Course detail
Strength of Materials II
FSI-5PP-A Acad. year: 2021/2022 Winter semester
Assessment of solids with cracks, fundamentals of Linear Elastic Fracture Mechanics. Fatigue: basic material characteristics, basic methods of fatigue analysis. 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. Closed form solutions of elementary problems: thick wall cylinder, rotating disc, axisymmetrical plate, axisymmetric membrane shell, bending theory of cylindrical shell. Introduction to numerical analysis of elastic bodies using finite element method. Oveview of experimental methods in solid mechanics, electric resistance strain gauges.
Language of instruction
English
Number of ECTS credits
5
Supervisor
Learning outcomes of the course unit
Students will be able to analyze common problems of general strength and elasticity, to choose an appropriate method of problem solution 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).
Planned learning activities and teaching methods
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
Conditions for granting the course-unit credit: Attendance, active participation in seminars and submission of given tasks, including their presentation.
Examination: Examination is split into two parts. The content of the first mandatory part is the theoretical written test, where the maximum of 70 points can be reached. The content of the second part, which is optional, is an oral examination, where the maximum of 30 points can be reached. Specific form of the examination, types of the tasks or questions and other details will be communicated during the semester by the lecturer and through e-learing.
Aims
The aim of the course is to enlarge the students' knowledge on possibilities of assessment of safety of engineering structures. Students should 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. Also knowledge on failure criteria is enhanced, especially under conditions of cyclic loading and existence of cracks in the body.
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.
Specification of controlled education, way of implementation and compensation for absences
Attendance at practical training is obligatory. Head of seminars carry out continuous monitoring of student's presence, their activities and basic knowledge.
The study programmes with the given course
Programme B-STI-Z: Fundamentals of Mechanical Engineering, Bachelor's, recommended course
Programme B3S-P: Engineering, Bachelor's
branch B-STI: Fundamentals of Mechanical Engineering, compulsory-optional
Type of course unit
Lecture
39 hours, optionally
Teacher / Lecturer
Syllabus
1. Introduction. Assumptions of the analytical stress-strain analyses. Fundamentals of Linear Elastic Fracture Mechanics.
2. Behaviour of a body with a crack – residual life prediction under cyclic loading.
3. Behaviour of solids under cyclic loading, material characteristics for low-cycle and high-cycle fatigue.
4. Actual approaches and procedures of fatigue strength assessment for bar-like bodies.
5. General theory of elasticity – basic quantities and system of equations.
6. Basic types of model bodies and their analytical solution, generalized Hooke's law.
7. Thick-walled cylindrical vessels – stress-strain analysis.
8. Rotating discs – stress-strain analysis.
9. Axisymmetric plates – stress-strain analysis.
10. Axisymmetric membrane shells – stress-strain analysis.
11. Bending theory of cylindrical shells – stress-strain analysis.
12. Application of Finite Element Method in stress-strain analyses.
13. Experimental methods of evaluation of stresses and other mechanical quantities, electric resistance strain gauges.
Exercise
14 hours, compulsory
Teacher / Lecturer
Syllabus
1. Evaluation of stresses and deformations in bars under combined loads
4. Criterion of unstable crack propagation, LEFM, estimation of the residual life.
6. Fatigue failure under non-symmetrical stress cycle.
8. Thick-walled cylindrical vessels – stress-strain analysis.
11. Axisymmetric membrane shells – stress-strain analysis.
12. Bending theory of cylindrical shells – stress-strain analysis.
13. Course-unit credit.
Computer-assisted exercise
12 hours, compulsory
Syllabus
2. Application of failure criteria for bars under combined loading.
3.Stress state in a point of a body, principal stresses, failure criteria under multiaxial stress states.
5. Limit state of fatigue fracture, endurance strength.
7. Fatigue under combined loading, safety under non-proportional loading.
9. Rotating discs – stress-strain analysis.
10. Axisymmetric plates – stress-strain analysis.