Course syllabus for Solid mechanics

Course syllabus adopted 2026-02-19 by Head of Programme (or corresponding).

Overview

  • Swedish nameHållfasthetslära
  • CodeMTM026
  • Credits7.5 Credits
  • OwnerTKMSK
  • Education cycleFirst-cycle
  • Main field of studyMechanical Engineering
  • DepartmentMECHANICAL ENGINEERING
  • GradingTH - Pass with distinction (5), Pass with credit (4), Pass (3), Fail

Course round 1

  • Teaching language Swedish
  • Application code 44124
  • Open for exchange studentsNo
  • Only students with the course round in the programme overview.

Credit distribution

0110 Project 1.5 c
Grading: UG		 1.5 c
0210 Examination 6 c
Grading: TH		 6 c

In programmes

Examiner

Eligibility

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

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

Calculus:
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 Python (code structure, functions, matrix calculations, curve constructions, plotting).

Aim

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., Python). 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)

  • Analyse the deformation, internal forces, and stability of beams under various loads and boundary conditions.
  • Analyse stresses, strains, and material response for two‑ and three‑dimensional stress states.
  • Apply relevant yield, fracture, and safety criteria to assess structural strength and functional performance.
  • Analyse axisymmetric structures and pressure vessels with respect to stresses and deformations.
  • Analyse structures and perform lifetime design based on risks of fatigue, fracture, and crack propagation.
  • Analyse strength‑of‑materials problems using numerical methods through discretisation and formulation of linear systems of equations and eigenvalue problems.
  • Use numerical computational tools (programming) and finite element software to determine deformations, stresses, and stability in two‑ and three‑dimensional structures.
  • Explain the assumptions and validity conditions of common strength‑of‑materials models, and critically evaluate the reasonableness, reliability, and limitations of analytical and numerical results based on model choice and boundary conditions.
  • Document and communicate analysis results, methodological choices, and assumptions in a technically correct and traceable manner.
  • Identify and discuss engineering‑ethical aspects related to safety, sustainability, and responsibility in structural analysis and design.

Content

The course is a continuation of the course Statics and Strength of Materials. Here, we continue studying the mechanics of deformable bodies. We begin with the deformation of beams, followed by elastic stability of axially loaded beams. Furthermore, general stress states are treated; in particular, stress concentrations due to holes, notches, fillets, and cracks, as well as stresses in pressure vessels and thick-walled cylinders. The concepts of principal stresses and effective (von Mises) stress are covered. An introduction to fracture mechanics and fatigue design is also given. In addition, the course provides an introduction to the Finite Element Method. Mathematical modelling and abstract reasoning are practiced, i.e., formulating and solving mathematical models of real-world phenomena and assessing the reasonableness of the solutions. Python is used to solve the mathematical models.
The following topics are covered:

  • The beam differential equation, elementary cases, statically indeterminate beam systems, displacement methods for beams.
  • Differential equation for axially loaded beams. Buckling loads and Euler buckling cases, displacement methods for beams.
  • Theory of elasticity, equilibrium equations, and symmetries.
  • Principal stresses and effective (von Mises) stress, yield criteria.
  • Rotational symmetry, disks and thick-walled cylinders subject to pressure, temperature, and rotational loads.
  • Fatigue design, stress concentrations, and linear elastic fracture mechanics.
  • Introduction to the Finite Element Method in strength of materials.
In relation to the UN Sustainable Development Goals, the course addresses the reliable design of loaded structures, components, products, and buildings. This relates to Goal 9: Industry, Innovation and Infrastructure and Goal 12: Responsible Consumption and Production.

Organisation

The course includes lectures where we primarily cover theory but also solve problems, problem‑solving sessions focused on worked examples, supervision related to the project assignment, and open help sessions. In addition, the course contains a project assignment consisting of five sub‑projects involving programming in Python and simulations using a finite element software package (ANSYS).

Literature

  • Formelsamling i mekanik, M.M. Japp, Inst. för teknisk mekanik, Chalmers.
  • Formelsamling i hållfasthetslära för Maskinteknik, Brouzoulis och Ekh.
  • Introduktion till Hållfasthetslära - Enaxliga tillstånd, Ljung, Ottosen och Ristinmaa, Studentlitteratur, 2007.
  • Hållfasthetslära - Allmänna tillstånd, Ottosen, Ristinmaa och Ljung, Studentlitteratur, 2007.
  • Exempelsamling i hållfasthetslära, Peter Möller, Skrift U77b, Institutionen för hållfasthetslära, Chalmers, Göteborg

Examination including compulsory elements

Written final examination and one project with three assignments. The course contains two voluntary quizzes which can give bonus points for the final 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 about disability study support.