ID: 1133
Course type: scientific and vocational
Course coordinator: Buljak V. Vladimir
Lecturers: Buljak V. Vladimir
Contact: Buljak V. Vladimir
Level of studies: M.Sc. (graduate) Academic Studies – Mechanical Engineering
ECTS: 6
Final exam type: written+oral
Department: Department of Strength of Structures
The objective of this course is to provide thorough methodological introduction to the Finite Element Method. Within the introductory part students will get familiar with the application of this method for solving boundary value problems in the elasticity. Emphasis will be given to formulation of weak form of problems both in statics and dynamics. The main goal of the course is to present to the students how displacement based finite elements can be used to solve linear problems. Detailed derivation of stiffness matrix will be shown with reference to finite elements of various types (both structural and continuum elements). Various technique for the application of boundary conditions, and different methods for solving linear algebraic equations will be outlined. Post processing techniques and recovery of strain and stress fields based on nodal displacements for finite elements of different types will be presented in a detailed manner. In closing sessions of the course students will be shown some of the most popular commercial software used for static and dynamic analysis of structures.
Upon completing the course students will be able to: -Write computer codes for the assembling of stiffness matrix for truss-, beam-, frame- and shell-elements, as well as continuum 2-dimensional and 3-dimensional finite elements; -Perform both static and dynamic analysis of simple structures within personally developed computer codes; -Write computer codes for the stress and strain recovery based on linear, small-deformation theory, starting from resulting nodal displacements; -Understand basics on which most commercial software are build and use them for performing static and dynamic analysis of more complex structures.
Introduction to numerical modeling. Principle of virtual work and its application to the formulation of weak form of the problem. Interpolation functions for representing the displacement field over finite element. Assembling of element and global stiffness matrix. Dicretization for Lagrangian types of meshes. Methods for solving the resulting system of linear algebraic equations. Stress and strain recovery from nodal displacement results. Solutions for dynamic problems. Implicit and explicit scheme for time integration. Stability of the solution.
Writing computer codes in MATLAB software, for truss-, beam, frame-, shell-elements, as well as continuum 2D and 3D elements. Assembling of global stiffness matrix and mass matrix. Application of boundary conditions: concept of reduced stiffness matrix, and alternative solution with Lagrange-multipliers technique. Developing codes for strain and stress recovery. Static and dynamic analysis of structures.
Passed exam Theory of elasticity
Each student should have the access to the personal computer.
Total assigned hours: 75
New material: 28
Elaboration and examples (recapitulation): 2
Auditory exercises: 15
Laboratory exercises: 10
Calculation tasks: 5
Seminar paper: 0
Project: 0
Consultations: 0
Discussion/workshop: 0
Research study work: 0
Review and grading of calculation tasks: 5
Review and grading of lab reports: 0
Review and grading of seminar papers: 0
Review and grading of the project: 0
Test: 3
Test: 5
Final exam: 2
Activity during lectures: 0
Test/test: 20
Laboratory practice: 5
Calculation tasks: 5
Seminar paper: 0
Project: 0
Final exam: 70
Requirement for taking the exam (required number of points): 0
"The finite element method - a practical course" G.R. Liu S. S. Quek, Butterworth-Heinemann, 2013.; "An Introduction to the Finite Element Method" J.N. Reddy, McGraw Hill India, 2006.; "The Finite Element Method: Linear Static and Dynamic Finite Element Analysis", T. Hughes, Dover Publications, 2000.; "Finite Element Method: Volume 1" O. C. Zienkiewicz and R. L. Taylor, Butterworth-Heinemann, 2000.