These links may be helpful

http://michael.friswell.com/PDF_Files/C159.pdf

https://link.springer.com/article/10.1023/A%3A1026236621486

http://michael.friswell.com/PDF_Files/C149.pdf

https://hal.archives-ouvertes.fr/hal-01183149/document

Dear Muhammad Ichsan,

You should consider the purpose of using Monte Carlo Simulation (MCS). For example, you want to determine the probability of failure of a structure under a seismic event with different cross sections of beams and columns. Firstly, you generate a set of random variables relating to the cross sections by MCS. Then, all the input data of cross-sections are applied to your model (if your model is a FEM model, coding for automatical running is the best way). After running the model throughout all the random variables, you can calculate the probability of failure by the equation, Pf = Nf/N (where N is the total number of running cases and Nf is the number of failure cases). You should remember that using MCS has a disadvantage that it is necessary to have about 1 million random variables to get a good result. Using Latin Hypercube Sampling should be considered if you want to reduce your random variables.

Hope it is helpful for you.

Dear Muhammad Ichsan,

This online course is good for you. They use Matlab together with ANSYS to solve the probabilistic problems.

http://nptel.ac.in/courses/105103140/

Thanks for your answer Mr Muhannad and Mr Huy Quan

Dear Mr Huy Quan,

Let me give you an example to be corrected by you,

For example in picture RSA.jpg. I have to replace the right equation with random variable result from MCS. So I can get value the displacement value?

am I right?

or should I change the left equation to do MCS?

Regards,

Ichsan

Here is the equation

Dear Mr. Muhammad Ichsan,

As my understanding, you want to generate a set of random variables for Sdi by using MCS, to obtain a set of random variables of Umax by your Equation. In my opinion, it is not a good way, especially for complex structures behaving in a nonlinear state. In our procedure, we generate random variables just for input parameters, then use these input parameters to analyze the structures (assign the input data to the model like natural randomness). All the output random variables are taken after the models to be analyzed. For example, If you have 1000 random variables (e.g. an earthquake event), you need to assign 1000 times to your FEM model, then you will receive 1000 random variables of output (e.g. the displacement of the top of the building).

Hope it helps you.

Dear Mr. Huy Quan,

I am sorry for long time no comment for your response. I really appreciate for your answer.

After I have some discussion with my supervisor. Now I have change my method from RSA to Response History Analysis (RSH).

The variable random that I think so far, I will use the Material Properties as input parameters.

As you said, the input would be used in analyze.

then, I would like to ask you again sir,

What is about if I make a earthquake load as variable random? (as my understanding RSH method used time domain)

Regards