1. FEM 1D Programming Term Project
Aerospace STructural Laboratory
T A : Park Kuk Jin

2. FEM Solver Procedure Take input file (or QT, MFC, Dialog Input)
Pre processing (set gauss quadratures, generate mesh, initialize vector & matrix and insert material variables(k,b,c,f))
Make element K matrix and force vector,
Assemble into global K matrix,
Apply boundary conditions
Invert K matrix (Apply Solver)
Post processing (Calculate Stress(Flux), Error norms(L2, H1,energy))

3. Take Input File Take Input Files
Set number of elements and nodes, k(x),b(x),f(x), boundary conditions, and load conditions
Use IO library like ifstream, istream, ostream, stdio(C,C++), ‘OPEN’ Function(Fortran), or MFC Dialog Input(C++)
Text Input File Example
Dialog Example

4. Take Input File
Simple Example for open input files(stdio)

5. Pre Processing Mesh Generation 1D Uniform meshes, Non-uniform meshes
1~9th order Shape function orders, 1~9th order Integral Points

6. Pre Processing
Mesh Generation

7. Pre Processing
Initialize All Vectors & Matrices

8. k(x),c(x),b(x),f(x)
MuParser : String  double values

9. Assemble Global K Matrix
Assemble Global Matrix (Global band matrix)

10. Set Gauss Quadrature

11. Element K Matrix

12. Boundary Conditions
Two-Points Boundary Conditions
Penalty Method

13. Load Conditions
Point Sources Conditions

14. Solver for linear equation Ax=b
Band Solver is recommended
High performance solver also
can be considered
If you can make faster and
more accurate solver than IPSAP,
You can get higher grades than
others

15. Post Process
Error Norms

16. Post Process
Stress(Flux) calculation

17. Post Process Example of Output File Node id, Nodes coordinate
Element id, connectivity
FEM, Exact Solutions at nodes
L2 norm, H1 norm, Energy norm
Flux Calculations