This tutorial shows how to perform uncertainty quantification and reliability analysis using a third party software. Uncertainties are considered in the geometry of the structure and in the Young modulus.
Description of the deterministic FE model
The problem to be modeled in this example is a simple bicycle frame shown in the following figure. The frame is to be built of hollow aluminum tubing having an outside diameter of 25mm and a wall thickness of 2mm for the main part of the frame. For the rear forks, the tubing will be 12mm outside diameter and 1mm wall thickness.
The input and output files of the tutorial can be found in the at the following link: Bike frame.
The probabilistic model used in this tutorial is summmarized in the following table:
Summary of the Probabilistic Model
|Distribution||Mean Value||CoV Value|
| Young's Modulus
||lognormal|| 70 GPa
| Thickness of the front beams
||lognormal|| 2 mm
| Thickness of the rear beams
||lognormal|| 1 mm
The quantity of interest is the displacement of the point #3 in the picture above (which corresponds to node #6).
The failure is defined as a displacement exceeding 3mm.
Definition of the inputs
The random variables dedicated to the Young modulus and to the walls thickness are created.
The parameter defining the threshold displacement is created.
Interaction with 3rd party software
The 3rd party solver is selected among the different configurations available, which have been initially predefined. Please select Ansys in the available configurations.
The input and output files are added. The addition of the are done in the following order:
- Import the original input and output files in the file management system (using the section File management, at the bottom left side of the editor of the connector).
- Set the Input file format.
- The input file of the finite element software is selected as the main input file. To do so, click on Select of the section Input at the top right side of the editor of the connector), and select the input file.
- The box in front of the input file needs to be ticked to define an injector related to the file.
- Add the output file to the Outputs section, on the bottom right side of the editor of the connector). An extractor with the file is automatically created.
Identifiers are set in order to inject the quantities of interest at the right position in the input file. In this example, identifiers are defined for the wall thickness and the material properties.
At the line 43 and 44 of the original input file, the values of the wall thickness (originally 1 and 2mm, respectively) are replaced by identifiers to the Random Variables thickness1 and thickness2, respectively. At the line 48 of the original input file, the value of the Young modulus (originally 70,000 MPa) is replaced by an identifier to the Random Variable E.
An extractor was created in order to retrieve the displacement of the node #6. An anchor is set at the header of the table showing the nodal displacement. It is not necessary to use the whole header sentence in the anchor, but enough characters have to be selected, so that the chain of characters does not repeat too many times. Then a response is set to extract the absolute value of the displacement of the node #6 in the x-direction. The response is named displacement. Finally the response is linked to the anchor by dragging the response towards the location of the anchor.
Definition of the models
A physical model is created. It is a general purpose object that will be used at the basis for a more specialised analysis (reliability analysis in this case). The connector previously defied has to be added in the evaluator section. The related inputs and outputs are automatically determined.
The performance function is defined using capacity and demand. The capacity is the parameter defining the threshold displacement, the demand is the displacement obtained from the finite element code.
A probabilistic model is created. It takes as an input the previously defined physical model and performance function. It is necessary to define one probabilistic model before performing the reliability analysis. The inputs related to the object and outputs are automatically determined.
Monte Carlo simulation is performed using 2,000 samples. In order to perform the analysis, use the icon in the top right corner of the probabilistic model, or right click on the object in the contextual menu and select run analysis.
The wizard for the analysis is displayed below, reliability analysis is selected.
The following wizard appears, the quantity of interest Failure Probability is selected.
The simulation method is then selected. In this example, Monte Carlo simulation is performed with 2000 samples in one batch. A simulation can be divided in several batches to improve the efficiency when a large number of samples are used, however, it is not necessary in this example.
The failure probability estimated from Monte Carlo simulation can be displayed:
The inputs (e.g. samples of the random variables, etc) and outputs (quantities of interest) from the simulations can be displayed. Several plots are available, such as histogram, scatter view, pie chart, etc.
- The input file of Ansys was taken from the tutorials provided by the Department of Mechanical Engineering, University of Alberta. The original tutorial can be found at the following link: .