Defining matrix variable to get numerical solution to the Winkler foundation differential equation

[gmprox23]

Following the solution to the differential equation for the deflection curve of a beam on an elastic foundation, am trying to get the bending moment M and shearing force V based on the 2nd- and 3rd-order derivatives.

I can come up with values based on the derivative expression BUT am unable to assign the results to matrix variables M and V for plotting the results to show variation along the length of the beam.

I tried to define matrices with matching size, BUT it won't evaluate the differential equation.

Should I use "for loop" instead? Or am I missing something? Can't seem to figure it out.

Thank you for the help.

 

[GregLocock]

First of all, yes that looks as though it should work, but since it doesn't I'd guess the vectorising operator is confusing things, I don't think Mathcad does Matlab styl structures. If you use an range index for lambda (and possibly M) it might work.

Cheers

Greg Locock


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[gmprox23]

Hi Greg,

I tried to implement a 'for loop' and defined the range index for the v (=distance x) and bending moment M, BUT it still won't assign the values to the matrix variable M (pls see below).

Not sure why the matrix variable M = zero, unlike the results of the 2nd order derivatire of the differential equation.

 

[GregLocock]

Sorry, beyond my pay grade, I'll leave it to someone with a current version of mathcad to comment. It still looks to me as though you are trying to assign multiple values to each row of M.

Cheers

Greg Locock


New here? Try reading these, they might help FAQ731-376

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[Stress_Eng]

I’ve done a few beam on elastic foundation problems in the past. I’ve found the use of displacement, gradient, moment and shear equations (differentials of the displacement equation) as functions of an independent variable x along the beam, incorporating the unknown constants in each of the equations, a good way to solve the problem. I use a solve block (Given and Find) with usually defined gradient, moment and / or shear equations set to known boundary conditions at defined values of x, to solve for the unknown constants of the general solution equation.