Non-linear functions
Definition, application
Non-linear function defines change of stiffness given by the graph. There are two possibilities: 'stiffness for displacement' = dependency of force on displacement or 'stiffness for rotation' = dependency of force on rotation. This non-linear parameter can be applied to hinges on beams and supports in all possible degrees of freedom. So this is another alternative to the standard options rigid / free/ flexible.
Where to find it
All non-linear functions are stored in Libraries / Structure, Analysis / Nonlinear functions in main tree. It is possible go there in menu Libraries / Structure, Analysis / Nonlinear functions too.
How to create new one
In 'Nonlinear functions' dialog there is possibility 'New' or 'Create new function'. Button 'New' opens new dialog 'Nonlinear function' where it is possible to define points of function. Button 'Create new function' allows you to specify a function as a combination of existing functions.
For each function it is necessary to define three important parameters: 'Variable on X-axis of graph', 'Positive axis' and ' Negative axis'.
'Variable on X-axis of graph' defines application of function, so if its define for displacement, rotation or soil. 'Positive axis' and ' Negative axis' define continuing of function before the first and after the last defined point in graph. Possibilities are 'Rigid', 'Free' and 'Flexible'. 'Rigid' means vertical end of function, 'Free' means horizontal end of function and 'Flexible' means continuing of function in same direction of last part of function.
What does it mean ends 'Rigid', 'Free' and 'Flexible' for real functions is shown on schemas below:
Limitations
- every function must contains point [0;0], which is automatically generated for new function
- it is not possible to set two nodes with same 'x' coordinate
- it is not possible to set vertical part of function
- for function defined only by one point [0;0], it is not possible to set 'Positive axis' and ' Negative axis' on 'Flexible'.
- points of function must have increasing 'x' coordinate, if it is set point with 'x' coordinate smaller than previous one, dialog automatically sorts points in right order.
- while defining a nonlinear function, the maximum allowed number for y-axis of the function (force / moment) is 1e10 (in basic units - N; Nm). When a steeper slope of the function is required, the x-axis difference needs to be altered. Few examples are in the chapter below.
Limitation example for y-axis
On the figure below, see the example of non linear function with the rigid end on both ends. There are 4 user defined values. In the table to the right it is visible how this function is internally considered. First user defined value [-1;-10 000] [m;MN] is internally considered as the second value. The negative rigid end is exported as a point [-2;-20 000] [m;MN]. The difference on y-axis is 1e10 N. The user cannot enter a value on y-axis, for which the absolute value would be larger then 1e10 N. The positive end is defined analogically.
If the value larger then the 1e10 (in basic units)for any slot on the y.axis is input, for example 10 001 MN:
The warning will be shown after the calculation is initiated:
If larger slope is desired, difference needs to altered on x-axis instead, for example:
Note: in the figure above, the rigid end (positive) is still internally considered as the additional difference of [1;1e10] [m;N] (between point 5 and 6 in the table to the right), therefore practically less rigid then the user defined part, however practically anything above 1e6 is almost ideally stiff.
A free end example is provided in the figure below:
A flexible end example is provided in the figure below. For x-values outside this range, the last tangent is considered.
Supported members
Table of members in model, for which it is possible to set nonlinear function with dependencies on functionality in project.
| Member | functionality in project data dialog |
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Nonlinearity - Support nonlinearity/Soil spring |
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Nonlinearity - Support nonlinearity/Soil spring |
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Nonlinearity - Support nonlinearity/Soil spring |
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Nonlinearity - Support nonlinearity/Soil spring |
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Nonlinearity Subsoil |
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Nonlinearity - Beam local nonlinearity |
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| Hinge on 2D member edge | Note : not supported in PPE v16 and older |
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Nonlinearity - Beam local nonlinearity |