Course detail

Structural mechanics

FAST-DD61Acad. year: 2022/2023

Advance topics on FEA. Introduction to nonlinear mechanics. Tensors, strain and stress measures, coordinate systems, solution methods tangent stiffness matrix, material and geometrical stiffness, two basic formulations of geometrical nonlinearity, numerical methods of solution of nonlinear algebraic equations. Energetical principles in statics, static stability, static nonlinear models, collapse, loss of stability, bifurcations and catastrophes, loss of symmetry. Energetical principles in dynamics, dynamic nonlinear models, conservative/dissipative system, solution and monitoring of dynamical systems, phase space and trajectory of dynamical system, nonlinear symptoms in dynamics.

Language of instruction

Czech

Number of ECTS credits

8

Mode of study

Not applicable.

Guarantor

prof. Ing. David Lehký, Ph.D.

Department

Institute of Structural Mechanics (STM)

Learning outcomes of the course unit

Not applicable.

Prerequisites

Basic knowledge of structure mechanics, matrix and vector algebra, infinitesimal calculus, fundamentals of numerical mathematics.

Co-requisites

Not applicable.

Planned learning activities and teaching methods

Not applicable.

Assesment methods and criteria linked to learning outcomes

Not applicable.

Course curriculum

1. Interesting problems in structural mechanics; equalizing of bending moments between supports and on the support; optimal and variable beam section; design of the beam shape dependent on load
2. Assumptions of linear mechanics; plane section remain plane and undeformed (plasticity, wall, torsion, shear lag), small deformations (loading by bending moment and by force), linear material
3. Exception cases; mechanism; follower load
4. Measurement of loading diagrams of nonlinear materials
5. Measurement of deflection of cantilever beam, von Mises truss, catastrophic machines
6. Energetical principles in statics, static stability
7. Design of static nonlinear models and its solution
8. Nonlinear symptoms in structural statics - collapse, loss of stability (beam buckling, bending of cantilever beam, frame, von Mises truss), bifurcations and catastrophes (beam buckling), loss of symmetry (beam buckling, torsion)
9. Energetical principles in dynamics (Lagrange and Hamilton function)
10. Design of dynamic nonlinear models, dynamical systems (definition, conservative/dissipative system)
11. Solution and monitoring of dynamical systems, numerical methods
12. Phase space and trajectory of dynamical system
13. Nonlinear symptoms in dynamics

Work placements

Not applicable.

Aims

Lectures are oriented to post gradual students with aim to make their knowledge in structure mechanics deeper. The topics are selected from the point of view of their application in advance structure analysis.

Specification of controlled education, way of implementation and compensation for absences

Extent and forms are specified by guarantor’s regulation updated for every academic year.

Recommended optional programme components

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

Not applicable.

Recommended reading

Not applicable.

Classification of course in study plans

  • Programme D-K-E-CE (N) Doctoral

    branch KDS , 1 year of study, summer semester, compulsory-optional

  • Programme D-K-C-SI (N) Doctoral

    branch KDS , 1 year of study, summer semester, compulsory-optional

  • Programme D-P-E-CE (N) Doctoral

    branch KDS , 1 year of study, summer semester, compulsory-optional

  • Programme D-P-C-SI (N) Doctoral

    branch KDS , 1 year of study, summer semester, compulsory-optional

Type of course unit

 

Lecture

39 hod., optionally

Teacher / Lecturer

prof. Ing. David Lehký, Ph.D.

Syllabus

1. Interesting problems in structural mechanics; equalizing of bending moments between supports and on the support; optimal and variable beam section; design of the beam shape dependent on load 2. Assumptions of linear mechanics; plane section remain plane and undeformed (plasticity, wall, torsion, shear lag), small deformations (loading by bending moment and by force), linear material 3. Exception cases; mechanism; follower load 4. Measurement of loading diagrams of nonlinear materials 5. Measurement of deflection of cantilever beam, von Mises truss, catastrophic machines 6. Energetical principles in statics, static stability 7. Design of static nonlinear models and its solution 8. Nonlinear symptoms in structural statics - collapse, loss of stability (beam buckling, bending of cantilever beam, frame, von Mises truss), bifurcations and catastrophes (beam buckling), loss of symmetry (beam buckling, torsion) 9. Energetical principles in dynamics (Lagrange and Hamilton function) 10. Design of dynamic nonlinear models, dynamical systems (definition, conservative/dissipative system) 11. Solution and monitoring of dynamical systems, numerical methods 12. Phase space and trajectory of dynamical system 13. Nonlinear symptoms in dynamics