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Nonlinear Loadcase versus Load Increment

Load Case

Each load attribute dataset contains just one load type and, in general, a loadcase comprises one or more load datasets which have been assigned to this loadcase. The number of load cases that may be applied to a structure is only limited by the capacity of the computer to solve the inevitably larger analysis.

An example of the MODELLER loadcase treeview structure for three loadcases is as follows

Model data
1:Loadcase 1
2:Loadcase 2
3:Loadcase 3

Linear analyses enforce the assumption that the stiffness of the structure does not change throughout the solution. This means that the stiffness matrix need only be evaluated and inverted once and the displacements for any number of loadcases computed directly from the static finite element equilibrium equation (in the back substitution phase of the solution):

d = F K-1

Because each load is applied to the original stiffness matrix, the effects of each loadcase are completely independent of each other. In other word, each load case is considered individually and has no memory of either previous loads or stress states. Because of this and as a result of the stiffness matrix being linear, the same result exactly will be obtained from applying the total load in one load case (case (2) below) or ramped over multiple load cases (case (1) below). Examining the effects of applying twice the load magnitude for a specified load case may be accomplished simply by using the load combination facility.

Case 1

Case 2

Model data

Model data
1:Loadcase 1 (magnitude 10kN) 1:Loadcase 3 (magnitude 30kN)
2:Loadcase 2 (magnitude 20kN)
3:Loadcase 3 (magnitude 30kN)

Nonlinear Load Incrementation

For nonlinear analyses, it is no longer possible to obtain a solution that equilibrates a set of external loads with the internal state of stress and strain in a direct "one-step" manner as permitted by linear analyses. This is because the stiffness of the structure may change at any point. In this case a solution procedure is adopted in which the load is applied in a number of increments, enabling a continual "tracking" of the structural response. The general assumption underlying the nonlinear analysis procedures is that the history of loading is important and alters the final stress state of the structure. See nonlinear loading incrementation procedures for further information.

A nonlinear analysis may only apply one loadcase at a time. This load case may be applied over one load increment (manual incrementation) or several load increments (automatic incrementation).

Consider three loadcases defined at the pre-processing stage:

Model data
1:loadcase 1 (manual load incrementation)
2:loadcase 2 (automatic incrementation – load applied gradually over 5 increments)
3:loadcase 3 (manual load incrementation)

These model loadcases will create the following results loadcases:

Results file:1
1:Loadcase 1 (manual load incrementation)
2:Loadcase 2 (automatic incrementation – 1st of 5 increments)
3:Loadcase 3 (automatic incrementation – 2nd of 5 increments)
4:Loadcase 4 (automatic incrementation – 3rd of 5 increments)
5:Loadcase 5 (automatic incrementation – 4th of 5 increments)
6:Loadcase 6 (automatic incrementation – 5th of 5 increments)
7:Loadcase 7 (manual load incrementation)

Loadcases 1 and 7 represent the manual load incrementation loadcase in the model data and load increments 2 through 6 are the five gradual steps taken by the second model data loadcase. Thus the number of results loadcases (increments) will, in general, will be greater than the number of model loadcases specified.

The correlation between the load cases and the load increments for this example is given in the following table.

Analysis Type

Load Case Handling

Stiffness Matrix Used

Loadcase correspondence

Linear Static Processed Simultaneously Original Stiffness One to one correspondence between the model and results data loadcases
Nonlinear Static Processed Sequentially Updated Stiffness Each model data loadcase may now span a number of load increments
Linear Dynamic Processed Sequentially Original Stiffness One to one correspondence between the model and results data time steps
Nonlinear Dynamic Processed Sequentially Updated Stiffness Each model data loadcase may now span a number of time steps

For linear and nonlinear dynamics the same concept is used as that in the nonlinear static solution, but the term load increment is replaced with time step.

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