Stochastic Simulation Techniques and Structural Reliability - Project -- 3
Budget: €30 – €250 EUR
1. Random Field Generation
Implement now your own random field generator, i.e., by choosing one of the
methods: Moving Average Method, or Turning bands.
Use different choices for the parameters µX, σX and Θ (change one parameter
each time and fix the others). Discuss the effects of the different choices of the
parameters on the field.
2. Random Fields and Finite Element Analysis - Structural Analysis (10
Points)
Please download the Finite Element Method (FEM) Package CALFEM 3.4. The
package provides a well implemented academic Finite Element Environment for
MATLAB.
Adapt the example using the material properties (E- Young’s modulus) of the three
bars are random with µX = 200.0 GP a, σX = 10 GP a, Θ = 10.
Generate a random field of length three. Assign the computed random material
properties to the three bars and repeat the computations.
By which probability does the vertical displacement at the point of loading exceed
1.2 mm? Perform a Monte Carlo Simulation assuming that a displacement larger
1.2 mm would lead to failure. What is the corresponding reliabilty index?
To which values does the standard deviation of the field needs to be changed that
the reliability index is at least 3.0? (try to find out by repeated MCS).
3. Random Fields and Finite Element Analysis - Heat Flow
From the CALFEM package have a precise look on example exs2.m, heat flow. See
the description of the problem in the manual calfem34.pdf, Page 9.3-6 (you can
find the file in the installed package).
Solve the problem using the outdoor temperature as −25oC and the temperature
inside is 20oC. Compute the temperatures, and the heat flow at the boundaries
q1, ..., q5.
Adapt now the problem ausing the following material properties assuming random
values for each section, i.e. the material properties of the structure follow a random
field with properties: µX = 30.0 W/K, σX = 4 W/K, Θ = 1.0 . Generate a
random field of length 5 and assign the generated values as material parameters
to each section.
Solve the problem with the random input and compute the temperatures and the
heat flow at the boundaries q1, ..., q5.
Run the simulation now many times (Monte Carlo Simulation). Save the heat-flows
in a vector. Plot the histogram of the heat flows.
4. Reliability Analysis
Implement now your own random field generator, i.e., by choosing one of the
methods: Moving Average Method, or Turning bands.
Use different choices for the parameters µX, σX and Θ (change one parameter
each time and fix the others). Discuss the effects of the different choices of the
parameters on the field.
2. Random Fields and Finite Element Analysis - Structural Analysis (10
Points)
Please download the Finite Element Method (FEM) Package CALFEM 3.4. The
package provides a well implemented academic Finite Element Environment for
MATLAB.
Adapt the example using the material properties (E- Young’s modulus) of the three
bars are random with µX = 200.0 GP a, σX = 10 GP a, Θ = 10.
Generate a random field of length three. Assign the computed random material
properties to the three bars and repeat the computations.
By which probability does the vertical displacement at the point of loading exceed
1.2 mm? Perform a Monte Carlo Simulation assuming that a displacement larger
1.2 mm would lead to failure. What is the corresponding reliabilty index?
To which values does the standard deviation of the field needs to be changed that
the reliability index is at least 3.0? (try to find out by repeated MCS).
3. Random Fields and Finite Element Analysis - Heat Flow
From the CALFEM package have a precise look on example exs2.m, heat flow. See
the description of the problem in the manual calfem34.pdf, Page 9.3-6 (you can
find the file in the installed package).
Solve the problem using the outdoor temperature as −25oC and the temperature
inside is 20oC. Compute the temperatures, and the heat flow at the boundaries
q1, ..., q5.
Adapt now the problem ausing the following material properties assuming random
values for each section, i.e. the material properties of the structure follow a random
field with properties: µX = 30.0 W/K, σX = 4 W/K, Θ = 1.0 . Generate a
random field of length 5 and assign the generated values as material parameters
to each section.
Solve the problem with the random input and compute the temperatures and the
heat flow at the boundaries q1, ..., q5.
Run the simulation now many times (Monte Carlo Simulation). Save the heat-flows
in a vector. Plot the histogram of the heat flows.
4. Reliability Analysis