# Cantilever Plate (Patran Plug-in)

In this tutorial, SFEM analysis of a simple cantilever plate will be performed using the Patran Plug-in.

## Description of the deterministic FE model

Consider the following cantilever plate constructed in PATRAN. The model is simply fixed in all DOFs at one side and transversely loaded on the other side. It is assumed that the plate consists of two different parts, one is made from steel, while the other part is made from aluminium.

A static loading with a magnitude of 100 N has been applied at every node on the free edge plate. Linear static analysis has been performed using NASTRAN as the FE solver, where the second order statistics of the z displacement of the node 421 are investigated (shown with the red dot in the figure).

## Definition of the probabilistic model

In this tutorial, the variation of the displacement at the free corner of the plate with respect to the stiffness of the plate is investigated. In order to take this variation into account, the uncertainty in the Young modulus will be modeled using random variables.

1. To start using Patran Plug-in, click on the COSSAN menu in the main PATRAN window
2. Then select DMCS analysis menu
3. Select the problem type as "Random Variable". This implies that the uncertain structural properties will be modeled using a single random variable over their whole domain. If the spatial variations are to be taken into account, random fields option should be chosen (see the Turbine Blade)
4. Select the distribution type, mean value and coefficient of variation for the random parameters (see the table below). In this example, the uncertainties in the thickness and young's modulus are taken into account.
5. Enter the number of simulation

## Performing the SFEM analysis

1. Next, click on the SIMULATE button to generate the realiations of the random structural paramaters.
2. Then, click on the SELECT RESPONSE button in order to determine the quantity of interest
3. Click on the RUN button to start the simulations

## Results of the SFEM analysis

The estimated statistics of the response obtained using various methods are summarized in the following table:

 Summary of Results Response DMCS (100 samples) Mean Value 0.0216 CoV 0.23