Re: Composing a stiffness matrix
- To: mathgroup at smc.vnet.net
- Subject: [mg20362] Re: [mg20328] Composing a stiffness matrix
- From: "Andrzej Kozlowski" <andrzej at tuins.ac.jp>
- Date: Sun, 17 Oct 1999 03:01:50 -0400
- Sender: owner-wri-mathgroup at wolfram.com
Your original message was sent with Japanese characters in place of . (Dot)
so I suppose people without Japanese fonts would have problems with it.
I am not sure what exactly you mean by "constructing a matrix from
equations". If you mean how to get the matrix K out of the two other
matrices in your equations, here is one possible way. It is convenient to
load in the package
In[1]:=
<< LinearAlgebra`MatrixManipulation`
In[2]:=
K1 = {{ka, -ka}, {-ka, ka}};
In[3]:=
K2 = {{kb, -kb}, {-kb, kb}};
In[4]:= AppendColumns[AppendRows[K1, ZeroMatrix[2, 1]], ZeroMatrix[1, 3]] +
AppendColumns[ZeroMatrix[1, 3], AppendRows[ZeroMatrix[2, 1], K2]] //
MatrixForm
Out[4]//MatrixForm=
ka -ka 0
-ka ka + kb -kb
0 -kb kb
--
Andrzej Kozlowski
Toyama International University
JAPAN
http://sigma.tuins.ac.jp
http://eri2.tuins.ac.jp
----------
>From: "Toshiyuki (Toshi) Meshii" <meshii at mech.fukui-u.ac.jp>
>To: mathgroup at smc.vnet.net
>Subject: [mg20362] [mg20328] Composing a stiffness matrix
>Date: Sat, Oct 16, 1999, 9:20
>
> Hi,
>
> I am wondering whether we can use Mathematica to systematically compose a
> stiffness matrix in Finite Element Method.
> Please give me an advice on this problem.
>
> An example problem is as follows:
> I know
> Eq (1) {f1,f2}={{ka,-ka},{-ka,ka}}.{u1,u2}
> Eq (2) {f2,f3}={{kb,-kb},{-kb,kb}}.{u2,u3}
> and want to construct Eq (3) from these two equations systematically.
> Eq (3) {f1,f 2,f3}=K.{u1,u2,u3}
> Here, matrix K is called a stiffness matrix and it's elements are
> K={{ka,-ka,0},{-ka,ka+kb,-kb},{0,-Kb,Kb}}
> How can we construct matrix K in Eq (3) from Eq (1) and Eq (2) by using
> Mathematica's commands ?
>
> *******************************************************
> Toshiyuki (Toshi) Meshii meshii at mech.fukui-u.ac.jp
> Associate Professor, Department of Mechanical Engineering
> Fukui University, 3-9-1 Bunkyo, Fukui, 910-8507, JAPAN
> Tel & Fax +81-776-27-8468
> *******************************************************
>
>
>
>
>