementation – 1st of 3 increments)
2:Loadcase 2 (automatic incrementation – 2nd of 3 increments)
3:Loadcase 3 (automatic incrementation – 3rd of 3 increments)
4:Loadcase 4 (automatic incrementation – 1st of 3 increments)
5:Loadcase 5 (automatic incrementation – 2nd of 3 increments)
6:Loadcase 6 (automatic incrementation – 3rd of 3 increments)

The applied load level in each of the result load increments is 5, 10, 15, 10, 20, 30 respectively. The load level from the first automatic increment is forgotten. In this instance only, the use of the total Prescribed Displacement loading will cause a departure from the previous rules to give applied load levels of 5, 10, 15, 25, 35, 45.

Manual followed by Manual

Model data
1:loadcase 1 (manual incrementation – load of 15 applied in 1 increment)
2:loadcase 2 (manual incrementation – load of 30 applied in 1 increment)

Results file:1
1:Loadcase 1 (manual incrementation)
2:Loadcase 2 (manual incrementation)

The applied load level in each of the result load increments is 15, 30 respectively. The load level from the first manual increment is forgotten.

Automatic followed by Manual

Model data
1:loadcase 1 (automatic incrementation – load of 15 applied gradually and evenly over 3 increments)
2:loadcase 2 (manual incrementation – load of 30 applied in 1 increment)

Results file:1
1:Loadcase 1 (automatic incrementation – 1st of 3 increments)
2:Loadcase 2 (automatic incrementation – 2nd of 3 increments)
3:Loadcase 3 (automatic incrementation – 3rd of 3 increments)
4:Loadcase 4 (manual incrementation)

The applied load level in each of the result load increments is 5, 10, 15, 30 respectively. The load level from the first automatic increment is forgotten.

Manual followed by Automatic

Model data
1:loadcase 1 (manual incrementation – load of 15 applied in 1 increment)
2:loadcase 2 (automatic incrementation – load of 30 applied gradually and evenly over 3 increments)

Results file:1
1:Loadcase 1 (manual incrementation)
2:Loadcase 2 (automatic incrementation – 1st of 3 increments)
3:Loadcase 3 (automatic incrementation – 2nd of 3 increments)
4:Loadcase 4 (automatic incrementation – 3rd of 3 increments)

The applied load level in each of the result load increments is 15, 25, 35, 45 respectively. The load level from the first manual increment is remembered, since the application of a manual increment will remain throughout an analysis until a further manual increment specification. This characteristic provides a straightforward method to apply a dead load as a constant loading for the analysis together with the live load gradually incremented over an number of increments.

II) Examples for Incremental Prescribed Displacements

The following examples illustrate common loading requirements for incremental prescribed displacements:

Automatic followed by Automatic:

Model data
1:loadcase 1 (automatic incrementation – load of 15 applied gradually and evenly over 3 increments)
2:loadcase 2 (automatic incrementation – load of 30 applied gradually and evenly over 3 increments)

Results file:1
1:Loadcase 1 (automatic incrementation – 1st of 3 increments)
2:Loadcase 2 (automatic incrementation – 2nd of 3 increments)
3:Loadcase 3 (automatic incrementation – 3rd of 3 increments)
4:Loadcase 4 (automatic incrementation – 1st of 3 increments)
5:Loadcase 5 (automatic incrementation – 2nd of 3 increments)
6:Loadcase 6 (automatic incrementation – 3rd of 3 increments)

The applied load level in each of the result load increments is 5, 10, 15, 20, 35, 45 respectively. The load level from the first automatic increment is remembered.