Course detail

Engineering Mechanics

FSI-UIM-A Acad. year: 2027/2028 Summer semester

During the course, students will become familiar with the fundamental concepts and principles of statics and mechanics of materials, including equilibrium of bodies, internal resultant forces and moments, stresses and strains, mechanical properties of materials, and fundamental relationships of linear elasticity. Attention is given to the basic types of loading of structural members, such as tension and compression, torsion, bending, and shear, including the solution of statically indeterminate problems, thermal loading, and stress concentrations. The course also covers the fundamentals of stress transformation and the determination of principal stresses. In the second part of the course, students will be introduced to the theoretical fundamentals of the Finite Element Method, the principles of discretization and approximation, basic types of finite elements, and the fundamentals of numerical modelling. The acquired knowledge is subsequently applied to solving typical problems in solid mechanics and other physical problems using ANSYS Workbench.

Language of instruction

English

Number of ECTS credits

7

Supervisor

prof. Ing. Jindřich Petruška, CSc.

Department

Institute of Solid Mechanics, Mechatronics and Biomechanics

Entry knowledge

Mathematics: linear algebra, matrix calculus, functions of one and more variables, differential and integral calculus, ordinary and partial differential equations. Basic knowledge of statics (especially equations of equilibrium and free body diagrams).

Rules for evaluation and completion of the course

The graded course-unit credit requirements:
- active participation in seminars,
- good results in the written test of basic knowledge.
The teacher will specify the specific form of assessment in the first week of the semester.

 

Attendance on the seminars is mandatory. A continuous control of the presence of students is conducted, including the control of activity and basic knowledge. Unexcused absence is grounds for not granting the course-unit credit.

Aims

The objective of the course is to equip the students with methodology for determination of strain and stress in various model bodies and risk assessment of basic limit states. Students are also introduced to theoretical background of the finite element method and its practical application to various problems of continuum mechanics.

Student will be able to categorize common types of tasks of strength of materials and is able to choose an appropriate methodology of problem solution in the given circumstances via the corresponding analytical solution. They will also learn how to use the finite element method for solving continuum mechanics problems in complicated two- and three-dimensional regions.

The study programmes with the given course

Programme N-ENG-A: Mechanical Engineering, Master's, compulsory

Type of course unit

 

Lecture

39 hours, optionally

Syllabus


  • Fundamentals of statics, force systems, equilibrium of bodies, and internal resultant forces and moments

  • Stress and strain, general states of stress and strain

  • Stress transformation, principal stresses, and Mohr's circle

  • Mechanical properties of materials, Hooke's law, and Poisson's ratio

  • Tension and compression: stresses, strains, and statically indeterminate problems

  • Thermal loading and thermal stresses

  • Torsion: stresses, strains, and angle of twist

  • Bending: normal stresses, beam deflections, and slopes

  • Shear loading: shear stresses and strains

  • Stress concentrations under different types of loading

  • Introduction to the Finite Element Method

  • Discretization, approximation, and variational principle

  • Shape functions, stiffness matrix, load vector, and fundamental FEM equations

  • Bar and beam elements (1D, 2D, 3D)

  • 2D and 3D elements, natural coordinates, and Gaussian quadrature

  • Finite element mesh generation and basic mesh settings

Computer-assisted exercise

26 hours, compulsory

Syllabus


  • Calculation of support reactions and internal resultant forces and moments

  • Calculation of stresses and strains, stress transformation, and Mohr's circle

  • Solution of problems involving tension and compression

  • Solution of statically indeterminate problems and problems involving thermal loading

  • Calculation of stresses and strains under torsional loading

  • Calculation of stresses, deflections, and slopes under bending

  • Calculation of shear stresses and strains

  • Solution of problems involving stress concentrations

  • Introduction to ANSYS Workbench

  • Analysis of beams and truss structures

  • Analysis of 2D problems (plane stress, plane strain, axisymmetry)

  • Analysis of 3D problems (solid and shell elements)

  • Steady-state and transient thermal analyses

  • Calculation of natural frequencies and mode shapes