By Professor Artur Portela, Dr. Abdellatif Charafi (auth.)
ISBN-10: 3642559360
ISBN-13: 9783642559365
ISBN-10: 3642627552
ISBN-13: 9783642627552
Providing the consumer with a special perception into the finite point approach, in addition to symbolic programming that essentially alterations the best way functions will be constructed, this e-book is an important device for undergraduate or early postgraduate direction, in addition to a reference publication for engineers and scientists who are looking to enhance fast finite-element courses. using symbolic computation in Maple approach gives you new advantages within the research and realizing of The finite point method.
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Additional info for Finite Elements Using Maple: A Symbolic Programming Approach
Example text
0. , 1. 4), TITLE(CUBE),STYLE(PATCH),COLOR(ZHUE))j > CUBE 34 Introduction to Maple The package plottools is quite useful since it can generate basic graphical objects for use in plot structures PLOT and PLOT3D. In addition, they can be viewed with the command display, as show the following examples. 17 Plotter: Package for Finite Element Graphics The package Plotter was specially developed to represent graphically the results of finite element computations. The package, as well as the procedure for its installation in Maple's repository, are included in the companion CDROM.
Nods:=[[O,O], [0,5], [5,0], [5,5], [10,0], [10,5]]: 37 38 Introduction to Maple > elems:=[[1,4,2],[4,1,3],[5,4,3],[4,5,6]]: The following commands plot the mesh and number the nodes. > start_2D_plot(); > draw_title('A Simple Mesh'); > for elem in elems do > n:=elem[1 .. 3]: > x,y:=seq([seq(nods[n[i]] [j] ,i=1. 3)] ,j=1. 2): > move_pen([x[3],y[3]],0); > seq(move_pen([x[i] ,y[i]] ,1),i=1 .. 3) > end do: > new_color(O,O,l): > for node in nods do > member(node,nods,'i'): > draw_text([node[l] ,node [2]] ,convert (i ,string) , > [-1]) > end do: show_2D_plot(); > A Simple Mesh lL---------------~~--------------~ To actually see an animation, the user must click on the picture and then use the tool-bar buttons to give animation commands.
The condition number represents the degree of singularity of a matrix. The condition number of a singular matrix is infinity, while the condition number of the identity matrix is the unity. 214285714, l. Compute eigenvalues. x is an eigenvalue of the matrix A and ¢ is the associated eigenvector. > eigenvalues(B); 3 1 3 1 12, -2 + 2 V65, -2 - 2 V65 > v := 3 v:=eigenvectors(B); 3 1 [-2 + 2 V65, 1 [-2 - 2 V65, [167 1, { 1, 116 35 + 116 V65, [ 167 35 1, { 1, 116 - 116 375 39 ~ -116 - 1164}]' 375 -116 V65, > v[lJ [lJ; # The first eigenvalue 3 1 -- + - V65 2 2 v[lJ [2J; # Its multiplicity > v[1J [3]; # Its eigenvectors > ~ 39 + 1164}]' [12, 1, {[1, 1, 2]}] 1 {[1, > 3 ~~~ + 13156 V65, - ~~: - 39 116 seq([seq(v[iJ [jJ ,j=1.
Finite Elements Using Maple: A Symbolic Programming Approach by Professor Artur Portela, Dr. Abdellatif Charafi (auth.)
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