# Category:Tutorials

This Category contains Tutorials examples. Although the following tutorials are created using COSSAN-X and tutorials are also available in OpenCossan. The following list shows the tutorials grouped according to the area of applicability.

## COSSAN-X and OpenCossan

ID Name
Description
Solver Analysis type Preview
1 Cantilever Beam

A cantilever beam is loaded at the end by a concentrated point load. All uncertainties are modelled mathematically by random variables. These random variables are characterized by its probability density function or alternatively by the cumulative probability function. The aim of the tutorial is to preform Uncertainty Quantification, Reliability Analysis and Sensitivity Analysis. • Static Analysis,
• Uncertainty Quantification,
• Reliability Analysis
• Sensitivity Analysis
• Reliability Based Optimization 2 Beam 3-point bending

This example considers a beam in three points bending. It will be studied using several third-party Finite Element software and various toolboxes from COSSAN-X. , , , FEAP , • Deterministic Analysis
• Uncertainty Quantification
• Reliability Analysis
• Optimization analysis 3 Infection Dynamic Model

This example shows how to perform the sensitivity analysis of a mathematical model representing an infective process at its early stafe, where we assume that the infection is propagated through some kind of contact between individuals who do not take any precaution to avoid contgion.

The first order and the total effect sensitivity indices of the input factors of the mathematical model are estimated, • Global Sensitivity Analysis 4 Bike Frame

This tutorial shows how to perform uncertainty quantification and reliability analysis using a third party software. The finite element solver Ansys is used. *Reliability Analysis
• Uncertainty Quantification 5 Truss Bridge Structure This example shows how to use the mode-based meta-model using a truss structure. The eigenvalues, eigenvectors and in the sequence the FRFs are approximated using the meta-model and compared to the extract solution computed in Matlab. • Mode Anaylsis
• Meta-Modelling 6 Bridge Model

This tutorial presents the application of the global sensitivity analysis approach to a practical problem in structural engineering, a mechanical model
of a long bridge.
The conceptual model contains 124 uncertain parameters summarized. All the uncertain parameters are considered to be uncorrelated. The bridge is subject to a harmonic load with a frequency of 10 Hz applied at the mid point of the 3rd bay. The aim of this numerical example is to identify the parameters that affect mostly the variance of the displacement and the parameters that have negligible effects. Dynamic Analysis

Global Sensitivity Analysis 7 Parallel  System This example analyze a system composed by parallel components.  The example is inspired by the Example # 5 (pag.271) from the paper: "A benchmark study on importance sampling techniques in structural reliability" S.Engelung and R. Rackwitz. Structural Safety, 12 (1993). System Reliability Analysis 8 Antenna Tower

This example show a robust design optimization of an antenna tower-like truss structure. The optimization constraints are based on a design-by-six-sigma approach. Robust Design 200px

A turbine blade is modeled within NASTRAN and ABAQUS (~12,000 DOFs). The model,  which consists of three parts (lower, middle and upper sections) is  fixed at the bottom nodes. A vertical acceleration is applied in order to see the effects of the centrifugal forces due to the rotation.

The uncertainties in the Young's modulus are modeled using independent  normal RV's, where the different portions of the structure are modeled  using different materials.

SFEM analysis is performed using different approaches.

Nastran

Abaqus

• Uncertainty Quantification (SFEM) 10 Building

A building consisting of 1-D (columns), 2-D (floors and stairs) and 3-D (soil) is modelled. Both NASTRAN and ABAQUS solvers are used to analyse the structure within SFEM analysis.

Nastran

Abaqus

• Uncertainty Quantification (SFEM) 11 Small Satellite

A satellite model is constructed in PATRAN (~5000 DOFs). The structure consists of horizontal and vertical panels attached to the central cylinder and a nozzle (modelled with 2-D shell elements).

Nastran
• Uncertainty Quantification (SFEM)
• Design of Experiments (DOE) 12 Cargo Crane

3-D model of light-service cargo crane--Dynamic drop load.

A stochastic transient analysis in Abaqus and the time-dependent response of one node is extracted.

Abaqus
• Stochastic Process
• Dynamic Analysis 13 Ishigami_Function

Connection to third party solver that execute the ishigami function

user defined solver
• Monte Carlo simulation
• Sensitivity Analysis ## Patran Plug-in

Name
Description
Solver Analysis type Preview
Cantilever Plate (Patran Plug-in) A cantilever plate simply fixed in all DOFs at one side and transversely loaded on the other side, is here analysed. It is assumed that the plate consists of two different parts, one is made from steel, while the other part is made from aluminum.  Nastran
• Uncertainty Quantification (SFEM) 12-Storey Building (Patran Plug-in) In this analysis, a building model consisting of 12 floors will be analysed, for which the FE model is constructed in PATRAN. The floors and walls are modelled with CQUAD shell elements, while the girders have been modelled using BEAM elements. A static loading, as well as the self weight of the building have been considered as Boundary conditions, while the building has been fixed at the bottom nodes of the elements, which model the foundation. Nastran
• Uncertainty Quantification (SFEM) A turbine blade is modelled within PATRAN. The model,  which consists of three parts (lower, middle and upper sections) is  fixed at the bottom nodes. A vertical acceleration is applied in order to see the effects of the centrifugal forces due to the rotation.

The uncertainties in the Young's modulus are modelled using random fields. DMCS analysis is performed for different correlation lengths in order to observe the effect of this parameter on the variation of the stresses and displacement of the structure.

Nastran

• Random Field Modelling
• Direct Monte Carlo Simulation ### Dynamics

• Baumechanik building in Matlab (MB)
• FE example to be added (BG) (with Random Field)
• Plate Box ? (BG)