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mehdibgh

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These are questions asked by mehdibgh

expand expression have free and dummy in...

mehdibgh 235
physics
February 24 2017
0 7

Hi

How Maple knows free and dummy index?

 

How to Change variable in multiple integ...

mehdibgh 235
integral
February 11 2017
1 14

I am tryng to change variables in multiple integral as below, but receive error. Help me to do so.
 

``

> 

restart

Error, invalid input: with expects its 1st argument, pname, to be of type {`module`, package}, but received shareman

  
> 

with(IntegrationTools):
> 

V := Int(Physics:-`*`(f(Physics:-`^`(x, 2)), g(y)), [x = a .. b, y = c .. d])

Int(f(x^2)*g(y), [x = a .. b, y = c .. d])

 (1)
> 

``
> 

Change(V, {x = u-W, y = v-Q})

Error, (in IntegrationTools:-Change) missing a list with the new variables

  
> 

``


 

Download inttt.mw

What is my mistake in this simple code?...

mehdibgh 235 Maple
syntax
January 28 2017
2 6

Where I made a mistake I got this error in for loop and how to fix it?


 

> 

restart

Error, invalid input: with expects its 1st argument, pname, to be of type {`module`, package}, but received shareman

  
> 

N := 5:
> 

c__1 := Matrix([[c1__11, c1__12, 0], [c1__12, c1__22, 0], [0, 0, c1__66]]):
> 

c__2 := Matrix([[c2__11, c2__12, 0], [c2__12, c2__22, 0], [0, 0, c2__66]]):
> 

c__3 := Matrix([[c3__11, c3__12, 0], [c3__12, c3__22, 0], [0, 0, c3__66]]):
> 

c__4 := Matrix([[c4__11, c4__12, 0], [c4__12, c4__22, 0], [0, 0, c4__66]]):
> 

c__5 := Matrix([[c5__11, c5__12, 0], [c5__12, c5__22, 0], [0, 0, c5__66]]):
> 

NULL
> 

Q := Array(1 .. 3, 1 .. 3, 1 .. N):
> 

A := Matrix([[0, 0, 0], [0, 0, 0], [0, 0, 0]]):
> 

Z := Matrix([[h__1], [h__2], [h__3], [h__4], [h__5], [h__6]]):
> 

for ii to 3 do for jj to 3 do Q(ii, jj, 1) := c__1(ii, jj); Q(ii, jj, 2) := c__2(ii, jj); Q(ii, jj, 3) := c__3(ii, jj); Q(ii, jj, 4) := c__4(ii, jj); Q(ii, jj, 5) := c__5(ii, jj) end do end do
> 

"for i from 1 to 3 do for j from 1 to 3 do Ar:=0:for k from 1 to N do Ar:=(Q (i,j,k)*(Z(k+1)-Z(k)))+Ar: end do A(i,j):=Ar: end do end do"

Error, invalid loop statement termination

"for i from 1 to 3 do for j from 1 to 3 do Ar:=0:for k from 1 to N do Ar:=(Q (i,j,k)*(Z(k+1)-Z(k)))+Ar: end do A(i,j):=Ar: end do end do"

  
> 

``

``


 

Download quest.mw

How to simplify more ?...

mehdibgh 235
simplify
January 22 2017
0 0

I have expression h1 as below:

 

 

 

Error, invalid input: with expects its 1st argument, pname, to be of type {`module`, package}, but received shareman

  
> 

restart

Error, invalid input: with expects its 1st argument, pname, to be of type {`module`, package}, but received shareman

  
> 

"`u__1`(`xi__1`,`xi__2`,Zeta,t):=`u__0`(`xi__1`,`xi__2`,Zeta,t)+Zeta*`phi__1`(`xi__1`,`xi__2`,t):"
> 

"`u__2`(`xi__1`,`xi__2`,Zeta,t):=`v__0`(`xi__1`,`xi__2`,Zeta,t)+Zeta*`phi__2`(`xi__1`,`xi__2`,t):"
> 

"`u__3`(`xi__1`,`xi__2`,Zeta,t):=`w__0`(`xi__1`,`xi__2`,Zeta,t):"
> 

`φ__n` := (diff(v__0(`ξ__1`, `ξ__2`, Zeta, t)*a__2(`ξ__1`, `ξ__2`, Zeta, t), `ξ__1`)-(diff(u__0(`ξ__1`, `ξ__2`, Zeta, t)*a__1(`ξ__1`, `ξ__2`, Zeta, t), `ξ__2`)))/(2*a__1(`ξ__1`, `ξ__2`, Zeta, t)*a__2(`ξ__1`, `ξ__2`, Zeta, t))
> 

`ϵ0__1` := (diff(u__0(`ξ__1`, `ξ__2`, Zeta, t), `ξ__1`)+v__0(`ξ__1`, `ξ__2`, Zeta, t)*(diff(a__1(`ξ__1`, `ξ__2`, Zeta, t), `ξ__2`))/a__2(`ξ__1`, `ξ__2`, Zeta, t)+a__1(`ξ__1`, `ξ__2`, Zeta, t)*w__0(`ξ__1`, `ξ__2`, Zeta, t)/R__1)/a__1(`ξ__1`, `ξ__2`, Zeta, t)
> 

`ϵ0__2` := (diff(v__0(`ξ__1`, `ξ__2`, Zeta, t), `ξ__2`)+u__0(`ξ__1`, `ξ__2`, Zeta, t)*(diff(a__2(`ξ__1`, `ξ__2`, Zeta, t), `ξ__1`))/a__1(`ξ__1`, `ξ__2`, Zeta, t)+a__2(`ξ__1`, `ξ__2`, Zeta, t)*w__0(`ξ__1`, `ξ__2`, Zeta, t)/R__2)/a__2(`ξ__1`, `ξ__2`, Zeta, t)
> 

`ϵ0__4` := (diff(w__0(`ξ__1`, `ξ__2`, Zeta, t), `ξ__2`)+a__2(`ξ__1`, `ξ__2`, Zeta, t)*`φ__2`(`ξ__1`, `ξ__2`, t)-a__2(`ξ__1`, `ξ__2`, Zeta, t)*v__0(`ξ__1`, `ξ__2`, Zeta, t)/R__2)/a__2(`ξ__1`, `ξ__2`, Zeta, t)
> 

`ϵ0__5` := (diff(w__0(`ξ__1`, `ξ__2`, Zeta, t), `ξ__1`)+a__1(`ξ__1`, `ξ__2`, Zeta, t)*`φ__1`(`ξ__1`, `ξ__2`, t)-a__1(`ξ__1`, `ξ__2`, Zeta, t)*u__0(`ξ__1`, `ξ__2`, Zeta, t)/R__1)/a__1(`ξ__1`, `ξ__2`, Zeta, t)
> 

`ω0__1` := (diff(v__0(`ξ__1`, `ξ__2`, Zeta, t), `ξ__1`)-u__0(`ξ__1`, `ξ__2`, Zeta, t)*(diff(a__1(`ξ__1`, `ξ__2`, Zeta, t), `ξ__2`))/a__2(`ξ__1`, `ξ__2`, Zeta, t))/a__1(`ξ__1`, `ξ__2`, Zeta, t)-`φ__n`
> 

`ω0__2` := (diff(u__0(`ξ__1`, `ξ__2`, Zeta, t), `ξ__2`)-v__0(`ξ__1`, `ξ__2`, Zeta, t)*(diff(a__2(`ξ__1`, `ξ__2`, Zeta, t), `ξ__1`))/a__1(`ξ__1`, `ξ__2`, Zeta, t))/a__2(`ξ__1`, `ξ__2`, Zeta, t)+`φ__n`
> 

`ϵ1__1` := (diff(`φ__1`(`ξ__1`, `ξ__2`, t), `ξ__1`)+`φ__2`(`ξ__1`, `ξ__2`, t)*(diff(a__1(`ξ__1`, `ξ__2`, Zeta, t), `ξ__2`))/a__2(`ξ__1`, `ξ__2`, Zeta, t))/a__1(`ξ__1`, `ξ__2`, Zeta, t)
> 

`ϵ1__2` := (diff(`φ__2`(`ξ__1`, `ξ__2`, t), `ξ__2`)+`φ__1`(`ξ__1`, `ξ__2`, t)*(diff(a__2(`ξ__1`, `ξ__2`, Zeta, t), `ξ__1`))/a__1(`ξ__1`, `ξ__2`, Zeta, t))/a__2(`ξ__1`, `ξ__2`, Zeta, t)
> 

`ω1__1` := (diff(`φ__2`(`ξ__1`, `ξ__2`, t), `ξ__1`)+`φ__1`(`ξ__1`, `ξ__2`, t)*(diff(a__1(`ξ__1`, `ξ__2`, Zeta, t), `ξ__2`))/a__2(`ξ__1`, `ξ__2`, Zeta, t))/a__1(`ξ__1`, `ξ__2`, Zeta, t)-`φ__n`/R
> 

`ω1__2` := (diff(`φ__1`(`ξ__1`, `ξ__2`, t), `ξ__2`)+`φ__2`(`ξ__1`, `ξ__2`, t)*(diff(a__2(`ξ__1`, `ξ__2`, Zeta, t), `ξ__1`))/a__1(`ξ__1`, `ξ__2`, Zeta, t))/a__2(`ξ__1`, `ξ__2`, Zeta, t)+`φ__n`/R
> 

`ϵ__1` := (Zeta*`ϵ1__1`+`ϵ0__1`)/(1+Zeta/R__1)
> 

`ϵ__2` := (Zeta*`ϵ1__2`+`ϵ0__2`)/(1+Zeta/R__2)
> 

`ϵ__4` := `ϵ0__4`/(1+Zeta/R__2)
> 

`ϵ__5` := `ϵ0__5`/(1+Zeta/R__1)
> 

`ϵ__6` := (Zeta*`ω1__1`+`ω0__1`)/(1+Zeta/R__1)+(Zeta*`ω1__2`+`ω0__2`)/(1+Zeta/R__2)
> 

epsilon := Matrix([[`ϵ__1`], [`ϵ__2`], [`ϵ__4`], [`ϵ__5`], [`ϵ__6`]])
> 

with(LinearAlgebra)
> 

e__1 := Matrix([[0, 0, 0, e1__15, 0], [0, 0, e1__24, 0, 0], [e1__31, e1__31, 0, 0, 0]])
> 

e__5 := Matrix([[0, 0, 0, e5__15, 0], [0, 0, e5__24, 0, 0], [e5__31, e5__31, 0, 0, 0]])
> 

E__1 := -Matrix([[diff(`ϕ1`(`ξ__1`, `ξ__2`, Zeta), `ξ__1`)], [diff(`ϕ1`(`ξ__1`, `ξ__2`, Zeta), `ξ__2`)], [diff(`ϕ1`(`ξ__1`, `ξ__2`, Zeta), Zeta)]])
> 

E__5 := -Matrix([[diff(`ϕ5`(`ξ__1`, `ξ__2`, Zeta), `ξ__1`)], [diff(`ϕ5`(`ξ__1`, `ξ__2`, Zeta), `ξ__2`)], [diff(`ϕ5`(`ξ__1`, `ξ__2`, Zeta), Zeta)]])
> 

`ε__1` := Matrix([[`ε1__11`, 0, 0], [0, `ε1__22`, 0], [0, 0, `ε1__33`]])
> 

`ε` := Matrix([[`ε5__11`, 0, 0], [0, `ε5__22`, 0], [0, 0, `ε5__33`]])
> 

f := Matrix([[f1, f2, f3]])
> 

D__1 := Multiply(e__1, epsilon)+Multiply(`ε__1`, E__1)
> 

D__5 := Multiply(e__5, epsilon)+Multiply(`ε__5`, E__5)
> 

h1 := simplify((Multiply(Transpose(E__1), D__1))(1))

(-R__1*(diff(varphi1(xi__1, xi__2, Zeta), Zeta))*e1__31*(R__2+Zeta)*(phi__2(xi__1, xi__2, t)*Zeta+v__0(xi__1, xi__2, Zeta, t))*(diff(a__1(xi__1, xi__2, Zeta, t), xi__2))-(diff(varphi1(xi__1, xi__2, Zeta), Zeta))*R__2*e1__31*(R__1+Zeta)*(phi__1(xi__1, xi__2, t)*Zeta+u__0(xi__1, xi__2, Zeta, t))*(diff(a__2(xi__1, xi__2, Zeta, t), xi__1))-a__2(xi__1, xi__2, Zeta, t)*R__1*(diff(varphi1(xi__1, xi__2, Zeta), Zeta))*e1__31*(R__2+Zeta)*(diff(u__0(xi__1, xi__2, Zeta, t), xi__1))-a__1(xi__1, xi__2, Zeta, t)*(diff(varphi1(xi__1, xi__2, Zeta), Zeta))*R__2*e1__31*(R__1+Zeta)*(diff(v__0(xi__1, xi__2, Zeta, t), xi__2))-a__2(xi__1, xi__2, Zeta, t)*R__1*(diff(varphi1(xi__1, xi__2, Zeta), xi__1))*e1__15*(R__2+Zeta)*(diff(w__0(xi__1, xi__2, Zeta, t), xi__1))-a__1(xi__1, xi__2, Zeta, t)*R__2*(diff(varphi1(xi__1, xi__2, Zeta), xi__2))*e1__24*(R__1+Zeta)*(diff(w__0(xi__1, xi__2, Zeta, t), xi__2))+`ε1__33`*a__1(xi__1, xi__2, Zeta, t)*a__2(xi__1, xi__2, Zeta, t)*(R__2+Zeta)*(R__1+Zeta)*(diff(varphi1(xi__1, xi__2, Zeta), Zeta))^2-e1__31*(a__2(xi__1, xi__2, Zeta, t)*R__1*Zeta*(R__2+Zeta)*(diff(phi__1(xi__1, xi__2, t), xi__1))+a__1(xi__1, xi__2, Zeta, t)*(R__2*Zeta*(R__1+Zeta)*(diff(phi__2(xi__1, xi__2, t), xi__2))+a__2(xi__1, xi__2, Zeta, t)*w__0(xi__1, xi__2, Zeta, t)*(R__1+R__2+2*Zeta)))*(diff(varphi1(xi__1, xi__2, Zeta), Zeta))+a__2(xi__1, xi__2, Zeta, t)*(`ε1__11`*(R__2+Zeta)*(R__1+Zeta)*(diff(varphi1(xi__1, xi__2, Zeta), xi__1))^2-e1__15*(R__2+Zeta)*(phi__1(xi__1, xi__2, t)*R__1-u__0(xi__1, xi__2, Zeta, t))*(diff(varphi1(xi__1, xi__2, Zeta), xi__1))+(R__1+Zeta)*(`ε1__22`*(R__2+Zeta)*(diff(varphi1(xi__1, xi__2, Zeta), xi__2))-e1__24*(phi__2(xi__1, xi__2, t)*R__2-v__0(xi__1, xi__2, Zeta, t)))*(diff(varphi1(xi__1, xi__2, Zeta), xi__2)))*a__1(xi__1, xi__2, Zeta, t))/(a__1(xi__1, xi__2, Zeta, t)*a__2(xi__1, xi__2, Zeta, t)*(R__1+Zeta)*(R__2+Zeta))

 (1)
> 

NULL

``

 

 

Download simplifymore.mw

 

 

How can i simplify h1 more in Maple?

How to use Maple to take a variation of ...

mehdibgh 235 Maple 2016
January 13 2017
1 15

Hi All,

To get EOM of a specific type of vibrating shell structure, I constructed the Hamilton equation of the system with messy and complex integrand (so many derivatives and variables are included). Now I have to calculate the variation of the Hamilton equation (del(int((T+U-V),t=t0..t1)=0) to get the EOMs and BCs of the system.

Is there anybody to know how to take a variation of such bulky integral in Maple?

Is there anyone to have experience in finding the EOM of shell structure using variational calculus in Maple?

Any comment will be useful.

Regards,

 

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