# Sök i programutbudet

Använd sökfunktionen för att leta efter kurser och program i Chalmers utbildningsutbud. Den programplan och utbildningsplan som avser dina studier är i allmänhet från det läsår du började dina studier.

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## Kursplan för

Läsår
TME235 - Mechanics of solids

Kursplanen fastställd 2012-02-19 av programansvarig (eller motsvarande)
Ägare: MPAME
7,5 Poäng
Betygskala: TH - Fem, Fyra, Tre, Underkänt
Utbildningsnivå: Avancerad nivå
Huvudområde: Maskinteknik
Institution: 42 - TILLÄMPAD MEKANIK

Undervisningsspråk: Engelska
Sökbar för utbytesstudenter
Blockschema: D

 Modul Poängfördelning Tentamensdatum Lp1 Lp2 Lp3 Lp4 Sommarkurs Ej Lp 0111 Tentamen 7,5hp Betygskala: TH 7,5hp 25 Okt 2012 em M, Kontakta examinator, 29 Aug 2013 fm M

#### I program

MPAME APPLIED MECHANICS, MSC PROGR, Årskurs 1 (obligatorisk)
MPENM ENGINEERING MATHEMATICS AND COMPUTATIONAL SCIENCE, MSC PROGR, Årskurs 1 (obligatoriskt valbar)

#### Examinator:

Professor  Magnus Ekh

#### Kursutvärdering:

http://document.chalmers.se/doc/762e01ce-58bb-4743-bfd5-5206b5a40e07

#### Behörighet:

För kurser inom Chalmers utbildningsprogram gäller samma behörighetskrav som till de(t) program kursen ingår i.

#### Kursspecifika förkunskaper

Linear algebra, Calculus in several variables, Mechanics, Solid mechanics and Fluid mechanics.

#### Syfte

The course provides an introduction to the mechanics of continuous media and, in particular, solids. A strong focus is placed on deriving and understanding the general field equations in three dimensions. These equations provide a generic basis for solid mechanics, fluid mechanics and heat transport. To be able to formulate the equations in three dimensions Cartesian tensors and the index notation will be used. The role of constitutive equations in distinguishing different types of problem will be emphasized. In particular, linear elastic solids as well as elastic plates will be studied in more detail. Some special cases when analytical solutions are possible to obtain will be highlighted. These analytical solutions will be compared with solutions obtained from finite elements. Energy methods will be introduced to show important concepts and phenomena in linear elasticity such as superposition and reciprocity.

#### Lärandemål (efter fullgjord kurs ska studenten kunna)

• Confidently manipulate tensor expressions using index notation, and use the divergence theorem and the transport theorem.
• Derive the equations of continuity, momentum and energy
• Extract essential aspects of a given stress state, such as principal values, principal directions, pressure, maximum values, stress vectors on planes, etc.
• Account for the role of a constitutive equation and determine its nature (e.g. solid/fluid, incompressible etc)
• Formulate linear constitutive equations: Hookean solid, Newtonian fluid, Fourier s law
• Formulate Hooke's law for general three dimensional stress-strain condition with specialization to plane stress and plane strain.
• Formulate the boundary value problem for linear momentum with proper boundary conditions.
• Derive Clapeyron's theorem and reciprocity relations.
• Derive the weak form (virtual work formulation) of linear momentum and show its relation to the finite element method.
• Establish the principle of minimum potential energy for linear elasticity and show the relation to the weak form.
• Show that elastic waves can be decomposed into pressure and shear waves.
• Derive the plate equation together with proper boundary conditions and specialize to axisymmetry.
• Derive the buckling loads for a rectangular plate.

#### Innehåll

Index notation; Tensors; Principal values and directions; Spatial derivatives and divergence theorem; Stress tensor; Eulerian and Lagrangian description of motion; The field equations of continuity, momentum and energy; Constitutive equations: Fourier's law, viscous fluids, elastic solids; Elastic solids; Superposition and reciprocity; Principle of minimum of potential energy; Virtual work formulation; Finite element method; Waves; Elastic plates; Buckling.

#### Organisation

Lectures, tutorials, assignment supervision

Lecture notes.

#### Examination

To pass the course the student must pass three assignments and a written exam. The grade is determined by the written exam.

Sidansvarig Publicerad: on 24 jan 2018.