Code: | EM0033 | Acronym: | ME II |
Keywords | |
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Classification | Keyword |
OFICIAL | Applied Mechanics |
Active? | Yes |
Responsible unit: | Applied Mechanics Section |
Course/CS Responsible: | Master in Mechanical Engineering |
Acronym | No. of Students | Study Plan | Curricular Years | Credits UCN | Credits ECTS | Contact hours | Total Time |
---|---|---|---|---|---|---|---|
MIEM | 38 | Syllabus since 2006/2007 | 4 | - | 6 | 45,5 | 162 |
To know, to understand and to analyse the Displacement Method and the Finite Element Method (formulated based on the displacement methods) applied to solving analysis problems of elastic linear structures. After a month, students should: 1. be acquainted with the principles of Displacement method 2. be capable of using on a spreadsheet the stiffness matrix and the solicitation vector of a reticulated structure (continuous, articulated or mixed, 2D or 3D) under the action of several types of loading. Students should also know how to introduce boundary conditions that simulate the connections to the exterior of a structure and to determine the nodal displacement vector. And should also know how to calculate the stress that act on critical sections of a structure. By the end of the semester, students should: 3. be acquainted with the principles of the Finite Element Method 4. be capable of using a spreadsheet with the stiffness matrix and the solicitation vector of a 2D finite element, isoparametric, of a triangular and quadrangular shape, with quadratic approximation, destined to the linear elastic analysis of 2D and axisymmetric structures, in state of plane stress and deformation, under the action of concentrated and/or distributed loads in the domain and/or boundary. 5. be capable of calculating from nodal displacements: displacement deformations and stresses in interior points of a finite element,. 6. be capable of analysing an 2D or axisymmetric structure under the action of mechanical stress and or thermal stress using commercial software.
Solving a structural problem based on computational mechanics.
DISPLACEMENT METHOD: Theoretical principles Flexibility coefficients and stiffness coefficients Deformation work Plastic energy Principles of virtual work Unit load theorem Flexibility and stiffness matrices STIFFNESS MATRIX of a beam in local and global axis Stiffness matrix of a reticulated structure ASSEMBLY of elementary stiffness matrices SOLICITATION VECTOR Introduction to BOUNDARY CONDITONS (prescribed displacements) Resolution of global system of equations Support REACTIONS Stress in bars Finite Element Method: Overview Discrete and continuous problems Discretization BI DIMENSIONAL LINEAR ELASTIC ANALYSIS by finite element method Equilibrium of a 2D domain Decomposition in three node triangular elements Displacement fields Stress fields System of nodal forces Equilibrium of the finite element Equilibrium of the whole domain Interpolation functions or shape functions Deformation matrix (B) Elasticity matrix (D) Stiffness matrix (K) Solicitation vector SHAPE FUNCTIONS: conditions that should follow Standard and hierarchical shape functions Shape functions for 1D, 2D (quadrangular and triangular) and 3D (hexahedrical and tetrahedrical) elements TRANSFORMATION OF COORDINATES: Overview Parametric transformation Isoparametric elements Errors related to transformation of coordinates NUMERICAL INTEGRATION: Overview Gauss numerical integration Elements of linear elastic analysis Beam half thickness
Two theoretical classes per week (one hour- lecture room) and one practical-theoretical class per week (2.30 h – computer room)
Designation | Weight (%) |
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Exame | 90,00 |
Participação presencial | 10,00 |
Total: | 100,00 |
Designation | Time (hours) |
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Estudo autónomo | 34,00 |
Total: | 34,00 |
Enrolment + attendance to classes (students must attend to 75% of the classes)
Final Exam (70% of the final mark) Theoretical part: questions (50% of the exam) Practical part: two problems (50% of the exam) Distributed assessment (30% of the final mark) a) Classes (theoretical and practical-theoretical classes) (10% of the final mark) This mark is given based on the work of students: - homework related with the theoretical classes - Exercises in theoretical-practical classes The following aspects will be taken into consideration: correctness, clarity, concision and plenitude 2- Students, who achieve a higher grade than 17 out of 20, must obligatorily attend an oral exam.
One practical assignment up to one week after the written exam (25% of the final mark)
Exam (75% of the final mark) – practical part using a computer Practical Assignment- (25% of the final mark) –up to one week after the exam
Exam (75% of the final mark) – practical part using a computer Practical Assignment (25% of the final mark) –up to one week after the exam
Attending to courses of Solid Mechanics and Structural Mechanics I is recommended.