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Graduate courses

Departments' graduate courses for PhD-students.


Syllabus for

Academic year
MTM026 - Solid mechanics
Syllabus adopted 2019-02-20 by Head of Programme (or corresponding)
Owner: TKMAS
7,5 Credits
Grading: TH - Pass with distinction (5), Pass with credit (4), Pass (3), Fail
Education cycle: First-cycle
Major subject: Mechanical Engineering

Teaching language: Swedish
Application code: 55122
Open for exchange students: No
Only students with the course round in the programme plan

Module   Credit distribution   Examination dates
Sp1 Sp2 Sp3 Sp4 Summer course No Sp
0110 Project 1,5 c Grading: UG   1,5 c    
0210 Examination 6,0 c Grading: TH   6,0 c   04 Jun 2021 am J,  10 Oct 2020 am J,  17 Aug 2021 am J

In programs



Mikael Enelund

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General entry requirements for bachelor's level (first 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

The same as for the programme that owns the course.
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

Solid Mechanics is a continuation of the course Statics and solid mechanics. We learn to construct and solve mathematical models. You need to have good background in the basic courses of Mathematics. More precisely knowledge about the following is needed:
Linear algebra:
vector algebra, matrix algebra, systems of linear equations,
eigenvalue problems

elementary functions (logarithmic, exponential, Hyperbolic, trigonometric).
inequalities, differential Calculus (derivatives, extremes of functions construction of curves), differential equations (separable, second and forth orders with constant coefficients, non-homogeneous, initial conditions). Solution of homogeneous equation and particular solution, Euler s differential equation, boundary value problems, basic theory on partial differential equations

Basic knowledge in Matlab (code structure, functions, matrix calculations, curve constructions, plotting).


The student should obtain the knowledge, skills and attitudes required for solving real world strength of materials problem by hand and by use of suitable numerical software (e.g., Matlab). The problems include design, analysis as well as prediction of function and reliability of constructions.

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

  • Derive and solve the differential equation for the deflection curve of beams subjected to distributed loads including dentify and apply appropriate boundary conditions. Use the solution to compute reaction forces, bending moment and shear force distributions.
  • Derive and solve the differential equation for axially loaded beams and columns.
  • Compute the instability load for axially loaded beams.
  • Discuss the importance of constitutive equations and apply linear elasticity, thermoelasticity and plasticity models to three dimensional problems.
  • Compute principal stresses and corresponding directions.
  • Compute stresses and strains on arbitrary surfaces in 2 and 3 dimensional bodies.
  • Compute stresses and strains in thin-walled pressure vessels.
  • Compute effective (equivalent) stresses according to Tresca and von Mises. Apply the corresponding yield criterion to judge the risk of initial yielding and failure.
  • Derive and solve the elastic solutions for circular plates and thick-walled cylinders subjected to pressure loads and thermal loads.
  • Compute stress concentrations near holes, shoulders, notches etc. by use of handbooks and by the Finite element metod.
  • Compute stresses and strains in elasticity structures and bodies by use of the finite element method in  ANSYS.
  • Use linear fracture mechanics to compute the stress states close to cracks and to judge the risk for crack propagation and failure.
  • Describe the principles of fatigue design and master design with respect to high cycle fatigue.
  • Use Paris law to estimate the carack propagation and estimate the numbers of load cycles to failure.
  • Perform mathematical modelling, i.e., to formulate mathematical equations based on experimental knowledge and judge how accurate this mathematical model is and whether or not a more accurate analysis must be performed.
  • Be able to carry out computations and simulations accordingly to engineering ethical codes and standards, i.e., use established physical laws or/and best practise as the basis and to document well.
  • Be able to identify and discuss ethical dilemmas in the context of strength of materials.


    • Differential equation for the deflection of beams, tables of beam deformations, method of superposition, statically indeterminate beams.
    • Differential equation axially loaded beams. elastic stability and buckling of columns. Euler cases.
    • Theory of elasticity, principal stresses. equilibrium equations.
    • Stress concentrations.
    • Thick-walled tubes and circular plates.
    •  Fatigue design.
    • Introduction to the Finite element method including beam, 2D and 3D structures and calculations of stresses, deformations, buckling loads and life lengths.
    •  Fracture mechanics.
    In relation to the UN's sustainability goals, the course deals with reliable design of stressed structures, components, products and buildings. This relates to Goal 9 Build resilient infrastructure, promote sustainable industrialization and foster innovation and Goal 12 Responsible  consumption and production.


    The course is the second part of three connected courses.
    Lecturers, exercises, tutorials, instructions and computer assignments using Matlab and the FE-code ANSYS.


    U77b, Institutionen för hållfasthetslära, Chalmers, Göteborg

    Handbok och formelsamling i hållfasthetslära, Bengt Sundström (red.), KTH, Stockholm, 1998

    Formelsamling i mekanik, M.M. Japp, Inst. för teknisk mekanik, Chalmers.

    Introduktion till Hållfasthetslära - Enaxliga tillstånd, Ljung, Ottosen och Ristinmaa, Studentlitteratur, 2007.

    Hållfasthetslära - Allmänna tillstånd, Ottosen, Ristinmaa och Ljung, Studentlitteratur, 2007.

    Examination including compulsory elements

    Written final examination and one project with five assignments.
    Two optional written quizzes that can give bonus to the final exam.

    Page manager Published: Thu 04 Feb 2021.