potentialFlow4.html

potentialFlow4.mws

FINITE ELEMENTS

SYMBOLIC PROGRAMMING IN MAPLE

by Artur Portela

Potential-Flow Example 4: Symbolic Variables

> restart:interface(verboseproc=3):printlevel:=3:

> libname := "C:/mylib/fem",libname:

> with(Plotter):

> with(Cgt_fem):

> with(G_cgt_fem):

>

Data Preparation

The best way to input data for Cgt_fem is to use the procedure read_save_data , which reads a file with the following structure:

* control * [title,point sources,element sources,boundary velocities]
title Potential Flow in a Rectangular Domain
point sources
element sources
boundary velocities

* materials * [material,x-permeability,y-permeability,angle of the local x-direction]
1 2 2 45
2 8 8 45

* nodes * [node,x,y]
1 0 0
2 0 1
3 0 2
4 1 0
5 1 1
6 1 2
7 2 0
8 2 1
9 2 2
10 3 0
11 3 1
12 3 2
13 4 0
14 4 1
15 4 2

* elements * [element,node1,node2,node3,material]
1 1 4 5 1
2 1 5 2 1
3 2 5 3 1
4 3 5 6 1
5 4 7 8 1
6 5 4 8 1
7 5 8 6 1
8 6 8 9 1
9 7 10 11 1
10 7 11 8 1
11 8 11 9 1
12 11 12 9 1
13 10 13 14 1
14 10 14 11 1
15 11 14 12 1
16 12 14 15 1

* constraints * [node,potential]
1 10
2 10
3 10
13 0
14 0
15 0

* boundary velocities * [node1,node2,normal velocity]
1 2 0
2 3 0
5 4 0

* point sources * [node,Q]
1 -50

* element sources * [element,q]
2 30

* end *

The data blocks, with the respective keyword on the top, can be defined in any order.

Alternatively, data can be given manually through the definition of the variables: tcase , control , nods , elems , mat_props , bdr_conds , b_velts , p_srcs and e_srcs . See bellow the structure of these variables.

>

Symbolic Variables

For the sake of simplicity, start reading the data of example 1

> read_save_data();

read data from a file (y/n) ? y;

file name: "dat_test1.txt";

save data into a file (y/n) ? n;

> #tcase;control;nods;elems;mat_props;bdr_conds;b_velts;p_srcs;e_srcs;

Redefine this data with symbolic variables :

> mat_props:=[[kx,ky,alpha]]:elems:=[[1,4,5,1],[1,5,2,1],[2,5,3,1],[3,5,6,1],[4,7,8,1],[5,4,8,1],[5,8,6,1],[6,8,9,1],[7,10,11,1],[7,11,8,1],[8,11,9,1],[11,12,9,1],[10,13,14,1],[10,14,11,1],[11,14,12,1],[12,14,15,1]]:

> #tcase;control;nods;elems;mat_props;bdr_conds;b_velts;p_srcs;e_srcs;

> cgt_fem(yes);