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Mechanics of Solids and Computational

Code:

MP11121

Sigla:

MSC

Áreas Científicas
Classificação	Área Científica
OFICIAL	Solid Mechanics

Ocorrência: 2021/2022 - 1S

Ativa?	Yes
Unidade Responsável:	Departamento de Engenharia Mecânica
Curso/CE Responsável:

Ciclos de Estudo/Cursos

Sigla	Nº de Estudantes	Plano de Estudos	Anos Curriculares	Créditos UCN	Créditos ECTS	Horas de Contacto	Horas Totais
MP	28	Plano de Estudos	1	-	6	0	162

Língua de trabalho

Portuguese

Objetivos

Supply basic knowledge of the theory of elasticity and finite element method.

Resultados de aprendizagem e competências

At the end of the course the student should be able to:
Know the basics of the theory of elasticity and apply them in formulating and solving simple problems;
Understand the general concepts of the finite element method and know how to use a commercial software in solving problems of statics, dynamics and stability of structures.

Modo de trabalho

Presencial

Programa

1 - Stress
Introduction. Stress vector. State of stress at a point, Stress components. Equilibrium equations of stress. Stress transformation. Principal stresses and principal directions. Stationary values of shear stress. Graphical representation of the state of stress. Mohr's circle. Stresses on an octahedral plane. Spherical and deviatoric components of stress. Particular stress states. Plane stress.
2 - Strain
Introduction; General concepts. Strain components. Strain transformation. Principal strains and principal directions. Volume and shape variation. Compatibility equations. Graphical representation of the state of strain. Mohr's circle. Plane strain.
3 - Linear Stress-Extension-Temperature Relationships
Hooke's law for isotropic materials. Thermoelasticity equations for isotropic materials.
4 - Formulating and solving some problems of linear elasticity
Beam in pure bending. Thick cylinder subjected to internal and external pressure. Plane stress and plane strain: Airy stress function. Torsion of prismatic section members.
5 - The finite element method in structural analysis
Introduction and fundamental concepts. Principle of minimum potential energy;the Rayleigh-Ritz method. Analysis of bars and beams: Truss finite element; beam finite element. Two-dimensional problems: CST element. Plate analysis: Plate elements. Free Vibrations: Natural frequencies and mode shapes. Stability: Critical loads and buckling modes.

Bibliografia Obrigatória

A. Valido; Teoria da Elasticidade - Texto de apoio, 2011
Zienkiewicz, Taylor and Zhu; The Finite Element Method: Its Basis and Fundamentals, Seventh Edition, Elsevier, 2013. ISBN: 978-1-85617-633-0

Bibliografia Complementar

Timoshenko, S.P. and Goodier, J.N; Theory of Elasticity, Third Edition, McGraw-Hill International Editions, 1970
Robert D. Cook, David S. Malkus, Michael E. Plesha; Concepts and Applications of Finite Element Analysis, Third Edition, John Wiley & Sons, Inc., 1989. ISBN: 0-471-50319-3
Boresi, A.P., Schmidt, R.J. and Sidebottom, O.M.; Advanced Mechanics of Materials, Fifth Edition, John Wiley & Sons Inc., 1993. ISBN: 0-471-55157-0

Métodos de ensino e atividades de aprendizagem

Theoretical-Practical classes: Theoretical exposure of the subjects and problems solving by students.

Software

Programa Comercial de Elementos Finitos

Tipo de avaliação

Distributed evaluation without final exam

Componentes de Avaliação

Designation	Peso (%)
Teste	60,00
Trabalho escrito	40,00
Total:	100,00

Componentes de Ocupação

Designation	Tempo (Horas)
Estudo autónomo	60,00
Frequência das aulas	60,00
Trabalho escrito	40,00
Total:	160,00

Obtenção de frequência

a) Distributed assessment:

Performance of 1 test (Te) and 1 work project (TR)

 b) Final exam assessment:

Performance a final exam (EX)

Fórmula de cálculo da classificação final

a) Distributed assessment:

NF = 0,6*Te + 0,4*TR

Conditions for approval in the course:

Te  >= 8,0 values
NF >= 9,5 values


b) Final exam assessment:

NF = EX

Conditions for approval in the course:

NF >= 9,5 values

Observações

Students can recover the test in the exam period. The work project is done in group.