Mathematica in Teaching, Research and Development

by: Nabil Fares

last modified: January 25, 2004

Objectives

How Mathematica helps in teaching

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How Mathematica helps in research and development

short example

Say you want to explore the deformation of Bernoulli-beam

Let v be the transverse deformation of a Bernoulli-beam, then:

firstEquation  =  ( v''[x]  ==  
            bendingMoment[x]);

bendingMoment::usage  =  "this is the bending moment \
...";

?bendingMoment

Moment equilibrium of section gives:

secondEquation  =  (bendingMoment'[x]  ==  
            shearForce[x]);

Force equilibrium gives:

thirdEquation  =  (shearForce'[x]  ==  
            distributedForce[x]);

Special case boundary conditions:

leftBoundaryCondition  =  {v[0]  ==  
            0,  v'[0]  ==  0};
rightBoundaryCondition  =  {v''[1]  ==  
            0,  v'''[1]  ==  0};

Special case of uniform distributed load:

uniformLoadRule  =  {distributedForce[
              x]  ->  -1};

Solve for all unknown functions:

soln  =  DSolve[ 
            Flatten[{firstEquation,  secondEquation,  thirdEquation,  
                  leftBoundaryCondition,  rightBoundaryCondition}]  /.  
              uniformLoadRule,  {v,  bendingMoment,  shearForce},  
            x ][[1]];

Substitute results for displacements:

disp[x_]  =  Evaluate[(v  /.  soln)[x] ]

Plot the displacements:

udDispPlot  =  Plot[ disp[x],  {x,  0,  1} ]

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