By Professor Artur Portela, Dr. Abdellatif Charafi (auth.)
Providing the person with a different perception into the finite point process, in addition to symbolic programming that essentially adjustments the best way purposes should be built, this e-book is a necessary instrument for undergraduate or early postgraduate direction, in addition to a reference e-book for engineers and scientists who are looking to enhance fast finite-element courses. using symbolic computation in Maple method gives you new advantages within the research and realizing of The finite aspect method.
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Extra info for Finite Elements Using Maple: A Symbolic Programming Approach
Example text
2, the discretization process leads to the replacement of the initial problem, the solution of a system of differential equations, by another problem which is solving an algebraic system of equations that will be carried out on a computer. CONTINUOUS MODEL • oInfinite number of degrees of freedom defined at each point of the domain t oContinuous conditions of Equilibrlnm and Compatibility t oSystem of differential equations + oAnalytical Methods t -Exact solution - - - ~ 'JJ. 2. 3 Continuous Models Under the point of view of continuum mechanics, physical systems can be classified through their respective continuous model, in accordance with the type of differential equation used to describe the model.
3]; x,y:=seq([seq(nods[n[i]] [j],i=l .. 3)] ,j=l .. 2); xg,yg:=add(x[i] ,i=1 .. 3)/3,add(y[i] ,i=1 .. 7*(x[i]-xg)+xg,i=1 .. 7*(y[i]-yg)+yg,i=1 .. 3)]; move_pen([x[3],y[3]],0); seq(move_pen([x[i] ,y[i]] ,1),i=1 .. 2 Example A finite element mesh can be plotted as an animation that shows the mesh deforming between two different sets of nodal values. The following commands, grouped in a procedure, plot a deforming triangular finite element mesh. 0*i/frms; > if j>l then j:=2-j end if; > deform_mesh([seq(uvals[k]*j,k=l ..
621670087799999993 + O. 256747130200000006 + O. 531875560599999964 + O. egvec[1 .. egvec[1 .. 16 Graphics Maple graphics fall into two major categories which are, respectively, twodimensional and three-dimensional graphics. Animation is among the facilities available in each category. The packages plots and plot3d are used frequently enough. 00000000), THICKNESS(3), AXESLABELS("", ""), VIEW(DEFAULT, DEFAULT)) > plt1; 5 4 3 2 o -1 -2 32 Introduction to Maple > > plt2:=plot(x-2,x=0 .. 4,color=gold,thickness=3): plots [display] ({pltl,plt2}); 16 14 12 10 8 6 4 2 o -2 3 4 Procedures plot and plot3d produce, respectively PLOT and PLOT3D data structures describing the images to be displayed.