# 330-0904/01 – Numerical Methods (NM)

 Gurantor department Department of Applied Mechanics Credits 10 Subject guarantor prof. Ing. Radim Halama, Ph.D. Subject version guarantor prof. Ing. Radim Halama, Ph.D. Study level postgraduate Requirement Choice-compulsory Year Semester winter + summer Study language Czech Year of introduction 2015/2016 Year of cancellation Intended for the faculties FS Intended for study types Doctoral
Instruction secured by
FRY72 doc. Ing. Karel Frydrýšek, Ph.D.
HAL22 prof. Ing. Radim Halama, Ph.D.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Examination 25+0
Part-time Examination 25+0

### Subject aims expressed by acquired skills and competences

Teach a students derive benefit from the newest knowledge of subject with possibility the knowledge further evolve and apply for complicated problems.

### Teaching methods

Individual consultations
Project work

### Summary

Finite Element Method Matrix Algebra. Definitions, additions and subtractions of matrices, matrix multiplication, determinants, matrix inverse, solution of simultaneous equations, integration and differentiation of matrices. Basic Structural Concepts and Energy Theorems. Stiffness and flexibility, stiffness matrix, the principle of virtual work, the principle of complementary virtual work, method of minimum potential, complementary energy theorem. The Discrete System. Electrical networks, fluid flow networks. The Application of the Principle of Virtual Work. Ritz method, application of Ritz method for bending of beams, application for tension and pressure, the solution of rotate-symmetric problems (rotate disc of constant thickness), complementary variant of Ritz method. Static Analysis of Pin-jointed Trusses. To obtain of stiffness matrix for a rod element, to obtain of stiffness matrix for a two-dimensional rod element, to obtain global stiffness matrix for plane pin-jointed trusses. Finite Element Analysis. Derivation of element stiffness matrices, virtual work approach, rod element, Hermite element, beam element, grid element, in-plane triangular element, in-plane quadrilateral element. Isotropic element, four- nod quadrilateral element, other higher-order elements. Finite Element Aanalysis. Global stiffness matrix, solution of simultaneous equations systems. Boundary Element Method Global System of Differential Equations. Formulation of the system of equations, introduction of boundary conditions, reactions, variable transformations. Numerical Procedures. Numerical integration, one-dimensional numerical integration (Gauss method), numerical integration in two dimensions (bi- directional methods), numerical integration in three dimensions. Fundamental Solutions. The point load (Kelvin) solution, reciprocal work theorem (Betti), Somigliana integral identity for displacements. Two Dimensional Potential Problems. Normal loading of the plane (Flamants solution), uniformly distributed load. The Direct Boundary Element Method. Influence coefficients, creation of equation system, the fundamental solution.

### Compulsory literature:

DHATT,G.-TOUZOT,G.: The Finite Element Method Displeyd, John Wiley and Sons, New York 1984 BEER,G.-WATSON,J.O.: Introduction to Finite and Boundary Elemetn Methods for Engineers, John Wiley & Sons,1992

### Recommended literature:

BORESI,A.P.-SCHMIDT,R.J.-SIDEBOTTOM,O.M.: Advanced Mechanics of Materials, John Wiley & Sons,Inc., 1993 CANDRUPATLA,T.R.-BELEGUNDU,A.D.: Introduction to Finite Elements in Engineering, Prentice-Hall International, Inc., 1991

### Way of continuous check of knowledge in the course of semester

Příprava zadané problematiky v písemné formě.

### Other requirements

The student prepare individual account on selected topic

### Prerequisities

Subject has no prerequisities.

### Co-requisities

Subject has no co-requisities.

### Subject syllabus:

The course extends the theoretical foundations of FEM and BEM acquired in the Bachelor's and Master's program. Numerical methods are currently in the general form used for solving numerical analysis of mechanical properties of structures.

### Conditions for subject completion

Part-time form (validity from: 2015/2016 Winter semester)
Min. number of points
Examination Examination
Mandatory attendence parzicipation:

Show history

### Occurrence in study plans

Academic yearProgrammeField of studySpec.ZaměřeníFormStudy language Tut. centreYearWSType of duty
2020/2021 (P2346) Mechanical Engineering (3901V003) Applied Mechanics P Czech Ostrava Choice-compulsory study plan
2020/2021 (P2346) Mechanical Engineering (3901V003) Applied Mechanics K Czech Ostrava Choice-compulsory study plan
2019/2020 (P2346) Mechanical Engineering (3901V003) Applied Mechanics P Czech Ostrava Choice-compulsory study plan
2019/2020 (P2346) Mechanical Engineering (3901V003) Applied Mechanics K Czech Ostrava Choice-compulsory study plan
2018/2019 (P2346) Mechanical Engineering (3901V003) Applied Mechanics P Czech Ostrava Choice-compulsory study plan
2018/2019 (P2346) Mechanical Engineering (3901V003) Applied Mechanics K Czech Ostrava Choice-compulsory study plan
2017/2018 (P2346) Mechanical Engineering (3901V003) Applied Mechanics P Czech Ostrava Choice-compulsory study plan
2017/2018 (P2346) Mechanical Engineering (3901V003) Applied Mechanics K Czech Ostrava Choice-compulsory study plan
2016/2017 (P2346) Mechanical Engineering (3901V003) Applied Mechanics P Czech Ostrava Choice-compulsory study plan
2016/2017 (P2346) Mechanical Engineering (3901V003) Applied Mechanics K Czech Ostrava Choice-compulsory study plan
2016/2017 (P2301) Mechanical Engineering (3901V003) Applied Mechanics K Czech Ostrava Choice-compulsory study plan
2015/2016 (P2346) Mechanical Engineering (3901V003) Applied Mechanics P Czech Ostrava Choice-compulsory study plan
2015/2016 (P2346) Mechanical Engineering (3901V003) Applied Mechanics K Czech Ostrava Choice-compulsory study plan
2015/2016 (P2301) Mechanical Engineering (3901V003) Applied Mechanics K Czech Ostrava Choice-compulsory study plan

### Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner