Course syllabus for Mechanics of solids

Course syllabus adopted 2021-02-17 by Head of Programme (or corresponding).

Overview

  • Swedish nameSolidmekanik
  • CodeTME235
  • Credits7.5 Credits
  • OwnerMPAME
  • Education cycleSecond-cycle
  • Main field of studyMechanical Engineering
  • DepartmentINDUSTRIAL AND MATERIALS SCIENCE
  • GradingTH - Pass with distinction (5), Pass with credit (4), Pass (3), Fail

Course round 1

  • Teaching language English
  • Application code 03111
  • Block schedule
  • Open for exchange studentsYes

Credit distribution

0111 Examination 7.5 c
Grading: TH		7.5 c
  • 26 Okt 2023 pm L_DATA
  • 05 Jan 2024 am J_DATA
  • 29 Aug 2024 am J_DATA

In programmes

Examiner

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Eligibility

General entry requirements for Master's level (second cycle)
Applicants enrolled in a programme at Chalmers where the course is included in the study programme are exempted from fulfilling the requirements above.

Specific entry requirements

English 6 (or by other approved means with the equivalent proficiency level)
Applicants enrolled in a programme at Chalmers where the course is included in the study programme are exempted from fulfilling the requirements above.

Course specific prerequisites

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

Aim

The course provides an introduction to the mechanics of continuous media with particular focus on solids. An important part of the course is the derivation 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 elasticity is used for different structural elements such as beams and plates. Energy methods are introduced to show important concepts and phenomena in linear elasticity such as superposition and reciprocity. The relation between energy methods and the finite element method is shown. A short introduction to the finite element method is given in terms of both running a commercial software and of own programming in Matlab or Python.

Learning outcomes (after completion of the course the student should be able to)

  • Manipulate tensor expressions using index notation, and use the divergence theorem and the transport theorem.
  • Derive the equations of continuity, momentum and energy for a continuum.
  • Extract essential aspects of a given stress state, such as principal values, principal directions, hydrostatic stress, deviatoric stress, stress vector on a plane, 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 equilibrium of a continuum with boundary conditions.
  • Derive and utilize Clapeyron's theorem and reciprocity relations.
  • Derive the weak form (virtual work formulation) of linear momentum and show how it is used in the finite element method.
  • Establish the principle of minimum potential energy for linear elasticity and show the relation to the weak form.
  • Derive the axisymmetric plate equation together with proper boundary conditions
  • Establish large deformation kinematics with polar decomposition.
  • Formulate balance law for momentum for large deformations,
  • Use hyperelasticity for modelling of mechanical response of e.g. rubber material.

Content

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; Potential energy; Virtual work formulation; Finite element method; Plates; Large deformations.

Organisation

Lectures, tutorials, assignment supervision

Literature

Lecture notes.

Examination including compulsory elements

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

The course examiner may assess individual students in other ways than what is stated above if there are special reasons for doing so, for example if a student has a decision from Chalmers on educational support due to disability.