elastics2.html

elastics2.mws

FINITE ELEMENTS

SYMBOLIC PROGRAMMING IN MAPLE

by Artur Portela

Elastics Example 2: Bending of a Short Cantilever

> 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.

>

Bending of a Short Cantilever

As another problem, consider the case of a square catilever plate, with 1 m of length, under the simultaneous action of the self weight and a load of 100 kN/ , uniformly distributed on the free end, perpendicular to the x direction. The analysis of this short cantilever will be carried out for 1 m of thickness. The material properties are E= 206* kN/ , and // . For the sake of simplicity, consider the discretization of the plate with 2 finite elements. Note that the distributed load is replaced by the equivalent nodal loads.