Application Note

GEOMETRIC

PARAMETERS FOR

SOLID ELEMENTS

 ● It is required that the user has basic knowledge of Akselos Modeler’s user interface. 

Detailed guidance is given in other tutorials. ● It is required that the user knows how to create a new component in Akselos 

Modeler. Detailed guidance is given in other tutorials. ● Note that Akselos Modeler only supports mapping functions for solid elements. 

 

Definition Geometric parameters are introduced into components by using parameterized geometric                   mapping functions. A mapping function is a function that transforms the model from a                           reference state to a real state, governed by the current choice of geometric parameter.                           The mathematical form of a mapping function is given as:  

x(s 1, s 2,…, sn ) = f(x(s 1ref, s2ref,…, s nref))  

 Example: A reference line with 5 nodes, which have coordinates from to . To scalex1

ref x5ref  

the line, we apply a simple scaling function f, with scaling parameter s. The new node coordinates will be: 

xx1 = s 1ref  

xx2 = s 2ref  

xx3 = s 3ref  

xx4 = s 4ref  

xx5 = s 5ref  

In this case the reference line will be scaled as shown in the image below: 

  Mapping functions can be arbitrarily complex, and can involve multiple parameters. For the sake of clarity, in this document we demonstrate how to create a simple scaling  mapping function with only one geometric parameter which specifies length.  

STEP 1: Create a component in Akselos Modeler 

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● Follow the same steps of creating a new component. These steps are described in detail in the Component Editor tutorials.  

 

 Fig. 1: Create a new component in Akselos Modeler. 

 

 Fig. 2: View the new component in Akselos Modeler. Note that the long axis of this beam is in 

the z-direction. 

    

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STEP 2: Create a mapping function ● Create a new parameter. Right click on Parameter field in the Object Tree, then 

choose New. 

 Fig. 3: Add new parameter. 

 ● Set the parameter's units. In this case the parameter specifies the scaling of the 

length with respect to the reference geometry, and as such the parameter is dimensionless so that no units need to be specified. 

● Set a range for this parameter. For example, in this case we set the range to be 0.5 to 5. 

 Fig. 4: Settings for Parameter 

 

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● Create a New Mapping Function. ○ Right click on Mapping Functions field on Left-hand side banner, then 

choose New. ○ Set the name for this mapping function. In this case, it is scale. 

 

 Fig. 5: New mapping function Scale 

 ● In the Properties Panel, write the function description. In this case, we want to scale 

this component in lengthwise in the z direction. To do that: ○ Multiple the z

ref with the parameter s. There is no scaling in the x and y directions, so they remain the same. Note that in the mapping function definition z

ref is denoted by “z”, and the mapped z value is denoted by “zp”. ○ Click Apply.  

 Fig. 6: Define the mapping function Scale. 

 

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● In the Properties Panel, set the subdomains in which the mapping function is assigned. 

 Fig. 7: Subdomain mapping assignments 

 ● Press Save Collection to save all the settings, which will apply the mapping function 

to the beam component.   

STEP 3: Using mapping functions  

● Choose Add Components, then add the beam that you have created above. 

 Fig. 8: Add the new component 

 ● On the Properties Panel , select the Components tab, then select Parameters. In the 

Geometric field, you can see the scaling parameter s that you have created above. 

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By changing the value of s , you can change the length of this beam, as shown in Figure 8. 

  

  

Fig. 8: Component geometry changing with different values of s. 

 ● Upload the component to the Akselos Cloud to perform FEA solve or run the 

component training process to enable an RB-FEA solve. ● Note that components with mapping functions will require a longer training time. 

Hence, it is recommended that each component has a maximum of two geometric parameters. 

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