Engineering Mechanics (FSI-UIM-A)

Academic year 2022/2023
Supervisor: prof. Ing. Jindřich Petruška, CSc.  
Supervising institute: ÚMTMB all courses guaranted by this institute
Teaching language: English
Aims of the course unit:
The aim of the course is to enlarge the students' knowledge on possibilities of assessment of safety of engineering structures. Students should get broader knowledge on failure criteria, especially under conditions of cyclic loading and existence of cracks in the body. They should also become capable to solve stresses and deformations in various model bodies analytically, and obtain basic information on possibilities of stress evaluation by means of both numerical methods (FEM) and experimental approaches.

This subject is included into study plan of the 3rd year of general bachelor's study as a compulsory-optional one. It is recommended as a prerequisite of branches M-ADI, M-ENI, M-FLI, M-IMB, M-MET or M-VSR.
Learning outcomes and competences:
Students will be able to analyze common problems of strength and elasticity, to choose an appropriate method of evaluation of stress, deformation and safety via either analytical solution or preparation of input data for a numerical solution or proposal of an experimental method. They will be able to distinguish and assess basic types of failures of engineering structures.
Prerequisites:
Mathematics: linear algebra, matrix notation, functions of one and more variables, differential and integral calculus, ordinary and partial differential equations. Ability of application of mathematical software (Maple) is required as well.
Basic knowledge of statics (especially equations of statical equilibrium and free body diagrams) and mechanics of materials (stress and strain tensors, elasticity theory of bars, failure criteria for ductile and brittle materials).
Course contents:
Fundamentals of Linear Elastic Fracture Mechanics, assessment of safety of solids with cracks under static and cyclic loading, . Fatigue of metals: cyclic curve, S-N curve, Manson-Coffin curve. Basic concepts of computational assessment of fatigue under dxymetric and asymmetric deterministic loading cycles, under uniaxial and biaxial state of stress, and under stochastic loading. General theory of elasticity - stress, strain and displacement of an element of continuum. System of equations of linear theory of elasticity, general Hooke's law. Analytical solutions of selected bodies: thick wall cylinder, rotating disc, axisymmetric plate, axisymmetric membrane shell, bending theory of cylindrical shell. Comparison of analytical and numerical approaches. Oveview of experimental methods in solid mechanics, electric resistance strain gauges.
Teaching methods and criteria:
The course is taught through lectures explaining the basic principles and theory of the discipline. Exercises are focused on practical topics presented in lectures.
Assesment methods and criteria linked to learning outcomes:
The course-unit credit is granted under conditions of active participation in seminars and passing seminar tests of basic knowledge (at least 10 ECTS points out of 20 must be gained). The points gained in seminar tests are included in the final evaluation of the course.
Final exam: Written part of the examination plays a decisive role, where the maximum of 80 ECTS points can be reached. It consists of a written theoretical test evaluated with max. 30 points and solution of two computational problems (50 pts max.). The problems concern typical profile areas of the subject. The lecturer will specify exact demands like types problems during the semester preceding the examination.
Final evaluation of the course is obtained as the sum of ECTS points gained in seminars and at the examination. To pass the course, at least 50 points must be reached.
Controlled participation in lessons:
Attendance at practical training is obligatory. Head of seminars carry out continuous monitoring of student's presence, their activities and basic knowledge.
Type of course unit:
    Lecture  13 × 3 hrs. optionally                  
    Exercise  7 × 2 hrs. compulsory                  
    Computer-assisted exercise  6 × 2 hrs. compulsory                  
Course curriculum:
    Lecture

General strength of materials - basic quantities and system of relationships between them.


Generalized Hooke’s law


Thick-walled cylindrical body


Rotating disks and cylindrical bodies


Circular and annular plates


Axisymmetric membrane shell


Cylindrical momentum shell


Composed bodies, comparison of analytical and numerical (FEM) solutions


Fatigue strength of beams – concept of nominal stresses


Fatigue strength of beams – concept of local stresses and strains, limited life


Brittle fracture, basics of linear elastic fracture mechanics


Crack growth at static and cyclic loading


Summary + examination
    Exercise

Stress and strain states and generalized Hooke’s law


Hooke’s law at assessment of strain gauge measurements


Thick-walled cylindrical body


Rotating disks and cylindrical bodies


Circular and annular plates


Axisymmetric membrane shell


Cylindrical momentum shell


Fatigue strength of beams – concept of nominal stresses


Fatigue strength of beams – concept of nominal stresses


Limit state of brittle fracture


Linear elastic fracture mechanics


Presentation of assignments


Presentation of assignments
    Computer-assisted exercise

Stress and strain states and generalized Hooke’s law


Hooke’s law at assessment of strain gauge measurements


Thick-walled cylindrical body


Rotating disks and cylindrical bodies


Circular and annular plates


Axisymmetric membrane shell


Cylindrical momentum shell


Fatigue strength of beams – concept of nominal stresses


Fatigue strength of beams – concept of nominal stresses


Limit state of brittle fracture


Linear elastic fracture mechanics


Presentation of assignments


Presentation of assignments
Literature - fundamental:
1. Dowling N.E.: Mechanical Behavior of Materials. Pearson, 2013.
2. Ugural A.C., Fenster S.K.: Advanced Strength and Applied Elasticity. Pearson, 4th ed. 2003.
3. Seed,G.M.: Strength of Materials, Saxe-Coburg Publications, 2000
The study programmes with the given course:
Programme Study form Branch Spec. Final classification   Course-unit credits     Obligation     Level     Year     Semester  
CŽV full-time study CZV Bases of Mechanical Engineering -- Cr,Ex 7 Compulsory 1 1 W
N-ENG-A full-time study --- no specialisation -- Cr,Ex 7 Compulsory 2 1 W
N-ENG-Z visiting student --- no specialisation -- Cr,Ex 7 Elective 2 1 W