C_R

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MaplePrimes Activity


These are replies submitted by C_R

@Maxie 

I have fixed your model in the sense that its simulating.

At a frist glance the rails and the sleepers are not assembled as you intended.

Furthermore, the axle falls off the rails.

You cannot use a single contact element (rectangle) for the entire flexible beam to realistically describe a traveling load. As you have done it the rail already deforms when the load is above the sleeper.

Overall the problem you have choosen is at the limit of the components of MapleSim libraray. I think a solution is possible with custom components.

If you are entitled consider also contacting Maplesoft support for advice.

4_fix.msim

@acer You are correct. A thetrahedron has 4 surfaces. 5 was from my first answer which I had to correct.

z<=1 and y<=z eliminate y<=1 (which I will do now in my update above).

In this question you will find an elegant way from the user Kitonum to plot the bounding surface of a cube which is

plots:-implicitplot3d(max(-x,x-1,-y,y-1,-z,z-1), x=-0.5..1.5, y=-0.5..1.5, z=-0.5..1.5, style=surface, axes=normal, grid=[100,100,100]);

The three inequalities (i.e. all points within the bounding surface and including the bounding surface) describing the cube as solid are

0<=x <= 1
0<=y <= 1
0<=z <= 1

This that what you are looking for?

@Maxie 

Without model its difficult to tell why forces are constant. If this is related to a question that I have seen but  has disappeared, consider adding it to this thread.

Here are two models which might help you with your problem.

The first is a (rigid) beam under a moving load. The second is not available for immediate download and you have to contact Maplesoft but its worth a try.

And: A rail with multiple (>2) sleepers must be overdetermined. What exactly do you mean with "the rail is supported by multiple sleepers without over-constraint".

@mmcdara 
Your idea is worth discussing. I have seen that it (screen shot instead of code) just happend again.

Perhaps a post would be better to gather more ideas.

You have to be more specific what you want to analyse.

If it is a mechanical problem you want to analyse:

The load case (e.g. bending) and the geometry would be helpfull.

Do you have drawings or a sketch?

It would be nice if convert/unit would offer

  1. symbols as yours for degrees minutes and seconds
  2. a compound output as yours

Here is what is possible with 2023

45.2365*Unit('arcdeg')

45.2365*Units:-Unit(arcdeg)

(1)

trunc(45.2365*Units:-Unit(arcdeg))

45*Units:-Unit(arcdeg)

(2)

frac(45.2365*Units:-Unit(arcdeg))

.2365*Units:-Unit(arcdeg)

(3)

convert(.2365*Units:-Unit(arcdeg), units, arcmin)

14.1900*Units:-Unit(arcmin)

(4)

trunc(14.1900*Units:-Unit(arcmin))

14*Units:-Unit(arcmin)

(5)

frac(14.1900*Units:-Unit(arcmin))

.1900*Units:-Unit(arcmin)

(6)

convert(.1900*Units:-Unit(arcmin), units, arcsec)

11.4000*Units:-Unit(arcsec)

(7)

45*Units:-Unit(arcdeg)+14*Units:-Unit(arcmin)+11.4000*Units:-Unit(arcsec)

45*Units:-Unit(arcdeg)+14*Units:-Unit(arcmin)+11.4000*Units:-Unit(arcsec)

(8)

NULL

(which represents a silent improvement over 2022 where trunc an floor did not work on expressions with units.

Thank you Maplesoft and please continue)

Download degminsec.mw

What version do you use?

restart; with(LinearAlgebra)

A[m] := (x/a)^(i+1)*(1-x/a)^2; B[n] := (y/b)^(i+1)*(1-y/b)^2; w := c[i]*A[m]*B[n]

TPE := (1/2)*(int(int(D__11*(diff(w, x, x))^2+2*D__12*(diff(w, x, x))*(diff(w, y, y))+4*D__66*(diff(w, x, y))^2+D__22*(diff(w, y, y))^2-2*q__0*w, x = 0 .. a), y = 0 .. b))

2*c[i]*(-512*a^4*b^4*i^8*q__0-6144*a^4*b^4*i^7*q__0-29184*a^4*b^4*i^6*q__0+36*D__11*b^4*i^8*c[i]+8*D__12*a^2*b^2*i^8*c[i]+36*D__22*a^4*i^8*c[i]+16*D__66*a^2*b^2*i^8*c[i]-69120*a^4*b^4*i^5*q__0+612*D__11*b^4*i^7*c[i]+168*D__12*a^2*b^2*i^7*c[i]+612*D__22*a^4*i^7*c[i]+336*D__66*a^2*b^2*i^7*c[i]-82368*a^4*b^4*i^4*q__0+4257*D__11*b^4*i^6*c[i]+1482*D__12*a^2*b^2*i^6*c[i]+4257*D__22*a^4*i^6*c[i]+2964*D__66*a^2*b^2*i^6*c[i]-38016*a^4*b^4*i^3*q__0+15570*D__11*b^4*i^5*c[i]+7068*D__12*a^2*b^2*i^5*c[i]+15570*D__22*a^4*i^5*c[i]+14136*D__66*a^2*b^2*i^5*c[i]+9824*a^4*b^4*i^2*q__0+31959*D__11*b^4*i^4*c[i]+19386*D__12*a^2*b^2*i^4*c[i]+31959*D__22*a^4*i^4*c[i]+38772*D__66*a^2*b^2*i^4*c[i]+13920*a^4*b^4*i*q__0+36198*D__11*b^4*i^3*c[i]+29352*D__12*a^2*b^2*i^3*c[i]+36198*D__22*a^4*i^3*c[i]+58704*D__66*a^2*b^2*i^3*c[i]+3150*a^4*b^4*q__0+20448*D__11*b^4*i^2*c[i]+19048*D__12*a^2*b^2*i^2*c[i]+20448*D__22*a^4*i^2*c[i]+38096*D__66*a^2*b^2*i^2*c[i]+4320*D__11*b^4*i*c[i]-3648*D__12*a^2*b^2*i*c[i]+4320*D__22*a^4*i*c[i]-7296*D__66*a^2*b^2*i*c[i]-8064*D__12*a^2*b^2*c[i]-16128*D__66*a^2*b^2*c[i])/(a^3*(2*i+7)*(2*i-1)*(i+4)^2*(i+3)^2*(2*i+5)^2*(i+2)^2*(2*i+3)^2*(2*i+1)^2*b^3)

(1)

NULL

Download total_PE.mw

@Kitonum 
I have been too hasty. x >= 0 leaves of course two choices for T2. 👍

@Kitonum 

Math put that way in only 2 lines is really nice.
S<=0 seems to be a quite broad definition for solids with a closed surface S=0 as a boundary. 

However, extending your method of defining an intersection with inequalities and max to polyhedrons does not work straight away. I tried to plot a cube and an infinite slice with planes without immediate success. At least with one plane it can be used to chop of the head of an egg.

z^2/9 + (x^2 + y^2)/(4*(1 - z/5)) - 1;
plots:-implicitplot3d(max(%, z - 2), x = -3 .. 3, y = -3 .. 3, z = -3 .. 4, style = surface, color = red, grid = [100, 100, 100]);

Thanks again.

@acer 
Thanks for the clarification

@acer 

Vertical adjustments become tricky. 

If I understand correctly, the question about linking such a user defined symbol to a name should be asked separately.
I am never quite sure when to branch off.

Thank you.

@acer 
HTML is not exactly straightforward either. Is it possible to nudge the Y up a bit?

Can this typesetting output now be liked to a name or user defined operator?

@mmcdara 

Maybe with plottools,extrude its easier to plot a solid.

@mmcdara 

, as you said, is as difficult

restart;
with(plots);
ce := (p, q, r, a, b) -> ((x - p)^2 + (y - q)^2 + (z - r)^2 + a^2 - b^2)^2 - 4*a^2*((x - p)^2 + (y - q)^2);
T1 := ce(1, 1, 1, 2, 1);
T2 := ce(1, 6, 1, 2, 1);
implicitplot3d(min(T1, T2), x = -4 .. 4, y = -2 .. 9.5, z = -1 .. 1, style = surface, color = "Red", grid = [100, 100, 100], scaling = constrained, axes = normal, orientation = [15, 80]);

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