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 |
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.
E-learning
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
Occurrence in study plans
Occurrence in special blocks
Assessment of instruction
Předmět neobsahuje žádné hodnocení.