Structural Mechanics II

Code:

EM0033

Acronym:

ME II

Keywords
Classification	Keyword
OFICIAL	Applied Mechanics

Instance: 2014/2015 - 2S

Active?	Yes
Responsible unit:	Applied Mechanics Section
Course/CS Responsible:	Master in Mechanical Engineering

Cycles of Study/Courses

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

Teaching language

Suitable for English-speaking students

Objectives

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.

Learning outcomes and competences

Solving a structural problem based on computational mechanics.

Working method

Presencial

Program

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

Mandatory literature

Carlos Magalhães Oliveira; Análise Matricial de Estruturas
Carlos Magalhães Oliveira; Introdução ao Método dos Elementos Finitos
F. Teixeira-Dias, J. Pinho-da-Cruz, R.A. Fontes Valente, R.J. Alves de Sousa; Método dos Elementos Finitos. Técnicas de Simulação Numérica em Engenharia, ETEP, 2010. ISBN: 978-972-8480-25-7

Complementary Bibliography

O. C.- Zienckiewicz + R. L. Taylor; The Finite Element Method
Bathe, Klaus-Jurgen; Finite element procedures. ISBN: 0-13-301458-4
A.J.M. Ferreira; MATLAB Codes for Finite Element Analysis, Springer, 2008. ISBN: 978-1-4020-9199-5

Teaching methods and learning activities

Two theoretical classes per week (one hour- lecture room) and one practical-theoretical class per week (2.30 h – computer room)

Software

Microsoft Office Excel
Ansys 5.7
Microsoft Office Excel
Ansys 5.7

keywords

Technological sciences > Engineering > Mechanical engineering

Evaluation Type

Distributed evaluation with final exam

Assessment Components

Designation	Weight (%)
Exame	90,00
Participação presencial	10,00
Total:	100,00

Amount of time allocated to each course unit

Designation	Time (hours)
Estudo autónomo	34,00
Total:	34,00

Eligibility for exams

Enrolment + attendance to classes (students must attend to 75% of the classes)

Calculation formula of final grade

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.

Examinations or Special Assignments

One practical assignment up to one week after the written exam (25% of the final mark)

Special assessment (TE, DA, ...)

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

Classification improvement

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

Observations

Attending to courses of Solid Mechanics and Structural Mechanics I is recommended.