102331 - MODELING AND SIMULATION

Subject type: Mandatory

Coordinator: Julián Horrillo Tello

Trimester: Third term

Credits: 6

L'idioma d'impartició serà Català/Castellà. Some materials, terminology and bibliography are in English, so you should have a minimum level.

1. Introduction to Modeling and Simulation in Mechanical Engineering. Types of models. Physical models, analytical mathematical models, numerical mathematical models. Modeling "language".

2. Matrix methods for bar structures. The Stiffness Method (Direct Stiffness Method): Concepts of matrices of rigidity, forces and nodal displacements. Concepts of local and global coordinate systems. Concepts of matrix assembly. Contour conditions and methods of application. Programming of matrix methods by static simulation of the behavior of bar structures exposed to external loads.

3. The introduction to the MEF (Finite Element Method). Principle of Virtual Works (PTV). Programming of numerical models with 1D elements. Programming simple codes to simulate 1D problems through the MEF.

Two-dimensional elasticity (2D): hypothesis of plane stress and plane deformation. Linear shape functions. Modeling of distributed forces. Discretization of finite elements: the mesh. Triangular and quadrilateral finite elements of three and four nodes. Lagrangian elements of 6 and 8 nodes.

4. Advanced elements (beam, plate, membrane, ...). Principle of Virtual Works (PTV) in 3D. 3D linear shape functions. Simplifications of three-dimensional models due to symmetric problems.

5. Hybrid and advanced models. Introduction to hybrid and object-oriented models. Introduction to advanced models: evolutionary algorithmic strategies, "white-box", "gray-box" and "black-box" models. Use of neural networks.

SOFTWARE: This course will use SolidWorks and Matlab / Python.

Prepare models for numerical calculation (CAD) and pre-process these models (applying contour conditions, loads, material properties).

Use MEF software for static problem analysis.

Understand the basic concepts of numerical modeling.

Easily find sources of errors in numerical simulations

Analyze results of simulations, draw conclusions and take measures to improve the design of mechanical components

The subject consists of 40 hours of face-to-face classes in the classroom (large group), where the concepts of theory will be developed, with examples and exercises and 20 hours of laboratory activities (small group).

Students have all the information necessary to follow the teacher's explanations and be able to study independently. Students will have access to the notes of the subject on the course website.

Small group sessions are mandatory. In the computer laboratory practices the students will be divided into teams of a maximum of 2 members to perform the tasks.

Internships involve programming algorithms for numerical simulation and learning to use numerical modeling and simulation software (SolidWorks and Matlab / Python).

The content of the subject is divided into 5 topics:

1. Introduction to Modeling and Simulation in Mechanical Engineering.

2. Matrix methods by numerical simulation.

1. Matrix Methods: Direct Stifness Method.
2. Direct Stifness Method for bar elements (trusses).

3. MEF (Finite Element Method)

1. Principle of Virtual Works (PTV)
2. Programming of 1D MEF numerical models.
3. Triangular Elements.
4. Quadrilateral Elements.
5. Lagrangian elements of 6, 8 and 9 nodes.

4. MEF 3D

1. Advanced 2D and 3D structural elements (beam, plate, membrane).
2. MEF for 3D problems.

5. Hybrid and Advanced Models

1. Hybrid Models
2. Advanced Models

The subject consists of 40 hours of face-to-face classes in the classroom (large group), where the concepts of theory will be developed, with numerous examples and exercises and 20 hours of laboratory activities (small group).

Students have all the information necessary to follow the teacher's explanations and be able to study independently. Students will have access to the notes of the subject on the course website.

Small group sessions are mandatory. In the computer laboratory practices the students will be divided into teams of a maximum of 2 members to perform the tasks.

Internships involve programming algorithms for numerical simulation and learning to use numerical modeling and simulation software (SolidWorks and Matlab / Python).

The subject is passed by doing internships, two course assignments and an exam note.

Internships will have a total weight of 20% in the final grade.

The written exam includes questions on theoretical concepts that can be assessed during the course and one or more practical problems that will be assessed on the day and time assigned for the final exam of the subject. The exam grade will have a weight of 30% on the final grade.

There will be two course assignments:

• The first course work will consist of the geometric modeling in CAD of a system, mechanism or piece, the approach of the conditions of contour and loads to which it will be subjected in its working conditions and the subsequent numerical simulation and analysis of results, with proposals for improvement, if any. It will also be necessary to make the 2D plans of the part or parts involved in the mechanism. The work will have a weight of 25% on the final course grade.
• The second course work will consist of the realization of a numerical model programmed in Matlab or Python for the optimization and / or numerical simulation of problems. The work will have a weight of 25% on the final course grade.

It is necessary to obtain a minimum grade of 35/100 in each of the evaluable concepts for the average mark to be made.

Class attendance is mandatory, unjustified absence in more than 3 sessions implies loss of the right to assessment.

The delivery of works more than 3 days late implies the loss of the right to evaluation.

Introduction to Finite Element Method, lecture notes of the course by C. Felippa

Oñate, Eugenio (1992). Calculation of Structures by the Finite Element Method. Ed. CIMNE.

Thompson EG Introduction to the finite element method: theory, programming and applications ..

Modeling and simulation fundamentals, J. Sokolowksi, C. Banks, Wiley, 2010

Martin J. Haigh: An Introduction to computer-aided design and manufacture, Oxford, 1985.

Shigley, JE Simulation of mechanical systems: an introduction. 1967. New York: McGraw-Hill