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## Syllabus for

MTM026 - Solid mechanics
Hållfasthetslära

Syllabus adopted 2019-02-20 by Head of Programme (or corresponding)
Owner: TKMAS
7,5 Credits
Grading: TH - Five, Four, Three, Fail
Education cycle: First-cycle
Major subject: Mechanical Engineering
Department: 30 - MECHANICS AND MARITIME SCIENCES

Teaching language: Swedish
Application code: 55117
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 1,5c Grading: UG 1,5c 0210 Examination 6,0c Grading: TH 6,0c 05 Jun 2020 am J, 12 Oct 2019 am SB_MU 18 Aug 2020 am J

#### In programs

TKMAS MECHANICAL ENGINEERING, Year 1 (compulsory)

Mikael Enelund

#### Replaces

MTM025   Mechanics and solid mechanics 2

#### Eligibility:

In order to be eligible for a first cycle course the applicant needs to fulfil the general and specific entry requirements of the programme(s) that has the course included in the study programme.

#### 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 Matlab (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., 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.

#### Content

• 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.

#### Organisation

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

#### Literature

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.

Published: Wed 26 Feb 2020.