Finite Element Method
Course Info
Solving partial differential equations of mechanics numerically. Fundamentals of the finite element method including weak form, shape functions, isoparametric approximation, Gauss quadrature, element types, assembly operation, sparsity pattern with application to 2D problems. Self-written finite element code in MATLAB. Computational simulations of elastic materials and stress analysis using the MATLAB code. Domain discretization, pre-processing and post-processing aspects.
Credits
Bilkent : 3 , ECTS : 5
Syllabus
01
Understanding finite elements through springs combinations
02
Truss elements and assembly of 1D objects in 2D and 3D space
03
Programming assembly of truss structures
04
Strong from, weak form, energy minimization
05
Approximation using shape functions
06
Integration via Gauss quadrature
07
Formulation of FEM in 1D adopting isoparametric concept
08
Programming 1D FE code and sparsity patterns
09
Strong and weak form for 2D problems
10
Domain discretization in 2D and pre-processing
11
Derivation of shape functions and Gauss quadrature in 2D
12
Formulation of FEM in 2D adopting isoparametric concept
13
Programming 2D FE code
14
Post-processing and visualization aspects
Grading
HW 1 ( 1D FEM ) => Quiz 1 5%
HW 2 ( 1D FEM ) => Quiz 2 5%
HW 3 ( 1D FEM ) => Quiz 3 5%
HW 4 ( 1D FEM ) => Quiz 4 5%
HW 5 ( 1D FEM ) => Quiz 5 5%
HW 6 ( 2D FEM ) 15%
Project 1 - 1D FEM 25%
Project 2 - 2D FEM 20%
Final 15%