Ramakrishnan

Dr. Ramakrishnan Vaidyanathan

259 Reputation

5 Badges

4 years, 360 days

Social Networks and Content at Maplesoft.com

I have retired as Professor-Mechanical in Sri Venkateswara College of Engineering and Technology under Anna University affiliated colleges in Tamil Nadu, India. I have 19 years of Industrial and 20 years of teaching experience. I am learning Maple for the past four and half years hoping to make at least one appreciable maple presentation.

MaplePrimes Activity


These are questions asked by Ramakrishnan

I do not know! I am a novice in maple as well as in graph theory. I attach a doc in which i attempted to learn what is network. It seems alright with maple as it gives as what it understands as horizontal and vertical network. I do not expect a horizontal line as horizontal network and vertical line as vertical network, in which case a horizontal line with nodes 1 and 2 will be vertical network if  draw it vertically. The maple, in my opinion ( i am not a maple man) gives the answer in a vertical pattern, rightly so for clarity and space constraint.

I am sorry if i am confusing.  The document in my attempt to know more may give you also more insight. Thanks.

with(GraphTheory):

with(RandomGraphs):

N := GraphTheory:-RandomGraphs:-RandomNetwork(4, 0):

IsNetwork(N):

DrawNetwork(N, vertical)

 

with(GraphTheory):

with(RandomGraphs):

O1 := GraphTheory:-RandomGraphs:-RandomNetwork(4, 1):

GraphTheory:-IsNetwork(O1):

GraphTheory:-DrawNetwork(O1, vertical)

 

``

with(GraphTheory):

with(RandomGraphs):

P := GraphTheory:-RandomGraphs:-RandomNetwork(4, 0):

GraphTheory:-IsNetwork(P):

GraphTheory:-DrawNetwork(P, horizontal)

 

with(GraphTheory):

with(RandomGraphs):

Q := GraphTheory:-RandomGraphs:-RandomNetwork(4, 1):

GraphTheory:-IsNetwork(Q):

GraphTheory:-DrawNetwork(Q, horizontal)

 

``

 

Download MyAttempt.mwMyAttempt.mw

 

Consider a taper steel plate of uniform thickness t := 25mm as shown in the Fig. In addition to its self weight, the plate is subjected to a point load P := 100N at its mid point. Find the global force vector [F] , global stiffness matrix [K] , displacement in each element (1 and 2) , stresses in each element  (1 and 2) and reaction force at the support.Take E := 2*10^5N/mm2; rho := 8.2*10^(-5)kg/m3;

restart

t__1 := 150:

t__3 := 75:

w := 25:

l := 600:

t__2 := (t__1-t__3)/l*((1/2)*l)+t__3 = 225/2

A__1 := t__1*w = 3750``

A__2 := t__2*w = 5625/2``

A__3 := t__3*w = 1875``

Revised areas:

A__1e := (A__1+A__2)*(1/2) = 13125/4``

A__2e := (A__2+A__3)*(1/2) = 9375/4``

  E := 2*10^11:m2; F__1 := R__1:is support reaction N; F__2 := 100:N;``

rho__1 := 82*10^(-6) = 41/500000  N/mm2

rho__2 := 82*10^(-6) = 41/500000 N/mm2

l := 600:``

Number of elements,

n__e := 2:

l__e := 300 = 300````

q__0 := 100:N/m ; l := 1: m; n__e := 4:  elementsl  l__e := l/n__e: m;

We shall consider a two element system as shown in the Fig.
For element 1 Stiffness matrix K is

                                           Vector[row](2, {(1) = 1, (2) = 2})
K__1 := A__1e*E/l__e.(Matrix(2, 2, {(1, 1) = 1, (1, 2) = -1, (2, 1) = -1, (2, 2) = 1})) = Matrix([[2625000000000000, -2625000000000000], [-2625000000000000, 2625000000000000]])  Vector(2, {(1) = 1, (2) = 2})

For element 2 Stiffness matrix K is

                                         Vector[row](2, {(1) = 2, (2) = 3})
K__2 := A__2e*E/l__e.(Matrix(2, 2, {(1, 1) = 1, (1, 2) = -1, (2, 1) = -1, (2, 2) = 1})) = Matrix([[1875000000000000, -1875000000000000], [-1875000000000000, 1875000000000000]])  Vector(2, {(1) = 2, (2) = 3})

Global stiffness matrix obtained by adding all the elemental stiffness matrices and given b

           Vector[row](3, {(1) = 0, (2) = 0, (3) = 0})

K__g := Matrix(3, 3, {(1, 1) = K__1[1, 1], (1, 2) = K__1[1, 2], (1, 3) = 0, (2, 1) = K__1[2, 1], (2, 2) = K__1[1, 2]+K__2[1, 1], (2, 3) = K__2[1, 2], (3, 1) = 0, (3, 2) = K__2[2, 1], (3, 3) = K__2[2, 2]}) = Matrix([[K__1[1, 1], K__1[1, 2], 0], [K__1[2, 1], K__1[1, 2]+K__2[1, 1], K__2[1, 2]], [0, K__2[2, 1], K__2[2, 2]]])  Vector(3, {(1) = 0, (2) = 0, (3) = 0})

For element 1 Load matrix F is

  F__1e := (1/2)*`ρ__1`*A__1e*l__e*(Vector(2, {(1) = 1, (2) = 1})) = Vector[column]([[861/25600], [861/25600]]) Vector(2, {(1) = 1, (2) = 2})

``

For element 2 Load matrix F isNULL

F__2e := (1/2)*A__2e*l__e*`ρ__2`*(Vector(2, {(1) = 1, (2) = 1})) = Vector[column]([[123/5120], [123/5120]]) 

``

 

Download wrong_answers.mwwrong_answers.mwwrong_answers.mw

Ramakrishnan V

rukmini_ramki@hotmail.com

how_do_i_get_floating_point_answer.mw

 solve({-(1/3)*(eta+5)/(eta-3) = 3*eta/(-2+eta)})

{eta = 6/5-(1/5)*61^(1/2)}, {eta = 6/5+(1/5)*61^(1/2)}

(1)

I want the answer

eta := 6/5-(1/5)*61^.5

-.362049935

(2)

what is the command i should use? Please help. Thanks.

``

 

Download how_do_i_get_floating_point_answer.mw

Ramakrishnan V

rukmini_ramki@hotmail.com

I want to know the mistakes i have made in the documents attached to get the expected results every time.

NULL

Case 1: control = works fine now.

M1 := K__1*A*(Matrix(2, 2, {(1, 1) = 1, (1, 2) = -1, (2, 1) = -1, (2, 2) = 1}))/l__1 = Matrix(2, 2, {(1, 1) = 0.30e-2, (1, 2) = -0.30e-2, (2, 1) = -0.30e-2, (2, 2) = 0.30e-2})

NULL

NULL

Case 2: control = prints answer in next line.M1 := K__1*A*(Matrix(2, 2, {(1, 1) = 1, (1, 2) = -1, (2, 1) = -1, (2, 2) = 1}))/l__1 = Matrix([[K__1*A/l__1, -K__1*A/l__1], [-K__1*A/l__1, K__1*A/l__1]]) = Matrix(2, 2, {(1, 1) = 0.300000000000000e-2, (1, 2) = -0.300000000000000e-2, (2, 1) = -0.300000000000000e-2, (2, 2) = 0.300000000000000e-2})

NULL

control = prints expression and answer in the next line.

case 3

M1 := K__1*A*(Matrix(2, 2, {(1, 1) = 1, (1, 2) = -1, (2, 1) = -1, (2, 2) = 1}))/l__1 = Matrix([[K__1*A/l__1, -K__1*A/l__1], [-K__1*A/l__1, K__1*A/l__1]]) = Matrix(2, 2, {(1, 1) = 0.300000000000000e-2, (1, 2) = -0.300000000000000e-2, (2, 1) = -0.300000000000000e-2, (2, 2) = 0.300000000000000e-2})

NULL

Numeric formating does not function in case2 and cae 3. I dont know shat hv i done for these things to occur. But what should i do?

NULL

 

Download onlineResultandNumeric_format_doesnot_work_in_some_casesWhy.mwonlineResultandNumeric_format_doesnot_work_in_some_casesWhy.mw

Ramakrishnan V

rukmini_ramki@hotmail.com

5 6 7 8 9 Page 7 of 9