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Question: HELP !! Maple doesn t want to give me the integral expression

Question:HELP !! Maple doesn t want to give me the integral expression

mathiaszip 15 Maple
integration 2dmath
December 01 2017
2


Hi

I have to create a function "I(epsilonc)" by integrating a function "sigma(y)"  from 0 to the variable "epsilonc"

but maple doesn t give me the actual formula of the integrated function, it only gives me equation 4 which is utterly useless to me.

 

How do I get Maple to actually calculate and give me the integrated function ??

Any help will be greatly appreciated

> 

restart


#data

> 

`ϵc1` := 2.1*10^(-3);

0.2100000000e-2

 (1)
> 

`ϵcu1` := 3.5*10^(-3):
> 

Ecm := 31000:
> 

fcm := 25:
> 

Fy := 500:
> 

Es := 200000:

#geometry

> 

As := 1885:
> 

b = 250:
> 

d := 450:


#coefficients

> 

eta := epsilon/`ϵc1`:
> 

k := 1.05*Ecm*`ϵc1`/fcm:
> 

``


#formula

 

> 

``
> 

`σc` := proc (epsilon) options operator, arrow; fcm*(k*epsilon/`ϵc1`-epsilon^2/`ϵc1`^2)/(1+(k-2)*epsilon/`ϵc1`) end proc;

proc (epsilon) options operator, arrow; fcm*(k*epsilon/`ϵc1`-epsilon^2/`ϵc1`^2)/(1+(k-2)*epsilon/`ϵc1`) end proc

 (2)
> 

plot(`σc`, 0 .. `ϵcu1`);

 
> 

``

#Pressure as a function of y (y=`ϵc`*y/x) :

> 

`σc` := proc (y) options operator, arrow; fcm*(k*`ϵc`*y/(x*`ϵc1`)-`ϵc`^2*y^2/(x^2*`ϵc1`^2))/(1+(k-2)*`ϵc`*y/(x*`ϵc1`)) end proc;

proc (y) options operator, arrow; fcm*(k*`ϵc`*y/(x*`ϵc1`)-`ϵc`^2*y^2/(x^2*`ϵc1`^2))/(1+(k-2)*`ϵc`*y/(x*`ϵc1`)) end proc

 (3)
> 

Iy := proc (y) options operator, arrow; int(fcm*(k*`ϵc`*y/(x*`ϵc1`)-`ϵc`^2*y^2/(x^2*`ϵc1`^2))/(1+(k-2)*`ϵc`*y/(x*`ϵc1`)), y = 0 .. `ϵc`/(`ϵc`+Fy/Es)) end proc;

proc (y) options operator, arrow; int(fcm*(k*`ϵc`*y/(x*`ϵc1`)-`ϵc`^2*y^2/(x^2*`ϵc1`^2))/(1+(k-2)*`ϵc`*y/(x*`ϵc1`)), y = 0 .. `ϵc`/(`ϵc`+Fy/Es)) end proc

 (4)
> 

Iy(`ϵc`/(`ϵc`+Fy/Es))

Error, (in int) integration range or variable must be specified in the second argument, got `ϵc`/(`ϵc`+1/400) = 0 .. `ϵc`/(`ϵc`+1/400)

  
> 

solve(Iyy*b = Fy*As, `ϵc`);
> 

``

``


 

Download HW1_-_EC2_strain-pressure_graph.mw
 

> 

restart


#data

> 

`ϵc1` := 2.1*10^(-3);

0.2100000000e-2

 (1)
> 

`ϵcu1` := 3.5*10^(-3):
> 

Ecm := 31000:
> 

fcm := 25:
> 

Fy := 500:
> 

Es := 200000:

#geometry

> 

As := 1885:
> 

b = 250:
> 

d := 450:


#coefficients

> 

eta := epsilon/`ϵc1`:
> 

k := 1.05*Ecm*`ϵc1`/fcm:
> 

``


#formula

 

> 

``
> 

`σc` := proc (epsilon) options operator, arrow; fcm*(k*epsilon/`ϵc1`-epsilon^2/`ϵc1`^2)/(1+(k-2)*epsilon/`ϵc1`) end proc;

proc (epsilon) options operator, arrow; fcm*(k*epsilon/`ϵc1`-epsilon^2/`ϵc1`^2)/(1+(k-2)*epsilon/`ϵc1`) end proc

 (2)
> 

plot(`σc`, 0 .. `ϵcu1`);

 
> 

``

#Pressure as a function of y (y=`ϵc`*y/x) :

> 

`σc` := proc (y) options operator, arrow; fcm*(k*`ϵc`*y/(x*`ϵc1`)-`ϵc`^2*y^2/(x^2*`ϵc1`^2))/(1+(k-2)*`ϵc`*y/(x*`ϵc1`)) end proc;

proc (y) options operator, arrow; fcm*(k*`ϵc`*y/(x*`ϵc1`)-`ϵc`^2*y^2/(x^2*`ϵc1`^2))/(1+(k-2)*`ϵc`*y/(x*`ϵc1`)) end proc

 (3)
> 

Iy := proc (y) options operator, arrow; int(fcm*(k*`ϵc`*y/(x*`ϵc1`)-`ϵc`^2*y^2/(x^2*`ϵc1`^2))/(1+(k-2)*`ϵc`*y/(x*`ϵc1`)), y = 0 .. `ϵc`/(`ϵc`+Fy/Es)) end proc;

proc (y) options operator, arrow; int(fcm*(k*`ϵc`*y/(x*`ϵc1`)-`ϵc`^2*y^2/(x^2*`ϵc1`^2))/(1+(k-2)*`ϵc`*y/(x*`ϵc1`)), y = 0 .. `ϵc`/(`ϵc`+Fy/Es)) end proc

 (4)
> 

Iy(`ϵc`/(`ϵc`+Fy/Es))

Error, (in int) integration range or variable must be specified in the second argument, got `ϵc`/(`ϵc`+1/400) = 0 .. `ϵc`/(`ϵc`+1/400)

  
> 

solve(Iyy*b = Fy*As, `ϵc`);
> 

``

``


 

Download HW1_-_EC2_strain-pressure_graph.mw

 
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