FINITE ELEMENTS

SYMBOLIC PROGRAMMING IN MAPLE

Artur Portela

Elastics Example 3: Symbolic Variables

> restart:

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

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

> with(Plotter):

> with(Cst_fem): with(G_cst_fem):

Data Preparation

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

*elements* [element, node1, node2, node3, material]
1 1 2 4 1
2 4 3 1 1

*nodes* [node, x, y]
1 1 1
2 0 1
3 1 0
4 0 0

*materials* [material, Young modulus, Poisson coef, specific weight, thickness]
1 210000000000. .28 -77000. 0.01

*forces* [node, fx, fy]
1 0 10
2 0 10

*constraints* [node, direction(x, y or angle measured from x), displacement]
4 x 0
4 y 0
3 90 0
2 0 0

*control* [title, plane stress/strain, point forces, self weight]
title Plate Under Uniaxial Traction
plane stress
point forces

*end*

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

Alternatively, data can be given manually through the definition of the variables: title , plane_case , control , nods , mat_props , elems , forces and bdr_conds . See bellow the structure of these variables.

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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_test4.txt";

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

> tcase;plane_case;control;nods;mat_props;elems;forces;bdr_conds;

Redefine this data with symbolic variables :

> nods:=[[l,l],[0,l],[l,0],[0,0]]:mat_props:=[[E,nu,b,1]]:forces:=[[1,0,P],[2,0,P]]:

> tcase;plane_case;control;nods;mat_props;elems;forces;bdr_conds;

> cst_fem(yes);

Print displacements :

> disp;

Print element stresses :

> e_sigma;

Print nodal stresses :

> n_sigma;

Print reactions :

> reacts;

Print total strain energy:

> total_strain_energy;

In order to display graphics, it is necessary to substitute symbolic variables by numeric values.

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