Structural Mechanics II

Code:

EM0033

Acronym:

ME II

Keywords
Classification	Keyword
OFICIAL	Applied Mechanics

Instance: 2009/2010 - 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	205	Syllabus since 2006/2007	3	-	6	70	160
		Plano de estudos de transição para 2006/07	3	-	6	70	160

Teaching language

Portuguese

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.

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; Introdução ao Método dos Elementos Finitos
Carlos Magalhães Oliveira; Análise Matricial de Estruturas
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

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

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

Ansys 5.7
Microsoft Office Excel

Evaluation Type

Distributed evaluation with final exam

Assessment Components

Description	Type	Time (hours)	Weight (%)	End date
Subject Classes	Participação presencial	22,00
Final examination	Exame	2,50
Final examination	Exame	2,50
Distributed evaluation - Problems from TP classes	Teste	50,00
Problems from T classes	Teste	10,00
Work of FEM by using software	Trabalho escrito	10,00		2010-05-23
	Total:	-	0,00

Amount of time allocated to each course unit

Description	Type	Time (hours)	End date
Study of the related subjects	Estudo autónomo	65
	Total:	65,00

Eligibility for exams

Enrolment + attendance to classes (students must attend to 75% of the classes) + one written exam + one practical assignment

Calculation formula of final grade

Final Exam (55% of the final mark)
Theoretical part: questions (50% of the exam)
Practical part: two problems (50% of the exam)


Distributed assessment (40% of the final mark)
a) Classes (theoretical and practical-theoretical classes) (15% 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

b) a written exam at the of the first month of classes (15% of the final mark)
(It will take place in a theoretical class)

c) practical work with commercial software (10% of the final mark)
Homework- a report must be delivered in the last week of classes

GRADES
1- The following aspects will be taken into consideration: correctness, clarity, concision and plenitude
2- Students, who achieve a higher grade than 16 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.